Authors/Peter of Spain/Summulae logicales/Summulaelogicales

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THE SUMMULAE LOGICALES OF PETER OF SPAIN BY JOSEPH P. MULLALLY.

COPYRIGHT 1945 BY THE UNIVERSITY OF NOTRE DAME


Latin English
TRACTATUS SUPPOSITIONUM TREATISE ON SUPPOSITIONS
>Eorum quae dicuntur, quaedam dicuntur cum complexione, ut "Homo currit"; quaedam vero sine complexione, ut "homo", quia est terminus incomplexus. Terminus, ut hic sumitur, est vox significans universale vel particulare, ut "homo" vel "Sortes" et sic de aliis. Terminorum autem incomplexorum unusquisque aut significat substantiam, aut qualitatem, aut quantitatem, aut ad aliquid, aut agere, aut pati, aut ubi, aut quando, aut situm, aut habitum. Significatio, ut hic sumitur, est rei per vocem secundum placitum repraesentatio. Quare, cum omnis res aut sit universalis aut particularis, oportet dictiones non significantes universale vel particulare non significare aliquid. Et sic non essent termini, ut hic sumitur "terminus", ut signa universalia vel particularia. Some linguistic expressions are complex, as “The man runs”; others are incomplex, as “man”, because it is an incomplex term. A term, as it is taken here, is a word which signifies the universal or the particular, ar “man” or “Sortes” and so forth. Moreover, each and every incomplex term either signifies substance, or quality, or quantity, or relation, or action, or passion, or place, or time, or position, or habit Signification, as it is taken here, is the representation, established by convention, of a thing by an utterance. Wherefore, since every thing is either a universal or a particular, it follows necessarily that words which do not signify a universal or a particular do not signify any thing. And so they would not be terms in the sense in which “term” is taken here, as for example the signs of universality and particularity are not terms.
Significationum, alia est rei substantivae et haec fit per nomen substantivum, ut "homo"; alia est rei adiectivae et haec fit per nomen adiectivum vel per verbum, ut "albus" vel "currit". Quae non est proprie significatio substantiva vel adiectiva, sed significat aliquid substantive vel adiective, quia significare aliquid substantive vel adiective sunt modi vocum, sed adiectivatio et substantivatio sunt modi et differentiae rerum quae significantur et non significant Of significations, one is that of a substantival thing and is accomplished through a substantive noun, as “man”; another is that of an adjectival thing and iB accomplished through an adjective, as “white”, or through a verb, as “running”. This is not, in the strict sense, substantival or adjectival signification, but is rather the signification of something substantively or adjectivally, because to signify something substantively or adjectivally are modes of words, while adjectivity and subatantivity are modes and differences of the things which are signified and which do not signify.
Nomina vero substantiva dicuntur supponere, sed nomina adiectiva vel verba dicuntur copulare. Suppositio est acceptio termini substantivi pro aliquo. Differunt autem suppositio et significatio, quia significatio fit per impositionem vocis ad significandum rem, sed suppositio est acceptio termini iam > significantis rem pro aliquo; ut cum dicitur: "Homo currit", iste terminus "homo" tenetur stare pro Sorte, Platone et sic de aliis. Unde significatio prior est suppositione. Et in hoc differunt, quia significatio est vocis, suppositio vero est termini iam compositi ex voce et significatione. Ergo, supponere et significare non sunt idem, sed differunt per locum a coniugatis. Item, significatio est signi ad signatum, suppositio vero est supponentis ad suppositum. Ergo, suppositio non est significatio. Copulatio est acceptio termini adiectivi pro aliquo. Substantive nouns are said to stand for or denote (supponere), but adjectives or verbs are said to characterize (copulare). Supposition (suppositio) is the acceptance of a substantive term as denoting something. Supposition and signification differ, however, because signification is accomplished through the imposition of a word to signify a thing, while supposition is the acceptance of a term, already significant, as denoting something; as when one says: “Man runs”, the term “man” is taken to denote Sortes, Plato and the rest of men. Thus, signification is prior to supposition. They also differ in that signification belongs to the word, whereas supposition belongs to the term already composed of the word and its signification. Therefore, to denote (supponere) and to signify (significare) are not the same, but rather are different, as holds by the topic of co-ordinates and inflections. Furthermore, signification is the relation of a sign to the signified, whereas supposition is the relation of that which denotes to that which is denoted. Therefore, supposition is not signification. Characterization (copulatio) is the acceptance of an adjectival term for something.
Suppositionum, alia communis; alia discreta. Suppositio communis est quae fit per terminum communem, ut "homo", "animal". Discreta est quae fit per terminum discretum, ut "Sortes", vel per terminum communem sumptum cum pronomine demonstrative ut "iste homo", qui est terminus discretus. Of suppositions, one type is general; the other, discrete. General supposition is that which is accomplished by means of a general term, such as “man”, “animal”. Discrete supposition is that which is accomplished by means of a discrete term, such as “Sortes”, or by means of a general term taken in conjunction with a demonstrative pronoun, as “this man”, which is a discrete term.
Item, suppositionum communium, alia naturalis; alia accidentalis. Suppositio naturalis est acceptio termini communis pro omnibus his pro quibus aptus natus est participari; ut iste terminus "homo", per se sumptus, supponit pro omnibus hominibus tam qui sunt quam qui erunt et qui fuerunt. Accidentalis suppositio est acceptio termini communis pro omnibus his pro quibus exigit suum adiunctum, ut "Homo currit". Hic iste terminus "homo" supponit pro omnibus hominibus praesentibus. Et, cum dicitur: "Homo fuit" vel "Homo cucurrit", supponit pro praeteritis. Et, cum dicitur: "Homo erit" vel "Homo curret", supponit pro futuris. Et sic, habet diversas suppositiones secundum diversitatem eorum quae ei adiunguntur. Again, of general suppositions, one type is natural; the other, accidental. Natural supposition is the acceptance of a general term for all those things of which, by its original imposition, it can be a sign; as the term “man”, when it is taken by itself, denotes all men, including those who exist, those who will exist, and those who have existed. Accidental supposition is the acceptance of a general term for all those things its adjunct determines, as in the statement: “Man runs”. In this instance the term “man” denotes all men who exist at the present time. When one says: “Man was” or “Man ran”, “man” denotes all men who existed in the past. And when one says: “Man will be” or “Man will run”, “man” denotes all men who will exist. Consequently, “man” has different suppositional values depending upon the diversity of those terms which are added to it.
Accidentalium suppositionum, alia simplex; alia personalis. Suppositio accidentalis simplex est acceptio termini communis pro re universali significata per ipsum ter>minum, ut cum dicitur: "Homo est species", "Animal est genus". Ibi, iste terminus "homo" supponit pro homine in communi et non pro aliquo inferiori, et iste terminus "animal" supponit pro animali in communi et non pro aliquo inferiori. Et similiter dicendum est de quolibet termino communi, ut "Risibile est proprium", "Rationale est differentia", "Album est accidens". Of accidental suppositions, one type is simple; the other, personal. Simple accidental supposition is the acceptance of a general term for the universal thing signified by that term, as when one says: “Man is a species”, “Animal is a genus”. In these instances, the term “man” denotes man in general and not any of the particulars included under it, and the term “animal” denotes animal in general and not any of the particulars included under it The same thing must be said about any general term whatsoever, as in the statements: “Risible is a property”, “Rational is a differentia”, “White is an accident”.
Item, suppositionem simplicium, alia est termini communis in subiecto positi, ut "Homo est species". Ibi iste terminus "homo" simplicem habet suppositionem, quia solum supponit pro natura speciei. Alia est termini communis positi in praedicato propositionis affirmativae, ut "Omnis homo est animal". Ibi iste terminus "animal", in praedicato positus, simplicem habet suppositionem, quia solum supponit pro natura generis. Alia est termini communis positi post dictionem exceptivam, ut "Omne animal praeter hominem est irrationale". Ibi iste terminus "hominem" simplicem habet suppositionem, quia non licet fieri descensum sub ipso. Unde non sequitur: "Omne animal praeter hominem est irrationale; ergo omne animal praeter hunc hominem est irrationale", ex quo ibi est fallacia figurae dictionis procedendo a supposition simplici ad personalem. Similiter hic: "Homo est species; ergo aliquis homo est species". Et similiter hic: "Omnis homo est animal; ergo omnis homo est hoc animal". In omnibus enim istia fit processus a simplici suppositione ad personalem. Further, of simple suppositions, one type is that of a general term functioning as the subject, as in the statement: “Man is a species”. In this case the term “man” has simple supposition because it denotes only the nature of the species. A second type is that of a general term functioning as predicate in an affirmative proposition, as in the statement: “Every man is an animal”. In this statement the term “animal”, functioning as predicate, has simple supposition because it denotes only the nature of the genus. A third type is that of a general term placed after an exceptive word, as in the statement: “Every animal, other than man, is irrational”. Here, the term “man” has simple supposition because its particular cannot validly be inferred. Hence, the following is not a valid inference: “Every animal, other than man, is irrational; therefore every animal, other than this man, is irrational”, because of the fact that a fallacy of figure of speech is involved in progressing from simple supposition to personal. likewise, [the following is not a valid inference]: “Man is a species; therefore some man is a species”. Nor again: “Every man is an animal; therefore every man is this animal”. In all these cases an inference is made from simple supposition to personal supposition.
Quod autem terminus, in praedicato positus, simplicem habet suppositionem patet, quia cum dicitur: "Omnium oppositorum eadem est disciplina", nisi ille terminus "disciplina" simplicem haberet suppositionem, sic fieret descensus sub ipso et esset falsa. Nulla enim particularis dis>ciplina est omnium contrariorum. Medicina enim non est omnium contrariorum, sed solum sani et aegri; grammatica non est omnium contrariorum, sed solum congrui et incongrui; logica autem veri et falsi et sic de aliis. However, it is dear that a term, functioning as predicate, has simple supposition because when one says: “There is the same science of all opposites”, unless the term “science” had simple supposition, its particulars could be validly inferred and the statement would be false. For there is no particular science of all contraries. For medicine is not a science of all contraries, but only of the healthy and the ill; grammar is not a science of all contraries, but only of the grammatically suitable and unsuitable; logic only of the true and the false and so on.
Personalis autem suppositio est acceptio termini communis pro suis inferioribus; ut cum dicitur: "Homo currit", iste terminus "homo" supponit pro suis inferioribus. Personal supposition, however, is the acceptance of a general term for its particulars; as when one says: “Man runs”, the term “man” denotes its particulars.
Item, personalium suppositionum, alia est determinata; alia confusa. Determinata suppositio est acceptio termini communis indefinite sumpti vel cum signo particulari sumpti, ut "Homo currit" vel "Aliquis homo currit". Et dicitur utraque illarum determinata, quia, licet in utraque istarum iste terminus "homo" supponat pro omni nomine, tam currente quam non currente, tamen pro uno solo homine currente vera dicitur. Et quia aliud est supponere et aliud est locutionem esse veram pro aliquo vel falsam, igitur in praedictis propositionibus, ut dictum est, iste terminus "homo" supponit pro omni homine, tam currente quam non currente, licet reddat locutionem veram pro currente solo. Quod autem in utraque istarum sit determinata suppositio patet, quia cum dicitur: "Animal est Sortes vel animal est Plato et sic de aliis; ergo, animal est omnishomo", ibi est fallacia figurae dictionis a pluribus determinatis ad unam determinatam. Et ideo, iste terminus "animal", indefinite positus, habet detenninatam suppositionem. Et similiter si sumatur cum signo particulari. Further, of personal supposition, one type is determinate; the other, indeterminate. Determinate supposition is the acceptance of a general term taken indefinitely or taken with a sign of particularity, as in the statements: “A man runs” or “Some man runs”. The supposition in each of these statements is said to be determinate because, although in each statement the term “man” may denote any man, both those running and those not running, the statement is nevertheless asserted as true of only one man who is running. And because it is one tiling to denote (evpponere) and another thing for a statement to be true or false of something, therefore in the above propositions, as has been said, the term “man” denotes every man, both those running and those not running, although it yields a true statement only with reference to the one man who is running. However, it is dear that there is determinate supposition in both of these propositions, because when one says: “An animal is Sortes, or an animal is Plato and so on; therefore, an animal is every man”, there is a fallacy of figure of speech involved in progressing from a determinate many to a determinate one. On that account, this term “animal”, posited indefinitely, has determinate supposition. The same holds true in the case of a general term taken with a sign of particularity.
Confusa suppositio est acceptio termini communis pro pluribus, mediante signo univereali, ut cum dicitur: "Omnis homo est animal". Ibi, iste terminus "homo" supponit pro pluribus, mediante signo univereali, quia supponit pro quolibet suo supposito. Indeterminate supposition is the acceptance of a general term for many by means of a universal sign, as when one says: “Every man is an animal”. In this case, the term “man” denotes many men by means of the universal sign, because it denotes any one whatsoever of the things it can denote.
Item, confusarum suppositionum, alia est confusa necessi>tate signi vel modi et alia necessitate rei, ut cum dicitur: "Omnis homo est animal". Ibi, iste terminus "homo", mediante signo universali, confunditur sive distribuitur pro quolibet suo supposito; et iste terminus "animal", a parte praedicati positus, confunditur necessitate rei. Et, cum unusquisque homo suam habeat essentiam, ideo hoc verbum "est", necessitate rei, tenetur pro tot essentiis pro quot hominibus tenetur iste terminus "homo". Et, cum unicuique homini insit sua animalitas, ideo iste terminus "animal", necessitate rei, tenetur pro tot animalibus pro quot hominibus iste terminus "homo" et pro quot essentiis hoc verbum "est". Unde iste terminus "homo" debet supponere confuse, mobiliter, et distributive. Et confuse et distributive tenetur, quia tenetur pro omni homine; mobiliter vero, quia licet fieri descensum sub eo pro quolibet suo supposito, ut "Omnis homo est animal; ergo, Sortes est animal". Sed iste terminus "animal" dicitur confundi immobiliter, quia non licet fieri descensum sub eo, ut "Omnis homo est animal; ergo, omnis homo est hoc animal". Ibi enim fit processus a simplici suppositione ad personalem, sicut hic: "Homo est dignissima creaturarum; ergo, hic homo vel aliquis homo" vel "Rosa est pulcherrima florum; ergo, aliqua rosa". Sed differunt in hoc, quia in istis est simplex suppositio ex parte subiecti, in illa vero ex parte praedicati. Further, of indeterminate suppositions, one type is indeterminate by the exigency of the sign or mode and the other by the exigency of the thing [signified], as when one says: “Every man is an animal”. In this instance, the term “man” is made indeterminate or is distributed by means of the universal sign for any one whatsoever of the things it can denote [its “values”]; and the term “animal”, functioning as predicate, is made indeterminate by the exigency of the thing [signified]. Also, since each and every man has his own essence, the verb “is”, by the exigency of the thing signified, is understood for as many essences as the term “man” is understood for men. And, since each and every man has his own animality, the term “animal”, by the exigency of the thing signified, is understood for as many animals as the term “man” is understood for men and as the verb “is” is understood for essences. Hence, the term “man” should have movably indeterminate and distributive supposition. It is understood as indeterminate and distributive because it is understood for every man; but it is taken as movably indeterminate because a valid inference can be made to any one whatsoever of its particulars, as “Every man is an animal; therefore, Sortes is an animal”. However, the term “animal” is said to be immovably indeterminate because a valid inference cannot be made to its particulars, as “Every man is an animal; therefore, every man is this animal”. Here, an inference is made from simple supposition to personal, just as in the case of: “Man is the noblest of creatures; therefore, this man or some man (is the noblest of creatures)”; or in the case of: “The rose is the most beautiful of flowers; therefore, some rose (is the most beautiful of flowers)”. But the latter cases differ from the former because in the latter there is simple supposition on the part of the subject while in the former the simple supposition is on the part of the predicate.
Licet videatur oppositum esse quod superius dictum est, quod in hac propositione: "Omnis homo est animal", iste terminus "animal", in praedicato positus, simplicem habet suppositionem, cum prius dicebatur quod habet confusam. > Ad hoc dicendum est, secundum quosdam, quod quia genus praedicatur de pluribus differentibus specie, iste terminus "animal", quando tenetur pro ipsa natura in communi secundum quod est genus, sic habet simplicem suppositionem; secundum autem quod ipsa natura communis ipsius generis multiplicatur per supposita "hominis", sic dicitur habere confusam suppositionem, non mobiliter sed immobiliter. Suppositio autem confusa immobiliter potest cum simplici accidere, non secundum idem sed secundum diversa, ut dictum est. Unde, secundum hoc, dicendum est quod suppositio confusa mobiliter non potest simul esse cum simplici, nec secundum idem nec secundum diversa, ut dictum est. This may seem to contradict what we said previously, namely, that in the proposition: “Every man is an animal”, the term “animal”, functioning as predicate, has simple supposition, whereas we just now asserted that it has indeterminate supposition. To this it must be replied, according to some people, that because a genus is predicable of many differing in species, the term “animal”, whenever it is taken for the common nature itself insofar as it is a genus, has simple supposition; but insofar as the common nature of that genus is multiplied by reason of the things denoted by the term “man”, it is said to have indeterminate supposition, not movably but immovably. However, immovably indeterminate supposition, can occur along with simple supposition not in the same [respect] but in different [respects], as has been affirmed. Wherefore, according to this view, it must be said that movably indeterminate supposition cannot coincide with simple supposition, either in the same [respect], or in different [respects], as has been stated.
Sed ego credo impossibile esse terminum communem, in praedicato positum, habere simplicem suppositionem et confundi mobiliter vel immobiliter, signo universali existente in subiecto affirmativae, ut "Omnis homo est animal", et sic de aliis consimilibus; quia, ut vult Porphyrius, omne quod praedicatur de aliquo aut est maius eo aut est aequale ei de quo praedicatur—et intendit de praedicatione per se. Sed in hac propositione: "Omnis homo est animal", est praedicatio per se et non praedicatur aequale; ergo maius. Non accidental; ergo substantiate vel essentiale. Ergo genus vel differentia. Non differentia; ergo genus. Sed natura generis, multiplicata mobiliter vel immobiliter, non est genus. Ergo, cum dicitur: "Omnis homo est animal", cum ibi praedicetur genus, non esset possibile terminum communem multiplicari mobiliter vel immobiliter, quia significat naturam generis, quae iam est actu, non esse genus; sicut si "homo" conf underetur mobiliter vel immobiliter, iam non esset species. But I believe that it is impossible for a general term, functioning as predicate, to have simple suppositional value and to be movably or immovably indeterminate when there is a universal sign in the subject of an affirmative proposition, as in the statement: “Every man is an animal”, and in similar propositions. The reason for this is, as Porphyry indicates,* that everything which is predicated of something is either greater than or equal to that of which it is predicated—and he had essential predication in mind. But in this proposition: “Every man is an animal”, the predication is essential and the predicate is not of equal extension with the subject; therefore, it is greater. It is not accidental; therefore, it is substantial or essential. Consequently it is a genus or a differentia. It is not a differentia; therefore, it is a genus. But the nature of a genus, when it is distributed either movably or immovably, is not a genus. Therefore, when one says: “Every man is an animal”, since the genus is there predicated, it would not be possible for this general term to be distributed either movably or immovably, because that would signify that what already has actual existence as the nature of a genua, is not a genus; just as if “man” were distributed, either movably or immovably, it would no longer be a species.
> Item, hoc idem videtur per Aristotelem in primo Topicorum dicentem, quod omne quod de alio praedicatur aut praedicatur conversim de eo aut non. Si conversim, est definitio vel proprium. Si autem non conversim predicatur de re, aut cadit in definitionem rei aut non. Si non, tunc est accidens. Si cadit in definitionem rei, aut est genus vel differentia. Non differentia; ergo genus. Et intendit Aristoteles quod ibi sit directa praedicatio et species subiiciatur secundum se vel multiplicetur. Sed in hac propositione: "Homo est animal", est directa praedicatio et subiicitur "homo". Et non aequale praedicatur, neque accidens ; ergo genus. Quare non est possibile terminum communem, in predicate positum, confundi mobiliter vel immobiliter. Again, this same conclusion is evident from what Aristotle says in the first book of the Topics, namely, that everything which is predicated of another is either predicated of it convertibly or not If it is predicated convertibly, it is a definition or a property. However, if it is not predicated of the thing convertibly, it either belongs to the definition of the thing or not If not, then it is an accident If it belongs to the definition of the thing, then it is either a genus or a differentia. Not a differentia; then a genus. And Aristotle had in mind the case of direct predication where the species, as such, is the subject or is distributed. But in this proposition: “Man is an animal”, there is direct predication and “man” is the subject Also, the predicate is not of equal extent and it is not an accident; therefore it is a genus. Wherefore it is not possible for a general terra, functioning as predicate, to be movably or immovably indeterminate.
Item totum universale, quod est genus, et totum in quantitate ex opposite se habent. Sed totum in quantitate est duplex: quoddam est totum in quantitate completum, ut ubicunque confunditur terminus communis mobiliter, ut "Omnis homo est animal"; aliud est totum in quantitate incompletum et diminutum, ut ubicunque confunditur terminus communis immobiliter et multiplicatur terminus communis simpliciter. Ergo, si impossible est totum in quantitate esse genus, inquantum huiusmodi, non erit possibile terminum communem, in praedicato positum, confundi mobiliter vel immobiliter, ut dicebatur. Furthermore, the universal [intensions!] whole which is a genus and the quantitative [extensional] whole are related to each other in an opposite manner. The quantitative whole is twofold: one kind of quantitative whole is complete, for example, wherever a general term is movably indeterminate, as in the statement: “Every man is an animal”; the other kind of quantitative whole is incomplete and limited, for example, wherever a general term is immovably indeterminate and whenever a general term is diversified unconditionally. Therefore, if it is impossible for a quantitative whole, as such, to be a genus, it will not be possible for a genera] term, placed in the predicate, to be movably or immovably indeterminate; which was what we asserted.
Item, comparatio illa secundum quam inferiora reducuntur ad superiora opposite est comparationi secundum quam superiora reducuntur ad sua inferiora. Sed secundum primam, sumitur commune in ratione communis. Sed secundum secundam, sumitur commune multiplicatum sive confusum. Cum ergo terminus communis ut sic sit in ratione >generis, non est possibile ipsum multiplicari inquantum huiusmodi. Also, that type of comparison by which the more particular is reduced to the more general is opposed to the type of comparison by which the more general is reduced to the more particular. In the first type, general is taken in the sense of that which is common. In the second type, general is taken as distributed or indeterminate. Therefore, since a general term as such has the character of a genua, it is not possible for it qua genus to be distributed.
Et haec quatuor argumenta sunt concedenda. Causa autem, propter quam movebantur, facilis est ad solvendum. Quae tantum est una, quia cum dicitur: "Omnis homo est animal", cum unicuique homini respondeat sua animalitas sive sua essentia—cum non possit esse homo quin sit animal, ideo dixerunt quod iste terminus "animal" teneretur pro tot animalibus pro quot hominibus" homo". Quod autem in illo argumento nulla sit apparentia patet, quia cum dicitur: "Omnis homo est albus", necesse est quod tot animalitates intelligantur in subiecto quot sunt homines in quibus tenetur "homo". Unde nihil est dicere quod habeat illas animalitates a praedicato, cum ibi praedicetur "album". Unde dicendum est quod homo, logice loquendo, non naturaliter, ex animali et rationali componitur; ideo de se habet illanun animalitatum multiplications. Unde, cum dico sic: "Omnis homo est albus", nullo modo habet illas animalitates a praedicato, cum ibi praedicetur "albus", ut dictum est. Sic autem est in proposito, cum ibi praedicetur genus de specie, ut "Omnis homo est animal". In hac enim propositione, subiicitur "homo", in quo intelligitur multitudo illarum animalitatum; et praedicatur hoc genus "animal", quod nullo modo confunditur mobiliter vel immobiliter sed stat ibi pro natura sive pro essentia ipsius generis communis de pluribus praedicabilis. Unde "animal" praedicatur et "animal" intelligitur in subiecto, sicut hic: "Omne animal rationale est animal". These four arguments must be granted. The difficulty which prompted them, which is just one difficulty, is easy to solve. For, given the statement: “Every man is an animal”, it was asserted that since each man has his own animality or his own essence—because he cannot be a man without being an animal, therefore the term “animal” should be understood for as many animals as the term “man” is understood for men. But it is manifest that that argument has no force, because when one says: “Every man is white”, it is necessary that as many animalities are understood in the subject as there are men of which “man” is understood. Whence there is no reason to assert that “man” has these animalities from the predicate, since in this case “white” is predicated. Whence it must be said that man, logically speaking, not naturally [speaking], is compounded from animal and rational; and therefore he possesses of himself this diversification of animalities. Hence, when I speak thus: “Every man is white”, those animalities do not in the least belong to man by reason of the predicate, since in this case “white” is the predicate, as was said. So it is in the matter under discussion, where a genus is predicated of a species, as in the statement: “Every man is an animal”. For in this proposition, “man”, under which is understood the diversification of those animalities, is the subject; and this genus “animal” is the predicate which is not distributed in any way, either movably or immovably, but in this case denotes the nature or the essence of the common genus itself which is predicable of many. Whence “animal” is the predicate and “animal” is understood in the subject, just as when one says: “Every rational animal is an animal”.
Similiter dico quod hoc verbum "est" non confunditur mobiliter vel immobiliter, quia, quod animal esset vel existeret in hoc nomine, hoc habet subiectum de se antequam in propositione subiiciatur praedicato essentiali vel accidentali. Et propter hoc destruimus quandam divisionem >factam, scilicet: confusarum suppositionum, alia est confusa necessitate rei; alia est conf usa necessitate modi sive signi. Dicimus enim quod omnis conf usio fit necessitate signi vel modi; ut cum dicitur: "Omne animal rationale est animal", iste terminus "animal", in subiecto positus, tenetur necessitate signi pro omni animali quod est homo. Similiter hic: "Omnis homo est animal", iste terminus "homo" tenetur pro omni nomine, et non solum pro homine sed etiam pro omni animali quod est homo; et ideo tot intelliguntur animalitates quot humanitates, naturaliter loquendo, quia eadem est humanitas in quolibet individuo hominis secundum viam logicorum et non secundum viam naturae. Sic homo in communi idem est. Unde quod sit haec animalitas vel illa, hoc est ratione materiae. In via enim naturae humanitas mea differt ab humanitate tua per se; et anima mea, per quam causatur humanitas mea in me, alia est ab anima tua, per quam causatur humanitas tua in te. Et propterea hoc signum "omne" confundit "hominem"; non tamen confundit "animal" in communi sed "animal" contractum ad hominem per suas differentias. Unde sequitur quod omnis confusio fit necessitate signi vel modi. Et haec de suppoaitione terminorum absolutorum. Similarly, I say that the verb “is” is not distributed either movably or immovably, because the fact that an animal might be or might exist in this man is implied in the subject itself prior to its becoming a subject in a proposition with respect to either an oaafnrisl or an accidental predicate. And, for this reason we discard a certain division which was made previously,’ namely: of indeterminate suppositions, one type is indeterminate by the exigency of the thing [signified]; the other is indeterminate by the exigency of the mode or sign. For we assert that all indeterminacy occurs by the exigency of the sign or mode; as when one says: “Every rational animal is an animal”, the term “animal”, functioning as subject, is taken by the exigency of the [distributive] sign for every animal that is a man. Similarly in this statement: “Every man is an animal”, the term “man” is taken for every man, and not only for man but also for every animal that is a man; and on that account as many animalities are understood as humanities, naturally speaking, because it is only according to the viewpoint of logic, and not according to the way of nature, that the humanity in each individual man is the same humanity; in this manner “man in general” is the same. Hence the fact that there exists this or that animality is by reason of matter. For, in the natural order my humanity differs of itself from your humanity; and my soul through which my humanity is caused in me, is other than your soul, through which your humanity is caused in you. And it is because of this that this sign “every” distributes “man”, and yet does not distribute “animal” in its full generality but as limited to man through his differentiae. Whence it follows that all indeterminacy occurs by the exigency of the sign or mode. This is sufficient concerning the supposition of absolute terms.
>TRACTATUS RELATIVORUM TREATISE ON RELATIVES
Relativum est duplex: uno modo relativum est cuius esse est ad aliud quodammodo se habere, et sic relativum est unum de decem praedicamentis; aliud est relativum quod est ante latae rei recordativum, quia, ut vult Priscianus in maiori suo volumine, relatio est ante latae rei recordatio, ut "Sortes currit qui movetur". Ibi hoc relativum "qui" facit recordationem sive relationem de Sorte qui est res ante lata. Omissis autem relativis secundum primum modum, de relativis secundo modo hic intendimus. Relative has two [meanings]: in one way, a relative is that whose essential character is to be in some way related to something else, and in this sense a relative is one of the ten categories; in another way, a relative is that which refers back to something mentioned previously, because, as Priscian indicates in his larger work, a relative is a reminder of something mentioned previously, as in the statement: “Sortes, who is moved, is running”. In this sentence the relative “who” produces a recollection of, or involves a reference to, Sortes who is the object mentioned previously. In this section we are not going to consider relatives of the first type[1]; we are going to consider relatives of the second type[2].
Relativorum autem, quaedam sunt relativa substantiae, ut "qui", "ille" et similia; quaedam vero sunt relativa accidentis, ut "talis", "qualis", "tantus", "quantus". Some relatives are relatives of substance, such as “who”, “he”, and the like; others are relatives of accident, such as “such a kind”, “such a sort”, “such a size”, “as great as”.
Relativum autem substantiae est quod refert eandem rem in numero cum suo antecedente ut "qui", "ille". Item, relativorum substantiae, quaedam sunt relativa diversitatis, ut "alius", et est illud quod refert eandem rem in numero et supponit pro alia, ut "Sortes currit et alius disputat"; quaedam vero identitatis, ut "qui", "ille", "idem". Relativum autem substantiae identitatis est quod refert et supponit pro eodem in numero pro quo supponit suum antecedens, ut "Sortes currit quo disputat". Ibi hoc relativum "qui" refert Sortem et supponit pro Sorte. A relative of substance is one which refers to an object which is numerically the same as its antecedent, such as “he”, “who”. Furthermore, some relatives of substance are relatives of diversity, as “another”, and such a relative refers to an object numerically the same but denotes another, as in the statement: “Sortes is running and another is debating”; others are relatives of identity, such as “who”, “he”, “the same”. Now a relative of identity of substance is one which refers to and denotes an object numerically the same as the object which its antecedent denotes, such as “Sortes who debates is running”. Here, the relative “who” refers to Sortes and denotes Sortes.
Relativorum identitatis substantiae, quaedam sunt nomina, ut "quis", "quidam"; quaedam sunt pronomina, ut "ille", "idem". Item, relativorum pronominum identitatis, quaedam sunt reciproca, ut "sui", "sibi", "se", cum suo posseasivo, ut "suus", "sua", "suum"; alia vero non reciproca, > ut "ille", "idem". Relativum autem reciprocum dicitur non quod sit patiens sed quia ponit modum patientis supra substantiam agentem; quia aliud est patiens et aliud est modus patientis. Quod patet per hoc, quod nominativus potest esse patiens, ut dicendo: "Sortes percutitur", sed non potest habere modum patientis. Unde modus patientis semper est in obliquis. Et sic patet quod aliud est patiens et aliud est modus patientis. Some relatives of identity of substance are nouns, such as “who”, “someone”; others are pronouns, such as “he”, “the same”. Furthermore, some relative pronouns of identity are reciprocal, such as “of 11101860*”, “to himself’, “himself*, along with its possessive, such as “his”; others are non-reciprocal, such as “he”, “the same”. A relative is called reciprocal not because it is passive but because it adds a mode of passivity to an active substance; for the passive is one thing, and a mode of passivity is another. This is dear from the fact that the nominative can be passive, as in saying: “Sortes is hit”, but it cannot have a mode of passivity. Hence a mode of passivity is always in a oblique case. Thus it is dear that it is one thing to be passive and another to be a mode of passivity.
Si quaeratur quid addatur supra patiens per relativum reciprocum, dicendum est quod addit identitatem substantiae et ponit eam sub modo patientis, ut "Sortes videt se". Ibi substantia, quae prius erat agens, ponitur sub modo patientis, ut in hoc pronomine "se". Unde reciprocum sic potest definiri: reciprocum est quod significat substantiam agentem sub modo patientis; vel sic: reciprocum est idem quod suiipsius passivum. Et ideo hoc relativum "sui" significat per modum patientis in quem dicitur transire actus verbi. Nominativus autem significat per modum agentis. If one asks what is added over and above passivity by the reciprocal relative, then we must answer that the reciprocal relative adds identity of substance and presents it under a mode of passivity, as in saying: “Sortes sees himself. In this case the substance which in the first place was the agent is presented under a mode of passivity, as in the case of the pronoun “himself”. Consequently, a reciprocal relative can be defined in the following fashion: a reciprocal relative is one which signifies an active substance under a mode of passivity; or in this way: a reciprocal relative is the very thing which is passive with respect to itself. Therefore, this relative “of himself’ signifies by means of a mode of passivity that into which the action of the verb is said to pass; a nominative case, however, signifies by means of a mode of activity.
Item, si quaeratur quare hoc pronomen "sui", "sibi", "se", caret nominativo, dicendum est quod solutio patet ex praemissis, quia agens non potest significare patiens sive sub modo patientis nisi in obliquis. Sed ipse nominativus dicit modum agentis. Et ideo natura nominativi repugnat naturae huius pronominis "sui". Et ideo non potest habere nominativum. Again, if it is asked why the pronoun “of himself, or “to himself, or “himself, is lacking in the nominative case, it must be said that the solution is dear from what has been said previously, for that which is active cannot signify the passive or under a mode of passivity except in the oblique cases. But the nominative case connotes the active mode. Therefore the nature of the nominative case is repugnant to the nature of the pronoun “of himself. Consequently, it cannot have a nominative.
Ex praedictis patet, quod relativa identitatis referunt eandem rem cum suo antecedente et semper supponunt pro eadem re in numero. Et ex hoc patet, quod maior est certitudo per relativum identitatis quam per suum antecedens > loco relativi positum, ut "Homo currit, homo disputat", quia dubium est utrum de eodem homine dicatur. Sed cum dicitur: "Homo currit et idem disputat", certum est quod de eodem homine dicatur. Hoc enim patet per Priscianum dicentem in maiori suo volumine quod cum dicitur: "Aiax venit ad Troiam et Aiax fortiter pugnavit", dubium est an de eodem Aiace dicatur an de diversis; sed cum dicitur: "Aiax venit ad Troiam et idem fortiter pugnavit", de eodem Aaice in numero statim intelligitur. Et sic patet quod maior est certitudo per relativum identitatis quam per suum antecedens loco talis relative positum. From what has been said previously it is dear that relatives of identity refer to the same thing as their antecedent and always stand for a thing numerically the same. From this it is dear that greater certitude results from the use of the relative of identity than from the use of the antecedent placed in the position of the relative, as in the statement: “The man is running, the man is debating”, because it is doubtful whether the same man is meant in both cases. But when one says: “The man is running and the same [one] is debating”, it is certain that the same man is meant in both cases. For this is made clear by Priscian* who, in his larger work, maintains that when one says: “Ajax came to Troy and Ajax fought courageously”, it is doubtful whether the same Ajax or different ones are meant; but when one says: “Ajax came to Troy and the same fought courageously,” one immediately understands that numerically the same Ajax is meant Hence, it is clear that greater certitude results from the use of the relative of identity than from the use of the antecedent placed in the position of such a relative.
Solet autem dubitari circa relativa identitatis utrum deceptio, facta ex diversa relatione, fiat secundum aequivocationem vel secundum amphibologiam vel secundum aliquam aliam fallaciam, ut dicendo: "Homo videt asinum qui est rationalis". Ibi hoc relativum "qui" potest referri ad hunc terminum qui est "homo" vel ad hunc terminum qui est "asinus"; et sic sunt ibi diversae relationes. Et ergo secundum aliquos solet ibi convenienter assignari aequivocatio. With respect to the relative of identity, there is the customary question as to whether a deception caused by a diverse relation results from equivocation, amphibology, or some other fallacy, as in the statement: “A man sees an ass who is rational”. In this proposition, the relative “who” can be referred to the term “man” or to the term “ass”; and in this way diverse relations exist in the statement. Therefore some maintain that equivocation is fittingly ascribed to such a proposition.
Sed contrarium arguitur, hoc nomen "qui", secundum quod est relativum, significat rem unam aequaliter se habentem ad illud quod significatur per modum substantiae, ut "color qui est in corpore", "locus qui continet rem locatam", et sic de aliis; ergo deceptio, facta ex diversa relatione, non facit aequivocationem. The argument against this position asserts that this noun “who”, insofar as it is a relative, signifies a single thing related equally to whatever is signified in the manner of substance, as in the expressions: “color which is in a body”, “place which contains the located thing”, and so on; consequently, a deception caused by a diverse relation does not constitute an equivocation.
Item, hoc nomen "qui", secundum quod est nomen, significat substantiam infinitam. Sed ista substantia infinita apta est finitari tam per unum antecedens quam per aliud. Ergo, cum illa substantia, infinite sumpta in se, sit una et potest referri ad quodlibet antecedens, ergo significatio > huius relativi erit una. Quare sequitur quod ibi non erit aequivocatio. Furthermore, this noun “who”, insofar as it is a noun, signifies an indefinite substance. But this indefinite substance is such that it can be determined by one antecedent quite as well as by the other. Therefore, since that substance, taken indefinitely in itself, is one and can be referred to any antecedent whatever, the signification of this relative will be one. Hence, it follows that in this case equivocation is not involved.
Item, ratio cuiuslibet relativi, secundum quod relativum, est tantum una, haec scilicet: "res ante lata" vel "rei ante latae recordaticum[3]". Ergo omne relativum, secundum quod relativum, participat unum nomen et unam rationem. Ergo, relativum est univocum inquantum est ante latae rei recordativum. Ergo, particularia relativa, ut "qui", "ille", et "alius", inquantum sunt relativa suorum antecedentium, non sunt aequivoca. Moreover, the definition of any relative whatsoever, qua relative, is one only, namely: “something previously mentioned” or “recollective of something previously mentioned”. Therefore every relative, qua relative, has in common one name and one definition. Consequently, the relative is univocal insofar as it is recollective of something mentioned previously. Hence, particular relatives, such as “who”, “he”, and “another”, insofar as they are relatives of their antecedents, are not equivocal.
Si aliquis obiiciat quod hoc relativum "qui" alterius est rationis secundum quod tenetur in hoc antecedente "homo" et alterius secundum quod tenetur in hoc antecedente "asinus", ut in praedicta oratione, ergo est commune et habet rationes diversas, ergo est aequivocum, dicendum est quod hoc argumentum non valet. Nam similiter posset probari quod quodlibet univocum esset aequivocum: ut "animal" esset aequivocum secundum quod est homo vel secundum quod est in homine et aliam habet rationem secundum quod est equus vel secundum quod est in equo; et sic hoc nomen "animal" aliam habet rationem hic et ibi et est commune; non tamen aequivocum sed univocum. Solvendum est breviter quod sicut univoca dicuntur habere eandem rationem, non secundum se, sed in univoco univocante, ut "homo", "bos", "equus", et similia in "animali", similiter omnia relativa dicuntur habere eandem rationem, non secundum se, sed in referente sive in relatione; et etiam habent idem nomen ; ideo univocantur in eo. Sed ille obiiciebat de rationibus relativorum secundum se. Unde praedictas obiectiones ab ista concedimus, et ideo concedimus quod deceptio, facta ex diversa relatione, non est secundum aequivocationem. If anyone objects that this relative “who” has one meaning when taken in relation to the antecedent “man” and another meaning when taken in relation to the antecedent “ass”, as in the aforementioned sentence, and that consequently it is a single term having diverse meanings, and is therefore equivocal, his argument must be declared invalid. For any univocal term whatever could be proved equivocal in this fashion: as “animal” would be equivocal [in that it would have one definition] insofar as it is man or in man and it would have another definition insofar as it is horse or in horse; and thus the name “animal” has a different definition in one case from that which it has in the other but [the name] is the same; yet it is not equivocal but univocal. It must be briefly explained that just as univocal terms are said to have the same definition, not as among themselves, but as agreeing in some one meaning (in univoco univocante), as “man”, “cow”, “horse”, and the like [agree] in “animal”, similarly all relatives are said to have the same definition, not as among themselves, but in [the character of] referring or relating; and they also have the same name; hence they agree (univoeantur) in that name. But the objection was concerned with the definition of relatives as among themselves. Consequently, we concede the objections stated other than this last one, and therefore we concede that a deception caused by a diverse relation is not due to equivocation.
Item, illa deceptio est in ordinatione dictionum inter se. > Ergo est in oratione, quia ordinatio dictionum nihil aliud est quam oratio. Ergo non est aequivocatio, cum aequivocatio solum fit in una dictione. Furthermore, that type of deception lies in the arrangement of words among themselves. Therefore it lies in the sentence, because the arrangement of words among themselves is nothing other than the sentence. Consequently it is not equivocation, since equivocation only occurs in the case of a single word.
Item, quod ibi non sit amphibologia probatur, quia ubicunque fit amphibologia, ibi est constructio unius cum alio, ut in hoc exemplo: "liber Aristotclis", quoad primum modum; quoad secundum modum, ut in hoc: "Littus aratur"; quoad tertium, ut in hoc: "Scit saeculum". Et secundum hoc patet inductive per omnes modos amphibologiae, quod ubicunque est amphibologia, ibi est constructio unius cum uno tantum. Sed ubicunque sunt diversa relativa, non est constructio unius cum uno tantum; immo unius cum diversis. Ergo, deceptio, facta ex diversa relatione, non facit amphibologiam. Again, we prove that amphibology is not present in this case, because wherever amphibology occurs, there is a syntactical relation of words, the one with the other, as in this example: “Aristotle’s book”, as a first mode; “The shore is ploughed” (Littus aratur), as a second mode; and “He knows [this] generation” (Scit saeculum), as a third mode[4]. And from this it is inductively obvious, with respect to all the modes of amphibology, that wherever amphibology exists, there is a syntactical relation of one word to but one other word. But wherever there are diverse relatives, there is not a syntactical relation of one word to just one other word; nay rather there is a syntactical connection of one word with diverse words. Therefore, a deception caused by a diverse relation does not constitute an amphibology.
Item, ubicunque est deceptio ex eo quod aliqua dictio potest referri ad diversa, est compositio vel divisio. Sed deceptio ex diversa relatione est ex eo quod aliqua dictio potest referri ad diversa. Ergo, deceptio ex diversa relatione est compositio vel divisio. Et hoc idem concedimus. Furthermore, wherever deception arises from the fact that some one word can be referred to diverse words, there is [a fallacy of] composition or division. But a deception caused by a diverse relation arises from the fact that some word can be referred to diverse words. Therefore, a deception caused by a diverse relation is [a fallacy of] composition or division. We subscribe to this view.
Sequitur de relativis diversitatis. Relativum diversitatis est quod supponit pro alio ab eo quod refert, ut "Sortes currit et alius disputat". Ibi hoc relativum "alius" refert Sortem et supponit pro alio a Sorte. Et ita facit recordationem de Sorte. Next we treat of relatives of diversity. A relative of diversity is one which denotes something other than that to which it refers, as in the statement: “Sortes is running and someone else is debating”. In this case the relative “someone else” refers to Sortes and denotes someone other than Sortes. Consequently, it is recollective of Sortes.
>De relativis autem diversitatis talis datur regula: si relativum diversitatis addatur superiori, fit inferius; et si addatur inferiori, fit superius. Verbi gratia, cum dicitur: "Aliud ab animali currit; ergo aliud ab homine currit", ibi est locus a specie ad genus sive a parte subiectiva ad suum totum universale, quia in hac propositione: "Aliud ab animali currit", hoc relativum diversitatis, "Aliud", cum additur "animali", quod est superius ad "hominem", facit ipsum inferius; et in hac propositione: "Aliud ab homine currit", additur inferiori, scilicet "homini", et ergo facit ipsum superius; et ergo "Aliud ab animali" est inferius ad "aliud ab homine". Et ideo ibi est locus a specie sive a parte subiectiva. As concerns relatives of diversity, the following rule is given: if a relative of diversity is added to a term of greater extension, the extension becomes less; and if it is added to a term of lesser extension, the extension becomes greater. For example, when one says: “What is other than an animal runs; therefore, what is other than a man runs”, there is a topical argument from species to genus, or from a subjective part to its universal whole, because in this proposition : “What is other than animal runs”, the relative of diversity, “What is other than”, since it is added to “animal”, which is a wider class than “man”, designates a class of lesser extension; and in the proposition: “What is other than man runs”, it is added to a term of lesser extension, “man”, and consequently it designates a class of wider extension; therefore, “What is other than an animal” is of less extension than “What is other than a man”. Thus there is, in this instance, a topical argument from species or from a subjective part.
De relativis identitatis talis datur regula ab antiquis: nulla propositio inchoata a relativo identitatis habet contradictoriam. Et assignant talem causam, quia cum dicitur: "Omnis homo currit et ille disputat", hoc relativum "ille" habet respectum ad hoc antecedens" homo" propter dependentiam suae relationis; sed cum negatio advenit propositioni inchoatae a relativo, dicendo sic: "Ille non disputat", tunc negat verbum quod sequitur et non negat respectum relationis quem habet ad antecedens; ergo negatio non negat totum, quicquid affirmatio affirmat; ergo, non contradicit. Sed cum hoc sit in qualibet propositione inchoata a relativo, sequitur quod nulla propoaitio inchoata a relativo habet contradictoriam. Concerning relatives of identity, the following rule is given by the older authors: no proposition beginning with a relative of identity has a contradictory. They assign the following reason, namely, that when one says: “Every man is running and he is disputing”, the relative “he” has reference to the antecedent “man” because of its dependent relation; but when negation occurs in the proposition beginning with a relative, as in stating the following: “He does not debate”, then the negation denies the verb which follows and does not deny the reference of the relative to the antecedent; therefore the negation does not deny the whole of that which the affirmation affirms; consequently, it does not contradict Since this is the case in any proposition whatever beginning with a relative, it follows that no proposition beginning with a relative has a contradictory.
Sed contra hoc obiicitur, quicquid contingit affirmare contingit et negare de quolibet supposito; sed verbum contingit negare de quolibet supposito, ergo et contingit affirmare > de quolibet supposito quod est dictio relativa; ergo, quaelibet propositio inchoata a relativo habet contradictoriam. But against this it is objected that whatever can be affirmed of any subject (gupposito), can be denied of it; but a verb may be denied of any subject whatever, and therefore it may be affirmed of any subject which is a relative word; therefore, any proposition whatever beginning with a relative has a contradictory.
Item quaelibet propositio sive enunciatio, quae est una, habet contradictoriam; sed propositio inchoata a relativo, dummodo ibi non sit aliqua dictio aequivoca neque plura subiiciantur neque praedicantur, est una propositio; ergo, propositio inchoata a relativo habet contradictoriam. Furthermore, any proposition or statement which is single has a contradictory; but a proposition beginning with a relative, as long as it does not contain any equivocal word nor a multiple subject or predicate, is a single proposition; therefore, a proposition beginning with a relative has a contradictory.
Item, dicit Aristoteles, in primo "Peri Hermenias", circa affirmationem et negationem, quod uni affirmationi una negatio est opposita, et e converso, una affirmatio uni negationi est opposita. Ergo, affirmationi inchoatae a relativo negatio una est opposita. Quod concedimus, dicentes praedictam regulam esse falsam. Moreover, in the first book of the De Interpretatione,[5] with regard to affirmation and negation Aristotle asserts that a single negation is opposed to a single affirmation, and conversely, that a single affirmation is opposed to a single negation. Therefore, a single negation is opposed to an affirmation beginning with a relative. This we concede, affirming that the aforementioned rule is false.
Ad rationes eorum respondemus quod relativum comparatur ad antecedens et comparatur ad verbum cui subiicitur. Unde, cum affirmatio vel negatio sit oratio affirmativa vel negativa alicuius de aliquo vel alicuius ab aliquo, hoc est, praedicati de subiecto, ideo, sicut patet per definitionem praedictam affirmationis et negationis, affirmatio et negatio respiciunt tantummodo comparationem subiecti ad praedicatum. Ergo, in propositione inchoata a relativo, tantummodo sumitur contradictorium per comparationem relativi ad verbum cui subiicitur et non per comparationem relativi ad antecedens, quia ille respectus non est ibi propter naturam affirmationis, nec propter dependentiam subiecti inquantum est subiectum, sed propter dependentiam eius quod est subiectum. Dicendum tamen est quia aliud est subiectum inquantum subiectum et id quod est subiectum, et aliud est praedictatum inquantum praedicatum et illud quod est praedicatum. Et sic quicquid affirmatur in propositione inchoata a relativo, negatur in sua contradictoria, quia con>tradictoria istius: "Ille disputat", est ista: "Non ille disputat"—negatione praeposita relative To the arguments of those [who uphold the rule] we reply that a relative is related both to the antecedent and to the verb whose subject it is. Thus, since an affirmation or a negation is a sentence asserting something or denying something of something, that is, a predicate of a subject, therefore, as is clear from the aforementioned definition of an affirmation and a negation, an affirmation and a negation only refer to the relation of a subject to a predicate. Therefore, in the case of a proposition beginning with a relative, the contradictory is only derived from the relation of the relative term to the verb whose subject it is and not from the relation of the relative to its antecedent, for this latter relation is not present by reason of the nature of an affirmation, nor by reason of the dependence of the subject, qua subject, but by reason of the dependence of that [word] which is the subject. It should, however, be said that a subject, qua subject, is not the same as that which is the subjected a predicate, qua predicate, is not the same as that which is the predicate. Thus whatever is affirmed in a proposition beginning with a relative, is denied by its contradictory, for the contradictory of this statement: “He is disputing:”, is this: “Not he is disputing”—the negation being placed before the relative.
De relativo identitatis non reciproco talis datur regula: omne relativum identitatis non reciprocum habet eandem suppositionem quam habet suum antecedens, ut cum dicitur: "Omnis homo currit et ille est Sortea", hoc relativum "ille" supponit pro omni nomine, quia sensus est: "Omnis homo currit et ille est Sortes", id est, "Omnis homo est Sortes". Dico autem "non reciprocum", quia cum dicitur: "Omnis homo videt se", non est sensus: "Omnis homo videt omnem hominem". Unde loco huius relativi "se" non licet ponere suum antecedens, loco autem alterius licet ponere. As concerns the non-reciprocal relative of identity, this rule is given: every non-reciprocal relative of identity has the same supposition which its antecedent has; as when one says: “Every man runs and he is Sortes”, the relative “he” denotes every man because the meaning of” that statement is “Every man runs and he is Sortes”, that is, “Every man is Sortes”. However, I say “non-reciprocal” because when one says: “Every man sees himself, the meaning is not: “Every man sees every man”. Therefore the antecedent cannot be substituted for the relative “himself”, although it can be substituted for the other relative [i.e. “he”].
Habito de relativo substantiae, dicendum est de relativo accidentia. Relativum autem accidentis est quod refert eandem rem per modum denominationis, ut "tale", "quale", et cetera. Unde haec est differentia relativi substantiae ad relativum accidentia, quia relativum substantiae refert rem univocam per modum quod quid est, ut "Albedo quae est in pariete", "Color qui est in corpore"; relativum autem accidentia est quod refert rem suam per modum denominationis, ut "Sortes est albus et talis est Plato". Alia autem differentia datur eorundem, quia relativum substantiae refert idem in numero cum suo antecedente, relativum vero accidentia refert idem in specie, ut "Sortes est albus et talis est Plato", quia idem in numero non potest esse in diversis subiectis sed bene idem in specie. The consideration of relatives of substance having been completed, we must consider relatives of accident A relative of accident is one which refers to the same thing in a denominative manner, as does “such”, “as”, and so forth. Consequently, there is a difference between a relative of substance and a relative of accident, because the relative of substance refers to a univocal thing according to the mode of its essential being, as in “Whiteness which is in a wall”, “Color which is in a body”; but a relative of accident is that which refers to its object in a denominative manner, such as “Sortes is white and such is Plato”. Another difference between them is that a relative of substance refers to that which is numerically the same as its antecedent, while a relative of accident refers to that which is specifically the same, as in the statement: “Sortes is white and such is Plato”, because the same in number cannot be in diverse subjects but the same in species can very well be [in diverse subjects].
Relativorum autem accidentia, aliud est relativum identitatis, ut "talis"; aliud vero diversitatis, ut "alteriusmodi". Relativum accidentia identitatis est quod refert eandem qualitatem in specie et supponit pro eadem in specie, ut "Sortea est albus et talis est Plato". Relativum autem acci>dentis diversitatis est quod refert eandem qualitatem in specie sed supponit pro alia diversa in specie, ut "Sortes est albus et alteriusmodi est Plato". Differt autem relativum substantiae identitatis a relativis accidentium identitatis, quia relativum identitatis substantiae refert eandem substantiam in numero, relativum autem identitatis accitis non refert idem accidens in numero sed solum refert idem accidens in specie. One type of relative of accident is the relative of identity, for example, “such”; another type is the relative of diversity, such as “otherwise”. A relative of identity of accident is one which refers to a quality the same in species [as its antecedent] and denotes a quality which is the same in species, as in the statement: “Sortes is white and such is Plato”. However, a relative of diversity of accident is one which refers to a quality the same in species [as its antecedent] but denotes a quality of diverse species, as “Sortes is white and Plato is otherwise”. But a relative of identity of substance differs from relatives of identity of accidents because a relative of identity of substance refers to a substance the same in number, whereas relative of identity of accident does not refer to an accident the same in number but only to an accident the same in species.
Relativorum accidentia identitatis, aliud est relativum quantitatis continuae, ut "quantus", "tantus"; aliud vero quantitatis discretae, ut "tot", "quot". Item, relativorum numerorum, quaedam sunt nomina, ut "totidem"; quaedam sunt adverbia, ut "totiens". One type of relative of identity of accident is a relative of continuous quantity, for example, “as great as”, “so great”; another type is the relative of discrete quantity [or of number], for example, “as many as”, “so many”. Furthermore, some relatives of number are nouns, such as “just as many”; others are adverbs, such as “so often”.
Sciendum quod "talis", "tantus", "tot", "totiens", "totidem", possunt dici relativa, redditiva, et demonstrativa: relativa, ut si ad praeaentes referantur; demonstrativa, ut cum dicimus, demonstrando mare: "Tale est Rubeum", et demonstrando Herculem: "Talis fuit Plato"; si autem non referantur ad praesentes sive per demonstrationem rerum praesentium, tunc aunt redditiva, quia reddunt responsionem interrogationi praecedenti, ut "Qualis est Plato, talis est Sortes". Relativa quandoque sine interrogatione proferuntur, ut "Talia est Sortes, qualis est Plato"; et quandoque ad nomina adiectiva specialium accidentium dicuntur, ut "Ethyopa est niger et talis est corvus" et "Sortes fuit albus et talis fuit Plato". It should be noted that “such”, “so great”, “as many as”, “so often”, “just as many”, can be called relative, responsive, and demonstrative: relative, when they are referred to things present; demonstrative, as when we say, pointing to the sea: “Such is the Red Sea”, and pointing to Hercules : “Such was Plato”; but if their reference is not to the things present or is not accomplished through pointing to things which are present, then they are responsive because they render a reply to a preceding interrogation, as “Of whatever kind Plato is, such is Sortes”. Sometimes relatives are used without a previous interrogation, as “Sortes is such as Plato is”; and sometimes they are used in connection with adjectives connoting special accidents, as in the propositions: “An Ethiopian is black and such is the raven” and “Sortes was white and such was Plato”.
>TRACTATUS AMPLIATIONUM TREATISE ON AMPLIFICATIONS
Personalis suppositio est acceptio termini communis pro suis inferioribus. Cuius, alia est determinata; alia confusa—ut prius patuit. Item, personalis suppositionis, alia est restricta; alia ampliata. Et ita ampliatio et restrictio 5 habent fieri circa suppositionem personalem. Personal supposition is the acceptance of a general term for its particulars. One type of personal supposition is determinate; the other is indeterminate—as we explained previously. Still another division of personal supposition is into restricted and amplified supposition. Hence, amplification and restriction have to occur in respect to personal supposition.
Restrictio est coartatio termini communis a maiori suppositione ad minorem, ut cum dicitur: "Homo albus currit", hoc adiectivum "albus" restringit "hominem" ad supponendum tantum pro albis. Restriction is the contraction of a general term from a greater supposition to a lesser supposition, as when one says: “A white man is running”, the adjective “white” restricts the denotation of “man” to white men alone.
Ampliatio est extensio termini communis a minori suppositione ad maiorem, ut cum dicitur: "Homo potest esse Antichristus", iste terminus "homo" non solum supponit pro his qui sunt sed etiam pro his qui erunt; unde ampliatur ad futuros. Dico autem "termini communis" quia terminus singularis, ut "Sortes", neque ampliatur neque restringitur. Amplification is the extension of a general term from a lesser supposition to a greater, as when one says: “A man can be the Anti-christ”, the term “man” not only denotes men who exist but also men who will exist; therefore, it is amplified to include those who will exist in the future. I say “of a general term” because a singular term, such as “Sortes”, is neither amplified nor restricted.
Ampliationum, alia fit per verbum, ut per hoc verbum "potest", ut "Homo potest esse Antichristus"; alia fit per nomen, ut "Hominem esse Antichristum est possibile"; alia fit per participium, ut "Homo potens est esse animal"; alia fit per adverbium, ut "Homo necessario est animal", "Homo" enim non solum ampliatur pro praesenti tempore sed etiam pro futuro. Et ideo sequitur alia divisio ampliationis, scilicet, quod ampliationum, alia fit respectu suppositorum, ut "Homo potest esse Antichristus"; alia fit respectu temporum, ut "Homo necessario est animal"—ut dictum est. One kind of amplification is accomplished by means of a verb, as, for example, by means of the verb “can”, as in the statement: “A man can be the Anti-christ”; a second kind is accomplished by means of a noun, [that is, a substantive verbal expression,] as in the statement: “That a man be the Anti-christ is possible”; a third kind is accomplished by means of a participle, as in the statement: “A man is able (potent) to be an animal”; a fourth kind is accomplished by means of an adverb, as in the statement: “A man necessarily is an animal”, because “man”, in this instance, is amplified so as to include not only the men existing in the present but also the men who will exist in the future. Another division of amplication follows as a consequence of this, namely, one kind of amplification occurs in relation to the things denoted, as in the statement: “A man can be the Anti-christ”; another kind occurs in relation to time, as, for example, in the statement: “A man necessarily is an animal”—as we mentioned previously.
>Circa praedicta, quaeritur de hoc sophismate: "Impossibile potest esse verum". Probatur quia illud quod est vel erit impossibile potest esse verum; sed Antichristum non fuisse post tempus suum est impossibile et modo potest esse possibile et verum; ergo impossibile potest esse verum. With respect to the aforementioned, there occurs the problem of the sophism: “The impossible can be true”. The sophism is proved in the following fashion: That which is or will be impossible can be true; but that the Antichrist has not existed is impossible after his time but it can now be possible and true; therefore, the impossible can be true.
Contra: "Quicquid potest esse verum est possibile; sed impossibile potest esse verum; ergo, impossibile est possibile", in tertio modo primae figurae. Sed conclusio est falsa; ergo aliqua praemissarum. Non maior; ergo minor. Sed haec est prima; ergo prima est falsa. Contra: Utilizing the third mode of the first figure: “Whatever can be true is possible; but the impossible can be true; therefore, the impossible is possible”. But this conclusion is false; therefore one of the premisses is false. Not the major; therefore the minor. But the minor premiss is the original statement; therefore, the original statement is false.
Solutio: Prima simpliciter est falsa, haec scilicet, "Impossibile potest esse verum"; et sophisma peccat contra fallaciam accidentia, quia cum dico: "Id quod est vel erit impossibile", duo dico, scilicet, subiectum illius impossibilitatis, et illam impossibilitatem sive ipsum "impossibile". Sed "illud quod est vel erit" est res subiecta; et "impossibile" accidit ei; et "posse esse verum" assignatur inesse utrique. Sicut haec: "Antichristum non fuisse erit possibile, scilicet, Antichristum non fuisse potest esse verum; ergo impossibile potest esse verum", non valet, quia "Antichristum non fuisse" est res subiecta, et "impossibile" est accidens, et "posse esse verum" assignatur inesse utrique. A solution is as follows: The original statement is unqualifiedly false, that is, “The impossible can be true”; and the sophism is guilty of the fallacy of accident because when I say: “that which is or will be impossible”, I affirm two things, namely, the subject of that impossibility, and that impossibility or the predicate “impossible”. But “That which is or will be” denotes a thing that is the subject; “impossible” belongs to this subject; and “can be true” is asserted to belong to both. For example, “That the Antichrist has not existed will be possible, that is, that the Antichrist has not existed can be true; therefore the impossible can be true”, is invalid because “That the Anti-christ has not existed” denotes the thing that is the subject, and “impossible” is an accident, and “can be true” is asserted to belong to both.
De ampliatione, quae fit ratione suppositorum, talis datur regula: terminus communis supponens verbo habenti vim ampliandi, a se vel ab alio, ampliatur ad ea quae possunt ease sub forma termini supponentis, ut "Homo potest esse animal". Hic iste terminus "homo" non solum supponit pro praesentibus sed etiam ampliatur ad omnes qui erunt >Dico autem "a se", quia hoc verbum "potest" de se habet vim ampliandi. Dico autem "ab alio", quia hoc participium "potens" et hoc nomen "possibile" dant virtutem ampliandi verbo cui adiunguntur, ut "Homo est potens esse animal" vel "Animal possibile est esse album", et sic de aliia. The following rule is offered in relation to amplification which is accomplished by reason of the things denoted: a general term occurring with a verb which has the power of amplifying, either intrinsically or extrinsically, is amplified to include in its denotation those things which can exist under the form of the denoting term, as in the statement: “A man can be an animal”. In this proposition, the term “man” not only denotes men existing at the present time but it is amplified to embrace all who will exist as well. However, I say “intrinsically” because this verb “can” has in itself the power of amplification. I say “extrinsically” because the participle “having the potency” and the noun “possible” bestow the power of amplifying on the verb with which they are united, as in the statements: “A man is able (potent) to be an animal” or “It is possible that an animal is white”, and so on.
De ampliatione autem, quae fit ratione temporis, talis datur regula: terminus communis supponens vel apponens verbo habenti vim ampliandi quoad tempus, supponit pro his quae sunt, quae erunt, vel quae f uerunt, ut "Homo necessario est animal". Ibi tam "homo" quam "animal" tenetur pro his quae fuerunt, quae sunt, et quae erunt Et haec de ampliationibus dicta sufficiant. The following rule is offered in relation to amplification accomplished by reason of the time element: a general term occurring as subject or predicate with a verb which has the power of temporal amplification, denotes those things which exist, which will exist, or which have existed, as in the statement: “Man necessarily is an animal”. In this proposition, both “man” and “animal” are understood to include those who have existed, those who exist, and those who will exist. These remarks concerning amplification may suffice.
>TRACTATUS APPELLATIONUM TREATISE ON APPELLATIONS
Appellatio est acceptio termini pro re existente. Dico autem "pro re existente", quia terminus significant "non-ens" non appellat, ut "Caesar" vel "Antichristus" vel "chimaera" et cetera. Differt autem appellatio a significatione et suppositione, quia appellatio est tantum de re existente sed suppositio et significatio sunt tam pro re existente quam pro re non existente; ut "Antichristus" significat Antichristum et supponit pro Antichristo sed non appellat. "Homo" enim significat hominem et de natura sua supponit tam pro existentibus quam pro non—existentibus hominibus, appellat autem tantum homines existentes. Appellation is the acceptance of a term for an existing thing. I say “for an existing thing” because a term signifying a nonentity does not name [anything], as “Caesar”, or “Anti-christ”, or “chimera”, and so forth. Moreover, appellation differs from signification and supposition because appellation is only of an existing thing, whereas supposition and signification are both of an existing thing and of a non-existing thing; as “Anti-christ” signifies Anti-christ and denotes Anti-christ but does not name [the Anti-christ]. For “man” signifies man and naturally denotes both existing and non-existing men. but it names only existing men.
Appellationum autem alia est termini communis, ut "homo"; alia est termini discreti vel singularis, ut "Sortes". Terminus singularis idem significat, supponit, et appellat, scilicet, rem existentem, ut "Petrus" vel "Ioannes". Item, appellationum termini communis, alia est termini communis pro re in communi, ut quando terminus communis simplicem habet suppositione, ut cum dicitur: "Homo est species", "Animal est genus"; et tunc terminus idem supponit, significat, et appellat, ut "homo" significat hominem in communi et supponit pro homine in communi et appellat hominem in communi: alia autem est appellatio termini communis pro suis inferioribus, ut quando terminus communis personalem habet suppositionem, ut cum dicitur: "Homo currit"; tunc "homo" non idem significat, supponit, et appellat, sed significat hominem in communi et supponit pro particularibus hominibus et appellat particulares homines tantum existentes. Et haec de appellationibus dicta sufficiant. One kind of appellation is that which belongs to a general terra, such as “man”; another, that which belongs to a discrete or a singular term, such as “Sortes”. A singular term signifies, denotes, and names the same thing, that is, the [same] existing thing, such as “Peter” or “John”. Again, one type of appellation by a general term consists in the appellation of the universal thing by the general term, such as occurs whenever a general term has simple supposition, as, for example, when one says: “Man is a species”, “Animal is a genus”; in such cases, the term denotes, signifies, and names the same thing, as “man” signifies man in general, denotes man in general, and names man in general: the other type of appellation which belongs to a general term consists in its naming its particulars, such as happens whenever the general term has personal supposition, as when one says: “A man runs”; in this case, “man” does not signify, denote, and name the same thing, but rather it signifies man in general, denotes particular men, and names only those particular men who exist These remarks concerning appellations may suffice.
>TRACTATUS RESTRICTIONUM TREATISE ON RESTRICTIONS
Restrictio est coartatio termini communis a maiori suppositione ad minorem, ut dictum est prius. Restrictionum autem, alia fit per nomen, ut "homo albus", iste terminus "homo" non supponit pro nigris neque pro medio colore coloratis sed restringitur ad albos; alia fit per verbum, ut "Homo currit", iste terminus "homo" supponit pro praesentibus tantum; alia fit per participium, ut cum dicitur: "Homo currens disputat", ille terminus "homo" supponit pro currentibus; alia fit per implicationem, ut cum dicitur: "Homo, qui est albus, currit", haec implicatio "qui est albus" restringit "hominem" ad albos. Restriction is the contraction of a general term from a greater supposition to a lesser supposition, as we said previously. One type of restriction is effected by means of an adjective (nomen), as in the expressipn “white man”, the term “man” does not denote black or intermediately colored men but is restricted to “white men”; a second type of restriction is effected by means of a verb, as in the statement : “A man is running”, the “term “man” only denotes men who exist at the present time; a third type is effected by means of a participle, as when one says: “A running man is arguing”, the term “man” denotes men who are running; a fourth type is effected by means of a subordinate clause, as when one says: “A man who is white is running”, the clause “who is white” restricts “man” to white men.
Item, restrictionum factarum per nomen, alia fit per inferius nomini superiori appositum, ut "Animal, homo, currit", ille terminus "animal" tantum supponit pro animalibus quae sunt homines; alia fit per differentiam advenientem generi, quae est essentialis cum sit constitutiva rei, ut cum dicitur "animal rationale", hic "animal" supponit pro rationalibus animalibus; alia fit per adiectivum accidentia, ut cum dicitur: "homo albus", iste terminus "homo" supponit tantum pro albis hominibus. Furthermore, of restrictions effected by means of a noun, one type is produced by the more particular being in apposition to the more general, as in the statement: “An animal, man, runs”, the term “animal” denotes only animals who are men; a second type is effected by the addition to the genus of a differentia which is essential since it is constitutive of the thing, as when one says “rational animal”, the term “animal” denotes rational animals; a third type is effected by an adjective of accident, as when one says: “white man”, the term “man” denotes only white men.
De restrictione facta per nomen communiter sumptum tales dantur regulae. Omne nomen, non diminuens nec habens vim ampliandi, adiunctum ex eadem parte termino magis communi, restringit ipsum ad supponendum pro his ad quae exigit sua significatio, ut patet in exemplis praedictis, ut "homo", per suam significationem, restringit "animal" ad animalia, quae sunt homines, ut cum dicitur > "animal homo" et "albus" restringit "hominem", per suam significationem ad homines albos, ut cum dicitur: "homo albus". Dico autem "non diminuens" ad removendum nomina diminuentia rationem adiuncti, ut "mortuus" vel "corruptus" et similia, quae non restringunt sed potius destruunt adiunctum. Dico autem "non habens vim ampliandi" ad removendum dictiones ampliativas, ut "potens", "potest", et "possibile", quae non restringunt sed potius ampliant. Et sciendum quod minus commune semper restringit magis commune, ut cum dicitur: "Homo albus currit", quia homo reperitur in albis hominibus et nigris et medio colore coloratis sed albus tamen non. Unde, quoad hoc, "homo" est magis commune et "albus" minus commune; et sic "albus" restringit "hominem". Sed secundum quod albus reperitur in hominibus, lignis, lapidibus, et brutis, homo autem non, ut sic, "albus" est magis commune et "homo" minus commune; et sic "homo" coartat "album" ad albedinem existentem in hominibus cum dicitur: "Homo albus currit". Et sic utrumque coartat alterum secundum diversa. The following rules are given for restrictions effected by mans of nouns, [both substantival and adjectival nouns]. Every noun which does not limit or which does not have the force of amplification, when added directly to a more general term, restricts that term to the denotation of those things which the restrictive term signifies, as is clear in the aforementioned examples, where “man”, on account of its signification, restricts “animal” to those animals which are men, as when one says “an animal, man” and where “white”, on account of its signification, restricts “man” to white men, as when one says: “white man”. However, I say “which does not limit” in order to exclude nouns limiting the nature of the adjunct, such as “dead”, or “corrupt”, and the like, which do not restrict but rather destroy the adjunct Moreover, I say ‘Vhich does not have the force of amplification” to exclude amplificative words, such as “being able”, “can”, “possible”, which do not restrict but rather amplify. It should be noted that the leas general always restricts the more general, as when one says: “A white man is running”, because man is found in white, black, and intermediately colored men but nevertheless white is not Therefore, in this respect “man” is more general and “white” is less general; consequently, “white” restricts “man”. But according as white is found in men, sticks, stones, and brutes, while man is not taken this way, “white” is more general and “man” is less general; thus “man” contracts “white” to the whiteness existing in men when one says: “A white man ia running”. So each contracts the other in diverse respects.
Item, de termino restricto talis datur regula: "si signum universale adveniat termino restricto, non distribuit ipsum nisi pro his ad quae restringitur. Cum enim dico: "Omnis homo albus currit", ibi "homo" restringitur ad albos et non potest distribui nisi pro albis. The following rule is also given concerning a restricted term: if a universal sign is added to a restricted term, it distributes the restricted term only among those things to which it is restricted. For when I say: “Every white man runs”, “man” is here restricted to white men and can only be distributed among white men.
Item, de restrictione datur regula talis: nihil positum a parte praedicati potest restringere terminum communem positum a parte subiecti quoad principalem eius significationem, ut "Homo est albus", iste terminus "albus", in praedicato positus, non potest restringere "hominem", in subiecto positum, ad albos, quia si restringeretur ad albos, ergo per regulam praecedentem—scilicet, si signum universale advenerit termino restricto, solum distribuit ipsum pro hia ad quae restringitur—ut in proposito "homo" distribueretur > solum pro albis hominibus. Et sic, istius propositionis: "Omnis homo est albus" sensus esset "Omnis homo albus est albus". Ergo, si una erit vera, reliqua erit vera; et si una erit falsa, reliqua erit falsa. Quod tamen est falsum. Ergo, cum dicitur: "Omnis homo est albus", iste terminus "homo" non restringitur. Et sic patet illa regula. Dico autem "quoad principalem eius significationem", quia praedicatum restringit subiectum quoad consignificationem, quae est genus; ut cum dicitur: "Cycnus est albus", iste terminus "cycnus" restringitur ad mares et non ad mulieres. Et sic, "albus" restringit ipsum quoad consignificationem, quae est genus, et non quoad suam significationem. The following rule is likewise given for restriction: no term which has the position of a predicate can restrict a general term having the position of subject as far as its principal signification is concerned; as in the statement: “A man is white”, the term “white”, in the position of predicate, cannot restrict “man”, in the position of subject to white men because if [”man”] were restricted to white men, then by the preceding rule—if a universal sign is added to a restricted term, it distributes the restricted term only among those things to which it is restricted—“man” would be distributed, in the case under consideration, only among white men. Consequently, the meaning of the proposition: “Every man is white” would be “Every white man is white”. Therefore, if one will be true, the other will be true; and if one will be false, the other will be false. However, this is false. Hence, when one says: “Every man is white”, the term “man” is not restricted. Thus this rule is clear. But I say “as far as its principal signification is concerned” because the predicate does restrict the subject as far as its consignification, which is its gender, is concerned; as when one says: “A swan is white”, the term “swan” is restricted to males and not to females. Thus, “white” restricts “swan” with respect to [its] consignification, that is, its gender, but not with respect to its signification.
Item, de restrictione facta per implicationem talis datur regula: omnis implicatio immediate coniuncta termino communi restringit ipsum sicut suum adiectivum, ut cum dicitur: "Homo, qui est albus, currit", iste terminus "homo" restringitur ad albos per hanc implicationem, scilicet, "qui est albus". The following rule is given for a restriction effected by means of a subordinate clause: every subordinate clause which is immediately conjoined to a general term restricts it just as its adjective does, as when one says: “A man, who is white, is running”, the term “man” is restricted to white men by the clause “who is white”.
Item, de eadem restrictione talis datur regula: quotienscunque signum universale et implicatio ponuntur in eadem locutione, duplex est oratio ex eo quod signum potest praecedere implicationem et sic distribuit terminum communem pro quolibet suo supposito, ut cum dicitur: "Omnis homo currit, qui est albus"; item, implicatio potest prius advenire et restringere terminum communem, et tunc signum, postea adveniens, non distribuit ipsum nisi pro his ad quae restringitur, ut "Omnis homo, qui est albus, currit". Et tunc aequivalet huic: "Omnis homo albus currit". The following rule is likewise given for the same type of restriction: whenever a universal sign and a subordinate clause are incorporated into the same sentence, the statement is ambiguous because of the fact that [a] the sign can precede the subordinate clause and so distribute the general term among all the things it can denote, as when one says: “Every man runs, who is white”; or again, [b] the subordinate clause can come first and restrict the general term, and then the sign, being added afterwards, does not distribute it except among those things to which it is restricted, as in the proposition: “Every man, who is white, runs”. In the latter case, it is equivalent to the proposition: “Every white man runs”.
Sequitur de restrictione facta per verbum, de qua plures dantur regulae, quarum prima talis est: terminus communis supponena vel apponens verbo praesentis temporis, simpliciter sumpto, non habente vim ampliandi, neque ex se > neque ex alio, restringitur ad supponendum pro his quae sunt sub forma termini communis supponentis. Dico autem "termini communis", quia terminus discretus neque restringitur neque ampliatur. Dico autem "verbo praesentis temporis" ad removendum alia verba aliorum temporum, quia terminus communis aliam habet suppositionem cum eis. Dico autem "simpliciter sumpto" ad removendum verba sumpta cum particulis diminuentibus, ut "est opinabile" et "inopinabile". Dico autem "non habente vim ampliandi" ad removendum verba ampliativa, ut "potest". Dico autem "neque ex se neque ex alio" ad removendum verba habentia vim ampliandi ex alio, ut puta, ex coniuncto, sicut hoc verbum "est" cum dicitur "est potens". Dico autem "sub forma termini communis supponentis", quia "homo" supponit pro his quae sunt sub humanitate et "animal" quae sunt sub animalitate, ut cum dicitur: "Homo est animal". We now treat of restrictions effected by verbs and give several rules, the first of which is the following: a general term which occurs as subject or predicate with a verb in the present tense which is taken simply and which does not have the power of amplification, either intrinsically or extrinsically, is restricted to the denotation of those things of the nature signified by the denoting general term, which are existing. I say “of a general term” because a discrete term is neither restricted nor amplified. Moreover, I say “a verb in the present tense” to exclude other verbs in other tenses, because a genera! term has another supposition when taken with such verbs. I say “taken simply” to exclude verbs taken with limiting particles, such as “it is believable” and “unbelievable”. I say “which has not the power of amplifying” to exclude amplifying verbs, such as “can”. I say “either intrinsically or extrinsically” to exclude verbs which have their power of amplifying extrinsically, for instance, from something conjoined, like this verb “is” when we say “it is able to”. I say “of the nature signified by the denoting general term” because “man” denotes those things which are included under humanity and “animal” denotes those things which are included under animality, as when one says: “Man is an animal”.
Item, alia datur regula: terminus communis supponens vel apponens verbo de praeterito, simpliciter sumpto, non habente vim ampliandi, nec ex se nec ex alio, restringitur ad supponendum pro his quae sunt vel fuerunt sub forma termini supponentis; ut cum dicitur: "Homo fuit animal", iste terminus "homo" supponit pro his qui sunt vel fuerunt homines et "animal" pro his quae sunt vel fuerunt animalia. Another rule is as follows: a general term which occurs as subject or predicate with a verb in the past tense which is taken simply and which does not have the power of amplification, either intrinsically or extrinsically, is restricted to the denotation of those things of the nature signified by the denoting general term, which exist or have existed; as when one says: “Man was an animal”, the term “man” denotes those who are or were men and [the term] “animal” denotes those who are or were animals.
Item, alia datur regula: terminus communis supponens vel apponens verbo de futuro etiam supponit pro his quae sunt vel erunt sub forma termini supponentis, scilicet, pro his quae sunt vel erunt in futuro, ut "Homo erit animal". Ex praedictis, patet quod verbum restringit quoad consignificationem, quae est tempus, et non quoad significationem principalem. A third rule follows: a general term which occurs as subject or predicate with a verb in the future tense denotes those things of the nature signified by the denoting term, which exist or will exist, that is, those things which exist or which will exist in the future as in the statement: “Man will be an animal”. From the aforementioned, it is clear that the verb restricts in its temporal consigniflcation but not in its principal signification.
Circa praedicta, quaeritur de hoc sophismate: "Omne animal fuit in arca Noe". Probatur: Homo fuit in arca > Noe; equus fuit in arca Noe et sic de aliis; ergo, omne animal fuit in arca Noe. With respect to what has just been discussed, the question of this sophism arises: “Every animal was in Noah’s ark”. The sophism is proved in the following fashion: A man was in Noah’s ark; a horse was in Noah’s ark and so forth; therefore, every animal was in Noah’s ark.
Contra: Omne animal fuit in arca Noe; sed Caesar fuit animal; ergo, Caesar fuit in arca Noe. Quod est falsum ergo, aliqua praemissarum est falsa. Non minor; ergo maior. It is argued to the contrary: Every animal was in Noah’s ark; but Caesar was an animal; therefore, Caesar was in Noah’s ark. This is false; therefore, one of the premisses is false. Not the minor; therefore the major.
Quod autem prima sit falsa, patet per quamdam regulam, quae dicit quod terminus communis supponens vel apponens verbo de praeterito, simpliciter sumpto, restringitur ad supponendum pro his quae sunt vel fuerunt sub forma termini supponentis. That the original statement [the sophism] is false, is also clear from that rule which asserts that a general term which occurs as subject or predicate with a verb in the past tense, taken simply, is restricted to the denotation of those things of the nature signified by the denoting general term, which exist or have existed.
Item, alia est regula, quod si signum universale adveniat termino restricto, distribuit ipsum pro omnibus illis ad quae restringebatur. Ergo, cum dicitur: "Omne animal fuit in arca Noe", iste terminus "animal" supponit pro omni animali quod fuit; sed non fuerunt omnia in arca Noe; ergo, prima est falsa. Furthermore, there is that other rule that if a universal sign is added to a restricted term, it distributes the term among all those things to which it was restricted. Therefore, when one says: “Every animal was in Noah’s ark”, the term “animal” denotes every animal which was; but all animals were not in Noah’s ark; consequently, the original statement is false.
Item, ad idem, in hac propositione: "Omne animal, quod tunc fuit, fuit in arca Noe", iste terminus "animal" restringitur magis quam in ista oratione: "Omne animal fuit in arca Noe", cum in prima plura supponantur. Sed iste terminus "animal" restringitur ad ea, quae fuerunt tunc in illo tempore, propter implicationem ibi positam. Ergo solum illa, quae fuerunt in illo praeterito, fuerunt in arca Noe, et non plura. Igitur oportet quod haec sit falsa: 'Omne animal fuit in arca Noe", cum in ea plura animalia supponantur. Again, on the same point, in the proposition: “Every animal, which existed at that time, was in Noah’s ark”, the term “animal” is more restricted than in the proposition: “Every animal was in Noah’s ark”, since more animals are denoted in the original statement. But the term “animal” is restricted to those animals which existed at that time due to the dependent clause introduced in that proposition. Therefore only those animals which existed in that past time were in Noah’s ark, and no more. Hence it is necessary that the following proposition be false: “Every animal was in Noah’s ark”, since more animals are denoted in it.
Solutio: Quidam dicunt quod haec: "Omne animal fuit in arca Noe", est duplex, eo quod potest fieri distribute pro singulis generum vel pro generibus singulorum. Primo modo est falsa; secundo modo est vera. Quia quando fit distributio pro singulis generum, tunc est distribute pro > singulis, quae sub eodem genere et sub eadem specie continentur. Tunc oportet quod omnia individua, contents sub "animali", fuissent in arca Noe. Quod est falsum. Sed quando fit distributio pro generibus singulorum, tunc solum est distributio pro generibus vel pro speciebus. Sed non fuit aliqua species animalis, quae non fuit in arca Noe. Et illo modo est vera. A solution is as follows: Some assert that the proposition: “Every animal was in Noah’s ark”, is ambiguous because the distribution can apply to the individuals of the genera or to the genera of the individuals. In the first sense, the proposition is false but in the second sense, the proposition is true. For whenever distribution is made among the individuals of the genera, then there is a distribution among the individuals which are included in the same genus and in the same species. Then it would be necessary that all the individual animals which are included in the genus “animal” would have been in Noah’s ark. [However,] this is false. But when there is a distribution of the genera of the individuals, then there is only a distribution of the genera or of the species. But there was no species of animal which was not in Noah’s ark. In this sense, the proposition is true.
Sed huic solutioni non acquiesco, quia species animalis non fuit per se in arca Noe sed tantum individuum. Unde, illo tempore non habuit veritatem nisi pro singulis generum, id est, pro individuis et non pro generibus singulorum. Unde dico quod propositio est falsa et concedo omnes rationes adductas ad hoc. Et probatio peccat secundum consequens ab insufficient inductione, quia non accipit omnes partes distributionis, quae sunt sub subiecto istius propositions: "Omne animal fuit in arca Noe". But I do not agree with this solution, because no species of animal as such was in Noah’s ark but only some individuals. Therefore, in that time the proposition was only true as denoting the individuals of the genera, that is, as denoting the individual animals and not merely the genera of individual animals. Consequently, I say that the proposition [the sophism] is false and I concede all the arguments advanced to disprove it The proof errs according to an inference from insufficient induction because it does not include all the members of the distribution which are included in the subject of the proposition: “Every animal was in Noah’s ark”.
Solet etiam quaeri utrum similiter termini restringantur in propositione negativa et affirmativa. Dicunt aliqui quod non, quia "esse" restringit ad existens et "non-esse" ad non-existens; ergo, non pro eodem fit restrictio in affirmativa et negativa. It is also customary to raise the question as to whether terms are restricted in the same fashion in a negative and in an affirmative proposition. Some assert that this is not the case, because “being” restricts to the existent and “non-being” restricts to the non-existent; consequently, restriction is not effected in the same way in an affirmative and in a negative proposition.
Item, videtur quod omnis negativa, in qua "esse" negatur, simpliciter est falsa, si similiter restringantur termini in propositione negativa et affirmativa. Quia in hac propositione: "Rosa est", iste terminus "rosa" restringitur ad existens; et si in hac: "Rosa non est", similiter restringatur ad existens, tunc est sensus quod "Rosa, quae non est, est". Et haec est falsa; ergo et haec: "Rosa non est". Et sic quaelibet negativa, in qua "esse" negatur, esset simpliciter falsa. Quod falsum est. Ergo, videtur quod non similiter restringuntur termini in propositione affirmativa et negativa. Furthermore, it seems that every negative proposition in which “being” is denied is false without qualification, if terms are similarly restricted in a negative and in an affirmative proposition. For in the proposition: “A rose is”, the term “rose” is restricted to the existent; and if in the proposition: “A rose is not”, it is similarly restricted to the existent, then the meaning would be “A rose, which is not, is”. But this is false; therefore, the proposition: “A rose is not” is also false. Thus any negative proposition in which “being” is denied would be false without qualification. But this too is false. Consequently, H seems that terms are not restricted in the same fashion in an affirmative and in a negative proposition.
> Sed probatur quod similiter restringantur, quia si in hac propositione: "Homo est", iste terminus "homo" restringitur ad existens et in hac: "Nullus homo est", ad non-existens, ergo utraque est vera, quia de existentibus vere praedicatur "esse" et de non-existentibus vere removetur "esse". Ergo contradictoriae sunt simul verae, quod est impossibile. Ergo illud etiam ex quo sequitur impossibile, scilicet, quod non similiter restringantur termini in affirmativa et negativa. But it is proved that they are restricted in the same fashion, because if in the proposition: “A man exists”, the term “man” is restricted to an existing thing and in the proposition: “No man exists”, it is restricted to a non-existing thing, then each of the propositions is true, because “being” is truly predicated of existing things and is truly denied of non-existing things. But then contradictories are simultaneously true, which is impossible. Hence that from which the impossible follows, namely, that terms are not restricted in the same fashion in an affirmative and in a negative proposition, is impossible.
Item, regula est quod omne verbum, simpliciter sumptum, non habens vim ampliandi, nec a se nec ab alio, restringit terminum supponentem quoad consignificationem, quae est tempus, et non quoad significationem. Ergo tempus est causa restrictionis illius. Sed idem tempus est in affirmativa et negativa, sibi opposite, ut "Rosa est", "Nulla rosa est". Ergo, eadem est causa restrictionis in utraque. Et ergo pro eodem fit restrictio in utraque. Et haec argumenta concedimus. Futhermore, the rule is that every verb which is taken simply and which has not the power of amplification, either intrinsically or extrinsically, restricts the denoting term with respect to its temporal consignification but not with respect to its [principal] signification. Therefore time is the cause of the restriction of that term. But the time element is the same in opposed affirmative and negative propositions, as in the statements: “A rose exists” and “No rose exists”. Consequently, the cause of the restriction is the same in each of them. Hence the restriction applies to the same thing in each proposition. We concede these arguments.
Ad hoc, quod primo obiicitur, est dicendum quod "esse" non restringit ad existens et "non-esse" non restringit ad non-existens, sicut nec hoc verbum "curro" ad currentes, quia nullum verbum restringit sibi terminum supponentem quoad significationem sed quoad consignincationem, quae est tempus. Unde non restringit ad supposita existentia sed praesentia supposita. Praesentia enim possunt esse in aliquibus terminis, tam existentia quam non-existentia, ut cum dico: "Enunciabile est", "enunciabile" supponit tam pro existentibus quam pro non-existentibus: omnia autem enunciabilia, quae sunt falsa in praesenti, sunt praesentia sed non-existentia, quia nullum falaum est. Et sic, "esse" non restringit ad existentia sed ad praesentia, cum idem tempus sit utrobique, quod est causa restrictionis. To the first objection, it must be said that “being” does not restrict to the existent and “non-being” does not restrict to the non-existent, just as the verb “run” does not restrict to running things, because no verb restricts to itself a denoting term with respect to signification but [only] with respect to temporal consignification. Hence [the verb] does not restrict to the denoted things as existing but to the denoted things as being present For present things, both existing and non-existing, can be in some terms, as when I say: “An assertible is”, “assertible” denotes both existing and non-existing assertibles; for all assertibles which are false in the present, are present and yet do not exist, because no false [assertible] exists. Consequently, “being” does not restrict to existing things but to present things, since the time element, which is the cause of the restriction, is the same for both.
>Ad aliam, dicendum est quod duplex est forma termini communis: quaedam est quae salvatur in rebus existentibus tantum, ut "humanitas", quae est forma "hominis", et "animalitas", quae est forma "animalis", et in talibus omnia supposita praesentia sunt existentia; alia est forma termini communis, quae salvatur tam in rebus existentibus quam non-existentibus, ut "enunciabilitas", quae est forma "enunciabilis", quia quaedam sunt enunciabilia existentia, ut "Deum esse" et "Omnia vera", et alia sunt non-existentia, ut "Hominem esse asinum" et "Omnia falsa", et in talibus non restringitur terminus communis ad existentia sed restringitur tam ad existentia quam ad non-existentia. Unde istius propositions: "Rosa non est", non est sensus "Rosa, quae est, non est" sed est sensus "Rosa, aliter sumpta quam in praesenti, non est". To the second objection, it must be said that the form of the general term is twofold: one is that form which applies to existing things alone, as “humanity” which is the form of “man” and “animality” which is the form of “animal”, and in such cases all the present things denoted are existing things; the other is the form of the general term which applies to both existing and non-existing things, as “assertibility”, which is a form of “assertible”, because there are some existent assertibles, such as “God-existing” and “All-things-being-true”, and other non-existent assertibles, as “Man-being-ass” and “All-things-being-false”, and in such cases the general term is not restricted to existing things but it applies both to existing and non-existing things. Consequently, the meaning of the proposition: “A rose is not”, is not that “A rose, which is, is not”, but rather “A rose, taken otherwise than in the present, is not”.
Solet autem poni quod quaedam restrictio fit ab usu, ut cum dicitur: "Nihil est in arca", quamvis plena sit aere, quia iste terminus "nihil" supponit ab usu pro rebus solidis sive firmis; et "rex" pro rege patriae et "magister" legit pro magistro proprio. It is also customary to say that a certain kind of restriction occurs by usage, as when one says: “Nothing is in the ark”, although it is full of air, because the term “nothing”, from its usage, denotes solid or firm objects; or again, the term “the king” denotes the king of one’s own country and the term “the teacher” stands for one’s own teacher.
Solet etiam poni quod quaedam restrictio fit per transitionem verbi; ut cum dicitur: "Sortes pascit hominem", iste terminus "homo" supponit pro alio a Sorte virtute transitionis verbi, quia dans et recipiens debent esse diversa. Et ideo (si aliquando sint eadem, hoc tamen est per accidens, quia per hoc quod idem subiectum est utriusque, sicut idem est dux et comes secundum accidens. Unde dicunt quod non sequitur: "Sortes pascit seipsum; et ipse est homo; ergo, pascit hominem", quod est fallacia accidentia, quia hoc pronomen "se" non potest supponere pro diversis a Sorte sed "homo" bene potest. It is also customary to say that a certain kind of restriction is effected by the transitive property of the verb; as when one says: “Sortes feeds a man”, the term “man” denotes another man distinct from Sortes by virtue of the transitive property of the verb, because the man giving and the man receiving should be different persons. On that account, if sometimes they are the same person, this is only accidentally because of the fact that the same thing is the subject of mention in both cases, just as the same person is accidentally a Duke and a Count Therefore, they say that the following is not a valid inference: “Sortes feeds himself; he is a man; therefore, he feeds a man”, for this involves the fallacy of accident because the pronoun “himself’ cannot denote persons distinct from Sortes but “man” can well do so.
>TRACTATUS DISTRIBUT10NUM TREATISE ON DISTRIBUTIONS
Distributio est multiplicatio termini communis per signum universale facta; ut cum dicitur: "omnis homo", iste terminus "homo" distribuitur sive confunditur pro quolibet suo inferiori per hoc signum "omnis", et sic est ibi 5 multiplicatio. Dico autem "termini communis", quia terminus singularis non potest distribui. Unde istae sunt incongruae: "omnis Sortes", "omnis Plato", et sic de aliis; et sic ibi est soloecismus per partes orationis. Distribution is the extension of a general term effected by a universal sign; as when one says “every man”, the term •*man” is distributed or referred indeterminately to any of its particulars by virtue of the sign “every”, and in this fashion extension occurs. I say “of a general term” because a singular term cannot be distributed. Hence, such expressions as “every Sortes”, “every Plato”, and so forth are incongruous, for they constitute solecisms.
Signorum universalium, alia sunt distributiva substantiae, ut "omnis", "nullus"; alia sunt distributiva accidentium, ut "qualis", "quantus". Signum autem distributivum substantiae distribuit res se habentes per modum eius quod est quid, ut "omnis", "nullus", ut cum dicitur "omnis albedo", "omnis nigredo". Substantiae autem communiter sumitur ad res cuiuslibet generis, cum dicitur "signum distributivum substantiae". Signum distributivum accidentia est quod distribuit res se habentes per modum accidentis, ut per modum qualis vel quanti, ut "qualiscumque", "quantuscumque". Some universal signs are distributive of substance, such as “every”, “none”; others are distributive of accident, such as “such a kind”, “such a size”. A sign distributive of substance distributes things essentially related, such as “every”, “none”, as when one says “every whiteness”, “every blackness”. But substance is taken in the broader sense to include things of any genus whatsoever when one says “A sign distributive of substance”. A sign distributive of accident is one which distributes things related by a mode of accident, such as quality or quantity, for example, “any kind whatever”, “any size whatever”.
Item, signorum distributivorum substantiae, alia sunt distributiva partium integralium, ut "totus"; alia autem sunt distributiva partium subiectivarum, ut "omnis", "nullus". Item, signorum distributivorum partium subiectivarum, alia sunt distributiva duorum, ut "uter", "neuter"; alia sunt distributiva plurium, ut "omnis", "nullus", et similia. Horum autem signorum, primo dicendum est de signis distributivia substantiae et, inter haec, primo de hoc signo "omnis". Some signs distributive of substance are distributive of integral parts, such as “the whole”; others are distributive of subjective parts, such as “every” (omnis), “none”. Further, some signs distributive or subjective parts are distributive of two parts, such as “either of two”, “neither of the two”; others are distributive of many parts, such as “every”, “none”, and the like. Of these signs, we must first treat those distributive of substance and, among these, primarily the sign “every”.
Sciendum quod "omnis" in plurali numero dupliciter sumitur: uno modo collective, ut "Omnes apostoli Dei sunt duodecim"—non aequitur: "Ergo isti apostoli Dei sunt > duodecim", demonstratis aliquibus de ipsis; alio modo sumitur distributive, ut hic: "Omnes homines naturaliter scire desiderant". It must be known that “every” (omnis) is taken in the plural in a twofold sense: in one way collectively, as in the statement: “All the apostles of God are twelve”—it does not follow: “Therefore these apostles of God are twelve”, some of them being pointed to; in another way it is taken distribuxtively, as in the statement: “All men naturally desire to know”.
Tunc quaeritur, quid significet hoc signum "omni". Et videtur quod nihil significet, quia omnis res aut est universalis aut particularis; sed hoc signum "omnis" non significat rem universalem vel particularem; ergo, nullam rem significat. The next question is what does the sign “every” signify. It appears to signify nothing, because every thing is either universal or particular; but the sign “every” does not signify a universal thing or a particular thing; therefore, it signifies no thing.
Item, ad idem, "omnis" neque est praedicabile de uno neque de pluribus; ergo nec est universale nec particulare; et sic nihil significat. Furthermore, on the same point, “every” is neither predicable of one nor of many; therefore it is neither universal nor particular; so it signifies nothing.
Sed contra, ab eo quod res est vel non est, oratio dicitur vera vel falsa. Ergo, si "omnis" nihil significet, propter appositionem vel remotionem eius non causabitur veritas vel falsitas in oratione. Sed haec est vera: "Animal est homo"; ergo et haec est vera: "Omne animal est homo". Quod est falsum. Ergo et prima, scilicet, quod "omnis" nihil significat. Yet, on the contrary, from the fact that a thing is or is not, a stateemnt is said to be true or false. Therefore, if “every” signifies nothing, the truth or falsity of a proposition will not be caused by its presence or absence. But this statement is true: “An animal is a man”; and therefore [if the presence or absence of “every” does not affect the truth of statements] this is also true: “Every animal is a man”. But this is false. Hence the first statement is false, namely, that “every” signifies nothing.
Solutio ad dubium: Dicitur quod "omnis" non significat universale sed universaliter, quia facit terminum communem suum stare pro omnibus suis inferioribus, ut "Omnis homo currit". Et sic, "omnis" significat aliquam rem. Sed duplex est res, quia quaedam est res subicibilis vel praedicabilis, ut homo, animal, currit, disputat, et cetera, et sic verum est quod "omnis" nihil significat, quia quaelibet talis res aut est universalis aut particularis; alia est res, quae est dispositio rei subicibilis vel praedicabilis, et talem rem significat hoc signum "omnis". Et tam ab ista re quam ab alia causatur Veritas vel falsitas in oratione. The solution of the problem follows: It is said that “every” does not signify a universal but signifies universally, because it makes the general term which it qualifies stand for all its particulars, as “Every man runs”. In this way, “every” signifies some thing. But “thing” is taken in two senses, because in one sense a thing is that which can be a subject or a predicate, as man, animal, runs, argues, and so forth, and in this case it is true that “every” signifies nothing, because any such thing is either universal or particular; [and] there is another thing which is a disposition of that thing which is a subject or a predicate, and the sign “every” signifies such a thing. But the truth or falsity of a proposition is caused by both things.
Obiicitur autem quod "omnis" non significet dispositionem rei subicibilis, quia in syllogismo medium debet reiterari cum suis dispositionibus in minori propositione. Ergo debemus syllogisare sic: "Omnis homo est animal; > Sortes est omnis homo; ergo. Sortes est animal", "quia "omnis" est dispositio in maiori propositione, ergo debet reiterari in minori. Quod est falsum. Ergo, "omnis" non est dispositio subiecti. However, it is objected that “every” does not signify a disposition of a subject thing, because the middle term of a syllogism must be repeated with its dispositions in the minor premiss. Therefore we should syllogize in the following fashion: “Every man is an animal; Sortes is every man: therefore, Sortes is an animal”, because “every” is a disposition in the major premise and therefore must be repeated in the minor premise. But this is false. Therefore, “every” is not a disposition of a subject.
Solutio: Sicut "pater" duo dicit, scilicet, illud quod est pater et pater inquantum pater, similiter "subiectum" duo dicit, scilicet, illud quod est subiectum et subiectum inquantum subiectum. Et secundum hoc est duplex dispositio subiecti, quia quaedam est dispositio illius rei quod est subiectum, ut albus, niger, et sic de talibus dispositionibus accidentalibus, et istae debent reiterari in minori propositione cum medio; alia est dispositio subiecti, scilicet, subiecti inquantum subiectum, videlicet, in ordine ad praedicatum, ut "omnis", "nullus", et omnia signa tam universalia quam particularia, et talis dispositio non debet reiterari cum medio in minori propositione, quia est respectiva, disponit enim subiectum in comparatione ad praedicatum. Ut cum dicitur: "Omnis homo albus currit", ista dispositio "albus" debet reiterari in minori propositione cum medio, cum sit dispositio eius quod est subiectum, quia est absoluta; ista autem dispositio "omnis" non debet reiterari, quia est respectiva subiecti ad praedicatum, et ita est dispositio subiecti inquantum subiectum est. Unde debemus dicere sic: "Omnis homo albus currit; Sortes est homo albus; ergo, Sortes currit"; et non; "Sortes est omnis homo albus". The solution follows: Just as “father” connotes two things, namely, that thing which is the father and the father insofar as he is a father, so “subject” connotes two things, namely, the thing which is the subject and the subject insofar as it is a subject. According to this, the subject has a twofold disposition, for one is a disposition of that thing which is the subject, as white, block, and such similar accidental dispositions, and these dispositions should be repeated with the middle term in the minor premiss; the other is a disposition of the subject insofar as it is a subject, that is, in relation to the predicate, as “every”, “none”, and all signs both general and particular, and such a disposition should not be repeated with the middle term in the minor premiss because it is relative, since it distributes the subject in relation to the predicate. For example, when one says: “Every white man runs”, that disposition “white” should be repeated with the middle term in the minor premiss because it is an absolute disposition of that which is the subject; but that disposition “every” should not be repeated because it is a sign of a relation of the subject to the predicate and so is a disposition of the subject insofar as it is the subject. Consequently, we should say: “Every white man runs; Sortes is a white man; therefore, Sortes runs”; and not: “Sortes is every white man”.
Habito quid significet hoc signum "omnis" - et cuius dispositionem significet, consequenter quaeritur utrum "omnis" exigat tria appellata. Et videtur quod sic, quia omnis perfectio est in tribus, ut habetur primo Coeli et Mundi; et sic omne perfectum est in tribus. Sed omne et perf ectum idem aunt, ut habetur ibidem. Ergo, omne est in tribus. Ergo "omnis" vult habere tria appellata. Having discussed how this sign “every” signifies things and their dispositions, the question naturally follows as to whether “every” requires three things named. This would seem to be so, because every perfection occurs in threes, as is held in the first book of the De Caelo et Mundi*; and thus all that is perfect occurs in threes. But the all and the perfect are the same, as is held in the same passage. Therefore, all occurs in threes. Hence “every” requires three things.
>Ad idem, dicit Aristoteles in eodem loco quod de duobus viris non dicimus "omnes" sed de tribus viris dicimus "omnes;" ergo, "omnis" vult habere tria appellate. Aristotle, speaking on the same point in the same passage, says that we do not predicate “all” of two men but we do predicate it of three men; wherefore, “every” requires three things named.
Sed contra, in qualibet demonstratione sunt propositiones universales; sed demonstrationes fiunt ex sole et luna; ergo oportet dicere "omnis sol", "omnis luna"; sed "sol" non habet nisi unicum suppositum et similiter "luna"; ergo "omnis" non vult habere tria appellate. To the contrary: There are universal propositions in any demonstration; but demonstrations can be formed involving the sun and the moon; therefore we must say “every sun”, “every moon”; but “sun” has only one denotation and so also “moon”; therefore “every” does not require three things named.
Ad idem: "Omne privatum lumine a terrae obiectu deficit". Haec propositio est concessa cum habeatur ab auctoribus. Sed "Omne privatum lumine a terrae obiectu" non habet nisi unicum suppositum, scilicet, hanc lunam singularem. Ergo "omnis" non vult habere tria appellate. On this same point: “Every [object] deprived of light by the interposition of the earth is eclipsed”. This proposition is conceded since it is held by the authorities. But “Every [object] deprived of light by the interposition of the earth” has only one denotation, namely, the individual moon. Therefore “every” does not demand three things named.
Ad idem, hoc signum "omnis" significat quantum universaliter. Sed hoc quod dico, "quantum universaliter", est modus proprius universalis. Proprium autem diversificatur secundum diversitatem sui subiecti, ut si "homo" est diminutus, et "risibile" est diminutum; et si homo est mortuus, et risibile est mortuum. Sed universale aliquando salvatur in pluribus, ut "homo", "equus"; aliquando in uno tantum, ut "sol", "luna". Ergo "omnis" quandoque vult habere tria appellate et quandoque non; immo unum solum. Again, the sign “every” signifies quantity universally. But “quantity universally” is a proper universal mode. However, a property is diversified according to the diversity of its subject, so that if “man” is of less extension, “capable of laughter” is of less extension; and if a man is dead, what is capable of laughter is dead. But the universal is sometimes preserved in many things, such as “man” and “horse”; sometimes in one thing alone, as “sun” and “moon”. Hence “every” sometimes requires three things named and sometimes not; indeed, at times, only one.
Ad idem, duplex est forma, quia quaedam est forma materiae, ut anima est forma corporis, et iste forma est pars et non praedicatur de eo cuius est pars; alia est forma, quae est forma praedicabilis, et sic omnia superiora—ut genera et species et differentiae—dicuntur formae inferiorum, ut "homo", "equus", et sic de aliis, et individua huius formae praedicabilis sunt materia eius. Ergo, cum forma neutro praedictorum modorum excedit suam materiam nec exceditur ab ea, nullum universale excedit sua individua nec exce>duntur ab eo. On the same point, form can be taken in a twofold manner, because one form is the form of matter, as the soul is the form of the body, and this form is a part of but is not predicated of that of which it is a part; the other is predicable form, and thus all the higher [predicates]—as genera, species, and differentia—are said to be the forms of the particulars included under them, for example, “man”, “horse”, and so forth, and the individuals included under the predicable form are its matter. Therefore, since form, in neither of the aforementioned modes, exceeds its matter nor is exceeded by it, no universal exceeds the individuals included under it nor are the individuals exceeded by it.
Ergo, cum "omnis" dicat adaequationem universalium cum suis individuia, ut "omnis homo", ideo oportet quod "sol" habeat unicum suppositum, ut vere dicatur "omnis sol". Quod concedimus dicendo praedictas propositiones esse veras et quod "omnis" non semper exigit tria appellata. Sed quando adiungitur termino communi habenti plura supposita, tunc exigit plura appellata; quando vero adiungitur termino habenti solum unum suppositum, tunc exigit solum unum appellatum. Therefore, since “every” bespeaks adequation of the universal with their particulars, as “every man”, it follows that “sun” has only one denotation so that one can truly say “every sun”. We grant this in affirming that the aforementioned statements are true and that “every” does not always require three things named. Nay rather, when it is joined to a general term denoting many things, it requires many things named; but when it is joined to a term denoting one thing only, it requires only one thing named.
Ad illud quod primo obiiciebatur, quod omnis perfectio est in tribus, dicitur quod verum est; et haec tria sunt, scilicet, substantia rei, virtus eius, et operatio eius. Et haec tria tangit Aristoteles sub brevibus verbis, cum dicit: "Natura apta nata sic facit". Per hoc enim quod dicit, "natura", tangit substantiam rei; et per hoc quod dicit, "apta nata", tangit virtutem eius; et per hoc quod dicit, "sic facit", tangit operationem debitam ei. Similiter, hoc signum "omnis" habet substantiam signi universalis; et virtutem, quae est posse distribuere; et operationem eius, quando distribuit. Et in his tribus est perfectio eius. To the first objection, that all perfections occur in threes, we still say that the statement is true; and these three are the substance of the thing, its potency, and its operation. Aristotle briefly touches upon these three when he says: “Nature, being so constituted, acts this way.”’ When Aristotle says “nature”, he touches upon the substance of a thing; when he says “being so constituted”, he touches upon its potency; and when he says “acts this way”, he touches upon the operation proper to it In like manner, this sign “every” has the substance of a universal sign, the potency to distribute, and its operation or act when it distributes. Its perfection lies in these three things.
Ad secundum, dicendum est quod "homo" et "homines" differunt, quia "homo" dicit istam aperient secundum se, quae est de pluribus praedicabilis; sed "homines", in plurali numero, non dicit istam speciem secundum se sed multiplicatam actu secundum materiam individuorum numero diversam. Unde "omnis", in plurali, ratione multitudinis factae, facit distributionem per diversas materias et vult habere tria appellata. Sed "omnis", in singulari numero, ex quo recipit speciem secundum se et non materiam individuorum, exigit essentiam aptam natam praedicari de pluribus, sive actu participetur a pluribus sive ab uno. Et ideo exigit tria appellata aut unum solum secundum naturam universalis cui adiungitur. With regard to the second objection, it must be said that “man” and “men” differ because “man” asserts that species as such which is predicable of many; but “men”, in the plural, does not assert species as such but species multiplied in act according to the matter diversified in the number of individuals. Whence “every”, in the plural, by reason of the multitude represented, effects distribution by reason of the diversified matters and requires three things named. But “every”, in the singular, embraces the species as such but not the matter of the individuals; and it requires an essence naturally predicable of many, whether it actually belongs to one or to many. Hence “every” requires three things named, or only one, depending on the nature of the universal to which it is conjoined.
>Quidam tamen dicunt quod "omnis" vult habere tria appellata ad minus et dant talem rationem. Quotiescumque signum universale additur termino communi non habenti sufficientiam appellatorum, recurrit ad non-ens, ut cum dicicitur: "Omnis Phoenix est", quia ly "Phoenix" non habet nisi unicum suppositum, ideo recurrit ad non-existentes Phoenices. Et ideo, cum dicitur: "Omnis Phoenix est", sensus est: "Unus Phoenix, qui est, est" et "Duo Phoenices, qui non sunt, sunt". Et ideo, dicunt has duas propositiones esse falsas: "Quidam Phoenix non est" et "Omnis Phoenix est", et non esse contradictorias, quia in negativa supponitur Phoenix, qui est, et in affirmativa supponuntur duo Phoenices, qui non sunt: et sic non est idem subiectum in utraque. Hoc autem potest multipliciter improbari, quia haec inconvenientia sequuntur ex falso quod supponunt, quia supponunt quod "omnis" semper vult habere tria appellata, quod superius ostensum est esse falsum. However, some say that “every” requires at least three things named and they assign the following reason. Whenever a universal sign is added to a general term lacking sufficient things named, it refers to a non-being, as when one says: “Every Phoenix is”, the term “Phoenix” refers to non-existent Phoenices because it denotes only one thing. Consequently, when one says: “ Every Phoenix is”, the meaning is “The one Phoenix, which is, is” and “The two Phoenices, which are not, are”. Hence, they say these two propositions are false: “Some Phoenix is not” and “Every Phoenix is”, but they are not contradictories because the Phoenix, which is, is taken for granted in the negative proposition and the two Phoenices, which are not, are taken for granted in the affirmative proposition; from this point of view the propositions do not have the same subject. However, their argument can be disproved in many ways since the difficulty arises from their begging the question in assuming that “every” always requires three things named, an assumption previously shown false.
Propterea vult Aristoteles quod propositio in qua subiicitur universale, universaliter sumptum, alicui praedicato, contradicat illi propositioni negativae in qua subiicitur universale, non universaliter sumptum, eidem praedicato. Sed istae sunt tales: "Omnis Phoenix est", "Quidam Phoenix non est"; ergo sunt contradictoriae. Quod tamen ipsi negant. Ergo regula eorum est falsa. Besides, Aristotle thinks that a proposition which has a distributed universal as the subject of any predicate, contradicts that negative proposition in which the universal, undistributed, is subject of the same predicate[6]. But the aforementioned propositions are such: “Every Phoenix is”, “Some Phoenix is not”; therefore they are contradictories. But this is what these people deny. Therefore, their rule is false.
Item, ad idem alia regula talis est: terminus communis supponens vel apponens verbo praesentis temporis, simpliciter sumpto, non habenti vim ampliandi nec ex se nec ab alio, restringitur ad supponendum pro his quae sunt sub forma termini supponentis. Ergo, cum dicitur: "Omnis Phoenix est", ly "Phoenix" restringitur ad supponendum pro Phoenice tantum qui est, cum ipsius non sit nisi unicum suppositum. Ergo per illam regulam prius datam, si sig>num universale adveniat ei, non distribuit ipsum nisi pro unico supposito. Ergo regula eorum est falsa et supra falsum fundatur. Quod concedimus. On the same point, another rule is as follows: a general term which occurs as subject or predicate with a verb in the present tense which is taken simply and which does not have the power of amplification, either intrinsically or extrinsically, is restricted to the denotation of those things of the nature signified by the denoting general term, which are existing. Therefore, when one says: “Every Phoenix is”, the term “Phoenix” is restricted to the denotation of that Phoenix alone which is, since it denotes only one thing. Therefore, utilising the rule just given, if a universal sign is added to it, it only distributes it in relation to the one thing denoted [by the term]. Consequently, the rule of those other people is false and rests on a fallacy. This we grant.
Circa praedicta, quaeritur de hoc sophismate: "Omnis homo est et quodlibet differens ab illo est non-homo". Probatio: Haec est una copulativa cuius utraque pars est vera; ergo ipsa est vera. With reference to the foregoing, the sophism arises: “Every man is and whatever differs from him is not-man”. Proof: This is a copulative [proposition] each of whose parts is true; therefore the copulative is true.
Improbatio: "Omnis homo est et quodlibet differens ab eo est non-homo; Sortes est homo; ergo, quodlibet differens a Sorte est non-homo", quod est falsum, quia haec est una copulativa cuius altera pars est falsa; ergo, ipsa tota est falsa. Disproof: “Every man is and whatever differs from him is not-man; Sortes is a man; therefore, whatever differs from Sortes is not-man”, which is false, because this is a copulative proposition one of whose parts is false; consequently, the whole is false.
Solutio: Prima est simpliciter vera et improbatio peccat penes fallaciam consequentis, quia ly "differens ab omni homine" in minus est quam "differens a Sorte", quia" differens ab omni homine" supponit solum pro aliis rebus ab homine sed "differens a Sorte" supponit pro eisdem et etiam pro aliis hominibus a Sorte. Unde bene sequitur: "Differens ab omni homine; ergo differens a Sorte"; et est locus a parte subiectiva ad suum totum. Sed si huic propositioni: "Differens ab omni homine" apponatur signum, erit processus ab inf eriori ad superius cum distributione. Et sic incidit fallaca[7] consequentis in improbatione secundum unum processum, quia duplex est processus in improbatione, quia bene sequitur: "Omnis homo est; ergo, Sortes est", et est locus a toto in quantitate ad suam partem; sed non sequitur: "Hoc est differens ab omni homine; ergo differens a Sorte", sed est fallacia consequentis sicut hic: "Omnis homo est; ergo omne animal est". Solution: The initial statement is absolutely true and the disproof is guiHy of the fallacy of the consequent because the phrase “different from every man” is less in extent than “different from Sortes” because “different from every man” only denotes things other than man but “different from Sortes” denotes these and all men other than Sortes as well. Therefore the following is a valid inference: “Different from every man; therefore different from Sortes”; and this is a topical argument from the subjective part to its whole. But if a [universal] sign is added to the statement: “Different from every man”, there will be, simultaneously with distribution, an inference from the particular to the general. Thus the [disproof] is guilty of the fallacy of the consequent according to one process of reasoning, for there is a twofold process of reasoning in the disproof because the following is a valid inference: “Every man is; therefore, Sortes is”, and it is a topical argument from a quantitative whole to its part; but this is not a valid inference: “This is different from every man; therefore it is different from Sortes”, but a fallacy of the consequent just as “Every man is; therefore every animal is”.
Item, quaeritur de hoc sophismate: "Omnis homo et alius homo sunt". Probatio: "Sortes et alius homo sunt: Plato et alius homo sunt, et sic de aliis; ergo, omnis homo et alius homo sunt. Let us now examine the sophism: “Every man and another man are”. Proof: Sortes and another man are; Plato and another man are, and so on; therefore, every man and another man are.
>Improbatio: "Alius" est relativum diversitatis substantiae; ergo supponit pro diverso ab homine. Sed non est alius homo ab omni homine. Ergo, prima est falsa. Disproof: “Another” is a relative of diversity of substance; therefore it denotes a thing different from man. But there is not another man distinct from every man. Therefore, the initial statement is false.
Solutio: Prima est simpliciter falsa et probatio peccat secundum fallaciam figurae dictionis a pluribus determinatis suppositionibus ad unam determinatam, quia iste terminus "alius" habet determinatam suppositionem in praemissis et in conclusione. Solution: The initial statement is absolutely false and the proof is guilty of the fallacy of figure of speech in arguing from several determinate suppositions to one determinate supposition, because that term “other” has determinate supposition in the premisses and in the conclusion.
Item, probatio peccat secundum fallaciam accidentis, quia licet "Sortes et Plato et sic de aliis" inferant omnem homiminem secundum se, tamen sub hac copulatione, quae est "omnis et alius homo", non potest inferre omnem hominem, ut cum dicitur: "Omnis homo et alius homo sunt"; sicut cognosco Coriscum secundum se, non tamen sub hoc accidente quod est venire. Again, the proof is guilty of the fallacy of accident, because although “Sortes and Plato and so on” makes an inference to every man as such, nevertheless every man cannot be inferred from the conjunction “Every and another man”, as when one says: “Every man and another man are”; just as I know Coriscus, as such, nevertheless I do not know him under this accident of coming.
Unde talis datur regula: quotiescumque aliquid sequitur ad alteram, sive conversim sive non, si aliquid conveniat uni quod non conveniat alteri et per illud cui convenit inferatur de eo cui non convenit, semper est fallacia accidentis. Verbi gratia: "Homo est; ergo, substantia est". Et species convenit homini et non substantiae. Ideo, si per hominem inferatur species de substantia, est fallacia accidentis, ut "Homo est species; ergo substantia est species". Similiter hic: "Risibile est proprium, ergo homo est proprium". Horum autem quae consequuntur, quaedam consequuntur conversim, ut "homo" et "risibile"; alia vero non, ut "homo" et "substantia". Wherefore, the following rule is offered: whenever something follows another, convertibly or not, if somettiing belongs to one which does not belong to the other, and if through that to which it belongs, an inference is made concerning that to which it does not belong, there is always a fallacy of accident. For example: “Man is; therefore substance is”. But species belongs to man and not to substance. Therefore, if through man species is inferred of substance, there is a fallacy of accident, as “Man is a species; therefore substance is a species”. Likewise in the case of “Risible is a property; therefore man is a property”. However, of things which are logically related, some are related convertibly, as “man” and “risible”; but others are not, as “man” and “substance”.
Dicto de hoc sophismate, restat dicere de isto: "Omnis homo est omnis homo". Probatio: Sortes est Sortes; Plato est Plato et sic de aliis; ergo, omnis homo est omnis homo. Having dealt with this sophism, we now discuss another: “Every man is every man”. Proof: Sortes is Sortes; Plato is Plato and so on; therefore, every man is every man.
Et, ut vult Boethius, nulla propositio est verior quam illa in qua praedicatur idem de seipso. Sed sic est hic, quia > "omnis homo" praedicatur de "omni homine". Ergo, nulla est verior ista; et per consequens est vera. And, as Boethius thinks, no proposition is more true than the one in which the same thing is predicated of itself.* But the proposition in question is such, because “every man” is predicated of “every man”. Therefore, no proposition is more true than that; and consequently it is true.
Improbatio: Sua contradictoria est vera, scilicet, ista: "Quidam homo non est omnis homo". Ergo, ipsa est falsa. Disproof: The contradictory of this proposition is true, viz., “Some man is not every man”. Therefore, the proposition is false.
Item, ad idem: Omnis homo est omnis homo; sed Sortes est homo; ergo, Sortes est omnis homo. Syllogismus est in Darii. Conclusio est falsa; ergo, aliqua praemissarum. Non minor; ergo maior. Sed maior est sophisma; ergo, soph ism a est falsum. On the same point: Every man is every man; but Sortes is man; therefore, Sortes is every man. This is a syllogism of the type Darii. The conclusion is false; therefore, one of the premisses. Not the minor; therefore the major. But the major is the sophism; therefore, this sophism is false.
Solutio: Prima est simpliciter falsa et probatio peccat secundum consequens ab insufficienti enumeratione singularium, quia cum illis, quas assumit, debet sumere has a parte subiecti: "Sortes est omnis homo; Plato est omnis homo et sic de aliis", et etiam istas debet sumere a parte praedirati: "Omnis homo est Sortes; omnis homo est Plato et sic de aliis"; quas dimittit. Et sic peccat secundum consequens ab insufficient enumeratione singularium. Ad aliud, dicitur quod ibi idem non praedicatur de seipso sed praedicatur "omnis homo" de "omni homine" sumpto pro-qualibet sui parte. Solution: The initial statement is absolutely false and the proof is guilty of the fallacy of the consequent due to an insufficient enumeration of the particulars, because along with those which it includes, it should include in the subject : “Sortes is every man; Plato is every man and so on”, and it certainly should include in the predicate: “Even-man is Sortes; every man is Plato and so on”; which things it fails to do. Thus it is guilty of the fallacy of the consequent from an insufficient enumeration of the particulars. With regard to the other point, it is said that in this case the same thing is not predicated of itself but “every man” is predicated of “every man” taken in extension.
Sequitur de hoc signo "nullus", quod significat quantum universaliter negative. Unde significat idem sicut hoc signum "omnis" cum negatione postposita; et ideo "omnis non" et "nullus" aequipollent. We now treat of the sign “no” (nullus) which signifies a universally negative quantity. Hence it signifies the same thing as the sign “every” with the negative placed after it; therefore “every not” and “no” (or “none”) are equipollent.
De hoc signo "nullus" talis datur regula: quotiescumque hoc signum "nullus" immediate adiungitur termino communi, confundit ipsum mobiliter et distributive, et similiter terminum communem sibi adiunctum mediate, ut "Nullus homo est asinus". Unde potest fieri descensus sub subiecto sic: "Ergo Sortes non est asinus, nec Plato et sic de aliis"; et etiam sub pradicato. We submit the following rule concerning “none”: whenever the sign “no” is immediately added to a general term, it distributes the term movably and distributively, and it does the same for the general term which is mediately added to it, as “No man is an ass”. Hence an inference can be made to the particulars included under the subject in the following way: “Therefore, Sortes is not an ass, nor Plato and so on”; and also under the predicate.
Circa praedicta, quaeritur de hoc sophismate: "Nullus homo est omnis homo". Probatur sic: Sortes non est omnis homo; Plato non est omnis homo et sic de aliis; ergo, > prima est vera. Vel sic: Sua contradictoria est falsa, scilicet, ista: "Quidam homo est omnis homo"; ergo, ipsa est vera. In this connection, we have the sophism: “No man is every man”. It is proved thus: Sortes is not every man: Plato is not every man and so on; therefore, the first, is true. Or in the following fashion: Its contradictory is false, viz., “Some man is every man”; therefore, the sophism is true.
Contra: Ibi praedicatur oppositum de opposite; ergo, locutio est falsa. To the contrary: In the sophism, a thing is predicated of its opposite; therefore, the statement is false.
Solutio: Prima est vera, et ad improbationem respondetur per interemptionem, quia ibi non praedicatur oppositum de opposite, sed removetur "omnis homo" ab "omni homine" sumpto pro quolibet suo supposito; et hoc est verum. Solution: The initial statement is true. As to the disproof, it is overruled because in the proposition, a thing is not predicated of its opposite, but rather “every man” is denied of “every man” taken as distributed; and this is true.
Sequitur de hoc signo "nihil" quod significat idem quod "nullus" sed includit in se terminum recipientem suam ditributionem, quia "nihil" est signum universale cum negatione et "res" est terminus recipiens eius distributionem. We now discuss the term “nothing” which signifies the same thing as “no” but which includes in itself the term it distributes, for “nothing” is a universal sign with a negation and “thing” is the term it distributes.
Circa praedicta, quaeritur de hoc sophismate: "Nihil videns est aliquid videns". Probatur sic: Non hanc rem videns est aliquid videns, quia non videns Sortem est videns Platonem; non illam rem videns est aliquid videns et sic de aliis; ergo, nihil videns est aliquid videns. Ergo, prima est vera. From what has been said, the problem of the sophism arises: “Seeing nothing is seeing something”. It is proved thus: Not seeing this thing is seeing something, because not seeing Sortes is seeing Plato: not seeing that thing is seeing something and so on; therefore, seeing nothing is seeing something. Therefore, the sophism is true.
Contra: Ibi praedicatur oppositum de opposite; ergo locutio est falsa. To the contrary: In this case a thing is predicated of its opposite; therefore the statement is false.
Quidam distinguunt hanc: "Nihil videns est aliquid videns eo quod haec dictio "nihil" potest esse accusativi casus et est sensus: "Nullam rem videns est aliquid videns", vel potest esse nominativi casus et est sensus: "Nulla res videns est aliquid videns"; et secundum hoc ponunt amphibologiam ex porte casus. Sed hoc non solvit, quia in utroque sensu est falsa. Some observe that in the proposition: Nihil videns est aliquid videns, the word “nothing” (nihil) can be in the accusative case and the meaning is: “Seeing nothing is seeing something”, or it can be in the nominative case and the meaning is: “Nothing seeing is something seeing”; and in this manner they posit amphibology by reason of case. But this does not solve the problem, for in each sense the sophism is false.
Sed alii iterum distinguunt hanc propositionem: "Nihil videns est aliquid videns" eo quod negatio inclusa in hoc termino "nihil" potest negare participium primo positum et est sensus: "Nullam rem videns est aliquid videns"—«t sic est divisa; vel potest negare hoc verbum "esr et tunc est sensus: "Quamlibet rem videns non est aliquid videns"— > et sic est composita. Sed hoc non solvit, quia in utroque sensu est falsa, cum opposita ponantur circa idem. Again, others observe in the proposition: “Seeing nothing is seeing something”, that the negation included in the term “nothing” can deny the first participle and the meaning is: “Seeing no thing is seeing something”—and in this way the proposition is taken in the divided sense; or it can deny the verb “is” and the meaning is: “Seeing anything whatever is not seeing something”—and in this way the proposition is taken in the composite sense. But this does not solve the problem because the proposition is false in each sense in that opposites are predicated of the same thing.
Solutio: Dicendum est quod prima simpliciter est falsa, et probatio peccat contra fallaciam figurae dictionis a pluribus determinatis ad unam determinatam respectu huius termini "videns", quia in praemisis habet suppositionem determinatam et in conclusione similiter. Vel peccat secundum fallaciam accidentis, quia quamvis videre communicetur omnibus, secundum se, non tamen secundum quod uniuntur in hoc toto "nihil videns"; unde totum accidit parti et esse "videns aliquid" assignatur inesse utrique. Solution: One must say that the sophism is absolutely false and the proof is guilty of the fallacy of figure of speech in reasoning from a determinate many to a determinate one with regard to this term “seeing”, because in the premisses, and likewise in the conclusion, it has determinate supposition. Or it is guilty of the fallacy of accident, because although “seeing” is predicable of all, as among themselves, nevertheless it is not predicable of all insofar as they are united in the whole “seeing nothing”; as a result, the whole belongs to the part and the being of “seeing something” is assigned to be in each.
Sciendum est quod eius praemissae sunt duplices, quia negatio potest determinare verbum vel participium, ut dictum est prius. Unde antiqui posuerunt praemissas esse duplices propter talem regulam quam dabant: quotiescumque negatio et distributio includuntur in uno termino, ad quodcunque refertur unum et reliquam. Unde cum distributio, posita in obliquo, non possit in praedicta oratione attingere verbum, ita neque negatio. Item, idem est iudicium de istis sophismatibus: "Nullum caput habens est aliquod caput habens", "A nullo homine differens est ab aliquo homine differens", etc. It should be understood that the premisses of the proof are ambiguous because the negation can determine the verb or the participle, as was stated above. On this account, the ancients reckoned the premisses ambiguous in the light of the following rule which they offered: whenever negation and distribution are included in one term, to whatever one is referred, the other is also. From this it follows that since distribution, posited in the accusative case, cannot affect the verb in the previous statement, neither can the negation. The same opinion holds concerning the following sophisms: “Having no head is having some head”, “Different from no man is different from some man”, etc.
Sequitur de signis distributivis duorum, et talia sunt "neuter" et "uterque". Et different a praedictis, quia > "omnis", "nullus", et similia distribuunt pro omnibus individuis termini communis, sed "uterque" et "neuter" distribuunt solum pro duobus per demonstrationem, ut "uterque istorum", "neuter istorum". We now discuss signs distributive of two things, as “neither” and “both” [taken separately]”. They differ from the terms discussed previously, because “every”, “no”, and the like, distribute all individuals included under the general term, while “both” and “neither” distribute only two such as may be pointed to, as “both of them”, “neither of them”.
Circa praedicta, quaeritur de hoc sophismate: "Ab utroque istorum enunciatum est verum". Posito quod Sortes dicat "Deum esse"; Plato vero dicat "hominem esse animal"; et ambo dicant simul "hominem esse asinum"; et illi duo demonstrantur per hoc pronomen "istorum". Probatio: A Sorte enunciatum est verum; a Platone enunciatum est verum; ergo, ab utroque istorum enunciatum est verum. With reference to this, we have the sophism: “What is stated by both of them is true”. Posit that Se*tes says “God is”; Plato says “Man is an animal”; and both simultaneously say “Bfan is an ass”; and suppose that those two are indicated by the pronoun “of them”. Proof: What is stated by Sortes is true; what is stated by Plato is true; therefore, what is stated by both of them is true.
Contra: Ab utroque istorum enunciatum est verum; sed nihil enunciatum est ab utroque istorum nisi "hominem esse asinum"; ergo "hominem esse asinum" est verum. Quod falsum est. To the contrary: What is stated by both of them is true; but nothing is stated by both of them except “Man is an ass”; therefore “Man is an ass” is true. But this is false.
Solutio: Prima est vera et probatio peccat secundum fallaciam accidentia. Sicut habetur ab Aristotele, haec propositio ponitur esse vera: "Omnium contrariorum est eadem disciplina". Et tamen nulla particularis disciplina est omnium contrariorum, sed disciplina communiter sumpta. Unde hic est fallacia accidentis: Omnium contrariorum est eadem disciplina; sed nulla est disciplina nisi haec vel illa et sic de aliis; ergo omnium contrariorum haec eadem est disciplina vel iata. Quod falsum est. Similiter hic: Homo est species; sed nullus est homo nisi Sortes vel Plato et sic de aliis; ergo, Sortes est species vel Plato et sic de aliis. Et sic est fallacia accidentis in proposito, quia haec dictio "enunciatum" et haec dictio "verum" tenetur pro ipso in communi, et sic "ab utroque ifltorum enunciatum est verum". Unde "enunciatum" non tenetur pro particulari enunciato ab utroque. Unde particulare "enunciatum ab utroque" accidit "enunciato" in communi, sicut particulare inferius accidit suo superiori; et "verum" > assignatur utrique inesse. Et appellatur superius hic omne illud quod est maius, sive sit essentiale sive accidentale. Solution: The initial statement is true but the proof is guilty of the fallacy of accident As it is held by Aristotle, the following proposition is posited as true: “There is the same science of all opposites”. Nevertheless there is no particular science of all opposites, for in this case “science” is taken distributively. Consequently, the fallacy of accident occurs in the following: There is the same science of all opposites; but there is no science apart from this science cr that science and so on; therefore, this or that science is the same for all opposites. But this is false. In like manner: Man is a species; but no one is man apart from Sortes or Plato and so on; therefore, Sortes is a species or Plato and so on. Hence there is the fallacy of accident in the sophism, because the expression “what is stated” and the word “true” are each taken for what they signify genetically, and in this way “What is stated by both of them is true”. It follows from this that “what is stated” does not stand for a particular statement by both. Consequently, “what is stated by both of them” in the particular sense is accidentally related to “what is stated” in the generic sense, just as a particular included under a general term is accidentally related to that genera) term; and “true” is said to belong to both. Here, general refers to all that is greater, whether essential or accidental.
Quidam tamen dicunt quod prima est simpliciter falsa. Et dicunt quod "enunciatum" accipitur pro particulari enunciato ab utroque et similiter "verum" pro particulari vero; et probatio peccat secundum fallaciam figurae dictionis a pluribus determinatis ad unam determinatam huius termini "enunciatum" et huius termini "verum". Sed prima solutio melior est et subtilior. However, some say that the sophism is absolutely false. They say that “what is stated” is taken for a particular statement by both and similarly “true” for a particular truth; and that the proof is guilty of the fallacy.of figure of speech in arguing from a determined many to a determined one with respect to both the term “what is stated” and the term “true”. But the first solution is the better and the more subtle.
Sequitur de hoc signo "neuter" quod significat idem quod "uterque" cum negatione sibi proposita. Unde sicut "nullus" de se habet distributionem et negationem, similiter et "neuter". Sed "neuter" est distributivum duorum tantum. We now treat of the sign “neither” which means the same as “both” with a negation placed before it Just as “no” intrinsically distributes and negates, so also does “neither”. But “neither” is only distributive of two.
Item, quaeritur de hoc sophismate: "Neutrum oculum habendo, tu potes videre". Probatio: Dextrum oculum non habendo, tu potest videre; sinistrum oculum non habendo, tu potes videre; ergo, prima est vera. Now the questions of this sophism arises: “Having neither eye, you can see”. Proof: Not having the right eye, you can see; not having the left eye, you can see; therefore, the sophism is true.
Contra: Neutrum oculum habendo, tu potes videre; ergo, neutrum oculum habens vel dum neutrum oculum habes, tu potes videre. Quod falsum est. Consequentia patet, quia gerundia terminata in do habent resolvi per "dum", per "si", vel per "quia". Sed utroque modo est falsa. Ergo prima est falsa. To the contrary: Having neither eye, you can see; therefore, having neither eye or while you have neither eye, you can see. But this is false. The consequence is obvious, for gerunds ending in do have to be resolved by “while”, “if, or “because”. But in each case it is false. Therefore the sophism is false.
Solutio: Prima est falsa et probatio peccat secundum fallaciam accidentia, quia posse videre convenit partibus secundum se, scilicet, prout sunt divisae, sed non convenit eis prout sunt unitae in suo toto. Unde hoc patet per primam regulam, cum ad partes sequatur totum, ut potestas videndi convenit partibus et non toti. Ideo, si partes inferantur de toto, ibi est fallacia accidentia. Solution: The sophism is false and the proof is guilty of the fallacy of accident because the ability to see is proper to the parts as such, that is to say, separately, but it is not proper to the parts taken together as a whole. Hence it is evident from a former rule that since the whole follows after the parts, the power of seeing is proper to the parts and not to the whole. Therefore, there is a fallacy of accident if the parts are inferred from the whole.
88}teles, in primo Peri Hermeneias, dicit quod illae contradicunt: "Homo est iustus", "Non homo est iustus". Ergo altera est universalis, cum subiiciatur terminus communis; sed non nisi haec: "Non homo est iustus"; ergo ille terminus "homo" distribuitur. Sed non est ibi aliquid a quo distribuatur nisi negatio. Ergo, distribuitur a negatione. Having treated signs distributive of subjective parts, the question next arises as to whether negation has the power ol distributing or of rendering indeterminate. It seems that it does, because Aristotle, in the first book of the De interpretatione[8], says that these are contradictory: “Man is just”, “Not man is just”. Hence, one of them is universal, since it has a general term as subject; but it can only be this one: “Not man is just”; therefore the term “man” is distributed. But there is nothing by which it is distributed except the negation. Therefore, it is distributed by the negation.
Contra: Si negatio habeat vim confundendi, ergo sicut ista est incongrua: "Omnis Sortes currit", similiter haec: "Non Sortes currit". Quod est falsum, quia quamvis signum distributivum non possit addi termino singulari, tamen negatio bene potest addi. To the contrary: If negation has the capacity to render indeterminate, then just as “Every Sortes runs” is incongruous, so “Not Sortes runs” is incongruous. But this is false, because although a distributive sign cannot be added to a singular term, nevertheless negation can.
Item, ubicunque est distributio, ibi est terminus communis sumptus universal iter. Ergo oportet quod ibi sit dictio significans quantum universaliter. Sed signum universale significat quantum universaliter tantummodo, negatio vero non. Ergo, non habet vim distribuendi. Quod concedimus, dicentes quod negatio non confundit sed negat hoc quod post se invenit. Unde cum adiungitur termino communi, negat ipsum. Sed ad negationem superioris, sequitur negatio cuiuslibet inferioris eo quod, destructo superiori, destruitur quodlibet eius inferius. Ergo negatio non confundit sed negat quod post se invenit, sive sit universale sive particulare. Secondly, wherever distribution takes place, a general term is taken universally. Wherefore, it is necessary that there be a word signifying quantity universally. But only a universal sign signifies quantity universally, for negation does not. Therefore, negation does not have the power to distribute. This we grant, maintaining that negation does not render indeterminate but denies that which follows it From which it follows that when negation is added to a general term, it denies the general term. But in the case of the negation of the more general, the negation of any inferior included under it follows from the fact that when the more general is nullified, any particular whatever included under it is nullified. Consequently, negation does not render indeterminate but denies what follows after it, be it universal or particular.
Solutio autem patet ad hoc quod obiicitur, quia quod haec est universalis: "Non homo est iustus", hoc non est propter naturam distributionis existentis in negatione sed hoc est quia negatur homo in communi; quo remote, removetur quodlibet eius inferius. The solution to the objection is obvious, because the fact that the proposition: “Not man is just” is a universal, is not due to the nature of distribution existing in the negation but rather because man in general is denied; and this being denied, any of its particulars whatsoever is denied.
Item, solet poni quaedam "distributio aptitudinis", ut "Omnis homo timet in mari", id est, aptus natus est timere in mari. Item, solet poni "distributio accomoda", ut Coelum tegit omnia praeter seipsum" et "Deus creavit om>nia alia a se". Sed ista duo genera distributions non sunt ita propria ut alia. Again, it is customary to posit a certain “distribution of aptitude”, as “Every man fears the sea”, that is, man is born apt to fear the sea. Or again, it is customary to posit “befitting distribution”, as “Heaven touches all things apart from itself and “God created all things apart from Himself. But these two kinds of distribution are not as proper as the other.
Sequitur de hoc signo "totus", quod est distributivum partium integralium, ut hic: "Totus Sortes est albus". Est enim sensus: "Sortes, secundum quamlibet sui partem, est albus". Ad quam sequitur: "Quaelibet pars Sortis est alba". Probatio: In hac, "Totus Sortes est albus", Sortes subiicitur albedini secundum se, et partes eius non secundum se sed prout sunt in suo toto sive sub forma totius. Ergo non subiiciuntur albedini nisi per totum. Et sic per prius sequitur haec: "Sortes, secundum quamlibet partem sui, est albus"; et postea illa: "Qualibet pars Sortis est alba". We now discuss the sign “whole” which is distributive of integral parte, as in the proposition: “Sortes as a whole is white”. The sense is: “Sortes according to any one whatsoever of his parts, is white”. From this it folloro: “Any part whatever of Sortes is white”. Proof: In the proposition, “Sortes as a whole is white”, Sortes as such is the subject of whiteness, and his parts are not white by reason of themselves but according as they are in the whole of Sortes or under the form of the whole. Therefore they are not the subject of whiteness except through the whole. Hence, this proposition follows first in order, “Sortes, according to any one whatsoever of his parts, is white”; and then there follows this proposition: “Any part whatever of Sortes is white”.
Item, in hac: "Totus Sortes est albus", totus subiicitur albedini in rectitudine; partes autem in obliquitate, quia in eo quod est totum partes intelliguntur in obliquis et in eo quod est pars totum sumitur oblique. Quod patet per divisionem eius quod est totum, ut domus est ex pariete, tecto, et fundamento et Sortes est ex partibus. Ergo illud quod est totum, dat intelligere partes obliquas. Ergo, ad hanc: "Totus Sortes est albus", immediate sequitur haec: "Sortes, secundum quamlibet sui partem, est albus"; et mediate sequitur ista: "Quaelibet pars Sortis est alba". Further, in the proposition: “Sortes as a whole is white”, the whole is the subject of whiteness directly; but the parts indirectly, because the parts are understood indirectly in that which is the whole and the whole is understood indirectly in that which is the part This is evident from a division of the whole, as a house is constructed of wall, roof, and foundation and Sortes is constituted by his parts. Therefore the whole causes us to understand the parts indirectly. Consequently, from the proposition: “Sortes as a whole is white”, there follows immediately the proposition: “Sortes, according to any one whatsoever of his parts, is white”; and mediately the proposition: “Any part whatever of Sortes is white”.
Item, ad idem, illud quod est pars non habet esse nisi ab eo quod est totum, quia non habet perfectionem nisi ab eo. Ergo non subiicitur alicui nisi per totum. Ergo totum prius subiicitur. Ergo, ad hanc: Totus Sortes est albus", immediate sequitur: "Sortes, secundum quamlibet sui partem, est albus"; et mediate: "Quaelibet pars Sortis est alba". Again, on the same point, that which is the part, has being only from that which is the whole because it derives its perfection only from the whole. Therefore it is the subject of something only through the whole. Consequently, the whole is the primary subject. Therefore, from the proposition: “Sortes as a whole is white” immediately follows: “Sortes, according to any one whatsoever of his parts, is white”; and mediately “Any part whatever of Sortes is white”.
> Circa praedicta, quaeritur de hoc sophismate: "Totus Sortes est minor Sorte". Probatio: Quaelibet pars Sortis est minor Sorte, et Sortes, secundum quamlibet sui partem, est minor Sorte; ergo, totus Sortes est minor Sorte. In reference to what has been said, we have the sophism : “Sortes as a whole is leas than Sortes”. Proof: Any part whatever of Sortes is less than Sortes, and Sortes, according to any one whatsoever of his parts, is less than Sortes; therefore, Sortes as a whole is less than Sortes.
Contra: Totus Sortes est minor Sorte; ergo, Sortes est minor Sorte. It is argued to the contrary: Sortes as a whole is less than Sortes; therefore, Sortes is less than Sortes.
Solutio: Prima est vera, scilicet, haec: "Totus Sortes est minor Sorte", et probatio peccat secundum fallaciam accidentis, quia in ista: "Totus Sortes est minor Sorte", praedicatum attribuitur partibus quibus vere convenit; Sorti autem non convenit; et ideo haec est simpliciter falsa: "Sortes est minor Sorte". Et ideo, si partes inferant esse minorem Sorte de toto sive de Sorte, erit fallacia accidentia per primam regulam supradictam. Unde "Totus Sortes" est res subiecta, et "Sortes" accidit ei, et "esse minor Sorte" aasignatur utrique inesse. Solution: The initial statement is true, viz., “Sortes as a whole is less than Sortes”, but the proof is guilty of the fallacy of accident because in the proposition: “Sortes as a whole is less than Sortes”, the predicate is attributed to the parts to which it truly belongs; but it does not belong to Sortes; therefore, the proposition: “Sortes is less than Sortes”, is absolutely false. On that account, if one infers that the parts are less than Sortes as a whole or as Sortes, there will be ? fallacy of accident by virtue of the previously mentioned rule. Hence Sortes as a whole is the subject thing, Sortes belongs accidentally to it, and “to be less than Sortes” is ascribed to both.
Etiam improbatio peccat secundum quid ad simpliciter, quia ista: "Totus Sortes est minor Sorte", non ponit Sortem secundum se sed secundum suas partes. Et ideo ponit Sortem secundum quid esse minorem Sorte. Ita cum simpliciter inferatur: "Ergo, Sortes est minor Sorte", peccat secundum quid ad simpliciter, sicut: "Sortes secundum pedem est minor Sorte; ergo. Sortes est minor Sorte". In like manner, the disproof is guilty of the fallacy of confusion of absolute and qualified statement (secundum quid ad simpliciter), because the proposition: “Sortes as a whole is less than Sortes”, does not posit Sortes as such but according to his parts. Therefore, it asserts that Sortes in a qualified sense is less than Sortes without qualification. So when one makes the unqualified inference: Therefore, Sortes is less than Sortes”, there is the fallacy of confusion of absolute and qualified statement, as in the case: “Sortes qua foot is less than Sortes; therefore, Sortes is less than Sortes”.
Item, in quibusdam sequitur: "Totus Sortes; ergo Sortes", ut: "Totus Sortes est albus; ergo, Sortes est albus"; et in quibusdam non. Quaeritur in quibus est et in quibus non. Dicendum est quod sunt quaedam accidentia quae indifferenter conveniunt parti et toti, ut album, nigrum, calidum, frigidum augeri, minui et in talibus bene sequitur: "Totus Sortes: ergo, Sortes"; alia sunt accidentia quae > conveniunt partibus et non toti et e converso toti et non parti et non partibus, ut totalitas minoritas, parvitas et in talibus non sequitur: "Totus Sortes; ergo Sortes". Furthermore, in some cases it follows: “Sortes as a whole; therefore Sortes”, as “Sortes as a whole is white; therefore Sortes is white”; in other cases it does not follow. We may ask in which cases it follows and in which cases it does not follow. It must be said that there are some accident* which belong to the part and to the whole indifferently, as white, black, hot, cold, growth and shrinkage, and in such cases, “Sortes as a whole; therefore Sortes” logically follows; there are other accidents which belong to the part and not to the whole and conversely to the whole and not to a part or parts, as totality, minority, smallness and, in such cases, “Sortes as a whole; therefore Sortes” does not follow.
Sequitur de signis distributivis accidentium inter quae primo dicendum est de signis distributivis qualitatis. Dicitur autem signum distributivum qualitatis quod distribuit res se habentes per modum qualitatis, ut "qualelibet" cuius particulare est "aliqualibet". We now discuss signs distributive of accidents among which we first treat those distributive of quality. A sign distributive of quality is said to be one which distributes things related through a qualitative mode, as “such a sort as you please” whose particular is “some one sort as you please”.
Sed tunc obiicitur quod si accidens multiplicetur, multiplicato subiecto, ergo cum signa distributiva substantiae distribuant sive multiplicent subiectum, oportet quod multiplicent sive distribuant ipsum accidens. Ergo, signa distributiva accidentium superfluunt. But it is objected that if an accident is multiplied when the subject is multiplied, it necessarily follows that since signs distributive of substance distribute or multiply the subject, they necessarily multiply or distribute the accident itself. Consequently, signs distributive of accidents are superfluous.
Ad hoc dicendum est quod duplex est multiplicatio accidentis, quia quaedam est multiplicatio accidentis secundum numerum et haec fit per signum distributivum substantiae, ut "Omnis homo albus currit"; alia est multiplicatio secundum speciem et haec fit per signa distributiva accidentis, ut "Qualelibet currit", id est, "Res, habens qualemcumque qualitatem, currit". To this it must be said that the multiplication of accidents is twofold, because one is the multiplication of accident according to number and is effected through a sign distributive of substance, as “Every white man runs”; the other is mulplication according to species and is effected through a sign distributive of accident, as “Such a sort as you please runs”, which is equivalent to the proposition: “A thing, having any quality whatever, runs”.
Circa praedicta, quaeritur de hoc sophismate: "Quodlibet qualelibet, de quolibet tali scit ipsum esse tale quale ipsum est". Posito quod Sortes sciat grammaticam, logicam et rhetoricam, et Plato et Cicero similiter, et sciant se habere eas; et sint alii tres homines quorum unus sciat logicam, alter grammaticam, et alius rhetoricam, et isti nesciant se habere eas, et de aliis nihil sciant, et alii sciant de se et de iatis; et non sunt plures homines neque plures qualitates. Probatio: Hoc "qualelibet", de quolibet tali scit ipsum esse tale quale ipsum est. Et sic de secundo et tertio; et non > sunt plura "qualelibet". Ergo, "quodlibet qualelibet, de quolibet tali scit ipsum esse tale quale ipsum est". In connection with the foregoing, this sophism is discussed : “Everything of whichever kind you please, knows, concerning that kind, that it is what it is”. Let it be supposed that Sortes knows grammar, logic and rhetoric and Plato and Cicero likewise, and that they know themselves to possess these; and suppose that there are three other men of whom oneknows logic, another grammar, and the third rhetoric and that these do not know themselves to possess these sciences, and that they know nothing of the other men, whereas the others know about themselves and also of these three; and suppose that there exist no other men and no other qualities. Proof: This “whichever kind you please” knows, concerning that kind, that it is what it is. Similarly with the second and the third; and there are not any more “whichever kind you please”. Therefore, “every thing of whichever kind you please, knows, concerning that kind, that it is what it is”.
Contra: Quodlibet qualelibet, et cetera; ergo, quodlibet grammaticum, de quolibet tali scit ipsum esse tale quale ipsum est. To the contrary: Everything of whichever kind you please, [knows, concerning that kind, that it is what it is]; therefore, every grammatical thing knows, concerning that kind of thing, that it is what it is[9].
Solutio prima est vera, et improbatio peccat secundum fallaciam consequentis ab inferiori ad superius cum distributione superioris, quia "qualelibet" supponit tantum pro tribus, scilicet, pro tribus primis; sed "grammaticus" supponit pro eisdem et etiam pro aliquo qui habet grammaticam tantum, et ita "grammaticum" est in plus quam "qualelibet". Unde, si apponatur signum universale distributivum sic: "Quodlibet qualelibet", et cetera, ergo "quodlibet grammaticum", fit consequens, ut hic: "Omnis homo; ergo omne animal". Et similiter in ultimo, ut "De quolibet qualelibet; ergo de quolibet grammatico", cum dicit "de quolibet tali". The first solution is true, and the disproof is guilty of the fallacy of the consequent in reasoning from the inferior to the superior with the distribution of the superior. For “of whichever kind you please” stands only for three [men], namely, for the first three; but “grammarian” stands for these and also for someone who possesses grammar only, and thus “grammatical thing” stands for more things than does “of whichever kind you please”. Hence, if the universal distributive sign is placed before it, as in saying “Everything of whichever kind you please”, et cetera, therefore “everything grammatical”, there arises a consequence like this one: “Every man; therefore every animal”. And the same occurs in the later expression, when it is said “concerning that kind”, as if [we argued] “Concerning everything of whichever kind; therefore concerning everything grammatical”.
Sequitur de signis distributivis quantitatis et sunt illa quae distribuunt res se habentes per modum quantitatis, ut "quotieacumque", "quantuscumque". We turn our attention to signs distributive of quantity and they are signs which distribute things related through a mode of quantity, as, for instance, “as often as”, “as much as”.
Et secundum hoc quaeritur de hoc sophismate: "Quotiescumque fuisti Parisius, totiens fuisti homo". Probatio: Una vice fuisti Parisius et illa vice fuisti homo; alia vice fuisti Parisius et illa vice fuisti homo, et sic de aliis; ergo, quotieacumque fuisti Parisius, totiens fuisti homo. In this relation we have the sophism: “As often as you were at Paris, so often you have been a man”. Proof: At one time you were at Paris and at that time you were a man; at another time you were at Paris and at that time you were a man, and so on; therefore, as often as yon were at Paris, so often you were a man.
>Improbatio: Quotienscumque fuisti Parisius, totiens fuisti homo; sed bis fuisti Parisius; ergo, bis fuisti homo. Quod falsum est, quia haec dictio "bis" importat interruptionem actus cui adiungitur sed actus essendi hominem non fuit interruptus in te. Disproof: As often as you have been at Paris, so often you have been a man; but twice you have been at Paris; therefore, twice you have been a man. This is false, because the word “twice” introduces the interruption of the act to which it is joined but the act of being man was not interrupted in you.
Solutio: Prima est falsa. Ad probationem autem respondendum est per interemptionem, quia secunda pars copulativae est falsa, scilicet, "illa vice fuisti homo", quia adhuc nulla vice fuisti homo, eo quod nondum vita fuit terminata ut iterum inciperes vivere et postea terminaretur, quod tamen requiritur ad hoc, quod bis fuisses homo; sicut bis incipitur cursus et bis terminatur ad hoc, quod aliquis bis currat. Et nota quod "bis" non importat interruptionem temporis sed terminum actus illius cui adiungitur; ad terminum autem sequitur interruptio. Si autem formaretur sic paralogismus: "Quandocumque fuisti Parisius, fuisti homo; sed bis fuisti Parisius; ergo, bis fuisti homo", prima est vera et improbatio peccat secundum fallaciam figurae dictionis ex mutatione praedicamenti, quia "quandoque" est in praedicamento quando et "bis" in praedicamento quantitatis, quia est de genere quantitatis discretae. Solution: The initial statement is false. The proof is to be answered by destroying it, because the second part of the copulative is false, viz., “at that time you were a man”, for as yet you have not been a man even once, because of the fact that life has not yet been terminated in such manner that you might once again begin to live and afterwards have your life terminated, which is required in order that you be a man twice; the same as a race must be begun and terminated twice in order that anyone run twice. Note that “twice” does not involve interruption of time but only the termination of that act to which it is joined; but interruption follows a termination. If, however, the paralogism were formed in the following fashion: “Whenever you have been at Paris, you have been a man; but twice you have been at Paris; therefore, twice you have been a man”, the initial statement would be true and the disproof would be guilty of the fallacy of figure of speech due to a change in category, because “whenever” is in the category of time and “twice” is in the category of quantity, for it is a member of the genus of discrete quantity.
Sequitur de "infinito", quod quinque modis dicitur. Primo modo dicitur "infinitum" quod non potest pertransiri, ut vox dicitur invisibilis eo quod non est apta nata videri. Alio modo, dicitur "infinitum" quod habet transitum imperfectum eo quod nondum est terminatum, tamen aptum natum est terminari, ut dum aliquis transit spatium et non dum pervenit ad suum finem. Tertio modo, dicitur "infinitum" secundum appositionem, ut numerus augmentabilis est infinitum appositione unitatis vel alterius numeri. Quarto modo, dicitur "infinitum" secundum divisionem, ut conti> nuum. Omne autem continuum divisibile est in infinitum. Unde sic definitur ab Aristotele in Quarto Physicorum: "Continuum est divisibile in semper divisibilia". Quinto modo, dicitur "infinitum" utroque modo, scilicet, per appositionem et divisionem, ut tempus; cum enim tempus sit continuum, est divisibile in infinitum in divisione et cum post unum tempus veniat aliud tempus, sic per appositionem unius temporis ad aliud est infinitum. Et quoad has tres ultimas significationes, definitur sic "infinitum": "Infinitum est cuius quantitatem accipientibus semper est aliquid extra sumere"; ut si post ultimam partem lineae accipiatur alia, et post alteram tertia, et numquam possit attingi terminus eius, ideo linea dicitur infinita. We now discuss the sign “infinite which is spoken of in five ways. In the first way, “infinite” is said to be that which is incapable of being gone through, as the voice is said to be invisible because of the fact that it is not its nature to be seen. In a second way, “infinite” is said to be that which has incomplete transition by reason of the fact that it has not yet been terminated, although it is its nature to be terminated, as while someone is crossing a space and has not yet arrived at its end. In a third way, we speak of the “infinite” in the sense of addition, as augmentable number is infinite by the addition of unity or another number. In a fourth way, “infinite” is spoken of in relation to division, as in the case of a continuum. But every continuum is infinitely divisible. Hence Aristotle defines it thus in the fourth book of the Physics: “The continuum is divisble ad infinitum”.” In the fifth way, “infinite” is spoken of in both ways, viz., according to addition and division, as in the case of time; for since time is a continuum, it is divisible ad mfinitum and since one time follows another, it is infinite through the addition of one time to another. With regard to the last three significations, “infinite” is defined thus: “Infinite is that whose quantity is such that we can always take a part outside what has been already taken” ; as if another part were taken after the last part of the line, and after this, a third, and [since] the end of the line could never be attained, the line is said to be infinite.
Solet autem poni quod "infinitum" quandoque sumitur pro termino communi, et tunc ista propositio: "Infinita sunt finita" aequivalet huic: "Aliqua infinita sunt finita"; quandoque sumitur pro signo distributivo, et tunc illa aequipollet huic, quoad distributionem: "Quolibet plura sunt finita". Et probatur sic: Uno plura sunt finita; duobus plura sunt finita; tribus plura sunt finita et sic de aliis; ergo, quolibet plura sunt finita. Et sic dicitur facere intrascalarem distributionem, vel interruptam vel discontinuam, quia haec dictio "plura" in prima propositione supponit pro duobus, et deinceps in secunda pro tribus, et sic gratatim et scalariter ascendendo. Et sic ista oratio "Quolibet plura" facit distributionem intrascalarem, quia pro aliis supponit hoc quod dico "quolibet" et pro aliis hoc quod dico "plura" secundum numerum ascendendo, ut supra dictum est. It is customary to assert that “infinite” is sometimes taken for a universal term, in which case the proposition: “Infinites are finite” is equivalent to the proposition: “Some infinites are finite”; and at other times it is taken as a distributive sign, in which case the proposition, as far as distribution is concerned, is equivalent to the proposition: “More than whatever number you please, is finite”. And it is proved thus: More than one is finite; more than two is finite; more than three is finite and so on; therefore, more than whatever number you please, is finite. In this fashion there is said to be an interrupted or discontinuous distribution within the numerical scale, because this word “more” in the first proposition stands for two, in the second for three, and in like manner, step by step, in the ascending numerical scale. So the expression “More than whatever number you please” effects distribution within the numerical scale, because the expression “than whatever number you please” stands for some [numbers] and “more” stands for other [numbers] according to increasing number, as was said above[10].
>Circa praedicta, quaeritur de hoc sophismate: "Infinita sunt finita". Probatio: Duo sunt finita; tria sunt finita et sic in infinitum; ergo, infinita sunt finita. In reference to what has been said, this sophism arises: “Infinites are finite”. Proof: Two is finite; three is finite and so on ad infinitum; therefore, infinites are finite.
Improbatio: Ibi praedicatur oppositum de opposite: ergo, locutio est impossibilis. Disproof: Here an opposite is predicated of its opposite: therefore, the statement is impossible.
Potest etiam sic probari: Quolibet plura sunt finita; ergo, infinita sunt finita. It also can be proved thus: More than whatever number you please, is finite; therefore, infinites are finite.
Solutio: Quidam distinguunt eo quod "infinitum" est aequivocum ad infinitum quoad nos et ad infinitum simpliciter. Unde, si sumatur infinitum quoad nos, prima potest esse vera et non praedicatur oppositum de opposite, quia infinitae quoad nos sunt stellae et arenae maris, quae non sunt infinitae simpliciter. Si autem sumatur infinitum simpliciter, est simpliciter falsa et praedicatur oppositum de opposite Alii autem distinguunt eo quod "infinitum" potest esse terminus communis et sic prima est falsa; vel potest esse dictio syncategorematica, importans in se distributionem, sicut dictum est, et sic ponunt eam esse veram. Solution: Some distinguish by reason of the fact that “infinite” is equivocal as regards what is infinite with respect to us and what is infinite in the absolute sense. Wherefore, if we take what is infinite with respect to us, the initial statement can be true and an opposite is not predicated of an opposite, for the stars and the sands of the sea, which are not absolutely infinite, are infinite with respect to us. But if we take what is infinite in the absolute sense, the initial statement is absolutely false and an opposite is predicated of an opposite. But others make a distinction by reason of the fact that “infinite” can be a universal term and thus the initial statement is false; or it can be a syncategorematic word, implying in itself distribution, as has been said, and in this way they consider the statement to be true.
Sed neutra istarum solutionum valet, quia si removeatur utraque distinctio et sumatur "infinitum" simpliciter et secundum quod est terminus communis, adhuc remanet probatio et improbatio huius sophismatis. Unde decendum est quod prima simpliciter est falsa, et probatio peccat secundum quid ad simpliciter, quia infinitum in appositione est infinitum quodammodo et non simpliciter. Unde, cum accipit partes numeri secundum appositionem, ut duo et tria, non accipit infinitum simpliciter sed quodammodo sive secundum quid; et ideo non potest ex his inferri infinitum simpliciter. But neither of these solutions has value, because if the distinction in each is denied and “infinite” is taken absolutely and as a universal term, the proof and the disproof of the sophism still remain. Wherefore, it must be said that the initial statement is absolutely false, and the proof is guilty of the fallacy of confusion of absolute and qualified statement because “infinite” in succession is infinite in a qualified sense and not absolutely. Wherefore, when the parts of number are taken in succession, as two and three, we do not grasp the infinite absolutely but in a certain fashion or a qualified sense; hence infinite in the absolute sense cannot be inferred from these.
>TRACTATUS EXPONIBILIUM TREATISE ON EXPONIBLES
Propositio exponibilis est propositio habens obscurum sensum expositione indigentem propter aliquod syncategoreuma in ea implicite vel explicite positum vel in aliqua dictione, ut in hac: "Tantum homo est animal", "Sortes incipit esse albus", "Infinita est linea", et sic de aliis. Pro quo notandum est quod ea, quae faciunt propositionem exponibilem, sunt in multiplici differentia. Nam quaedam sunt signa exclusiva, ut "tantum", "solum"; quaedam exceptiva, ut "praeter", "nisi"; quaedam reduplicativa, ut "inquantum", "secundum quod"; quaedam important inceptionem vel definitionem, ut "incipit", "desinit"; quaedam important privationem finis, ut "infinitum"; quaedam important excessum, ut nomina comparativi et superlativi gradus; quaedam important distinctionem, ut "differt", "aliud ab", et sic de aliis; quaedam important specialem modum distributionis, ut "totus", "quilibet", et sic de aliis. Unde propter ista, propositio redditur obscura et indiget expositione, et ideo dicuntur facere propositionem exponibilem. Quare de ipsis videndum est per ordinem et primo de exclusivis. An exponible proposition is one whose meaning is obscure and requires an exposition because of some syncategorematic [word] implicitly or explicitly contained in it, or contained in some word, as in the following: “Man only is animal”, “Sortes begins to be white”, “The line is infinite”, and so on. In cases of this kind it must be noted that those things responsible for a proposition being exponible differ in many ways. For some are exclusive signs, as “only”, “alone”; others are exceptive, as “with the exception or’, “but” (nisi); some ar reduplicative, as “insofar as”, “according as”; others introduce beginning or ending, as “begins”, “ends”; others introduce privation of end, as “infinite”; others introduce excess, as adjectives in the comparative and the superlative degree; others introduce a distinction, as “differs”, “other than”, and so on; others introduce a special mode of distribution, as “whole”, “any one you please”, and so on. On account of these [syncategorematic words] the proposition becomes obscure and re quires exposition, and so they are said to make a proposition exponible. Consequently we must investigate them in turn and we will first investigate exclusive [signs].
Sequitur de signis exclusivis. Unde signa exclusiva sunt quae ex sua consignificatione exclusionem important et a quibus redditur propositio exclusiva, ut sunt istae dictiones > "solus", "unicus", "tantum", "tantummodo", "dumtaxat", et 25 sic de aliis. Haec enim signa quandoque excludunt gratia alietatis et quandoque gratia pluritatia; quandoque ponuntur in propositione sine negatione et quandoque cum negatione praecedente aut sequente. De istis autem dantur quaedam regulae. We now discuss exclusive signs. Exclusive signs are those which, in virtue of their consignification, introduce exclusion and so render a proposition exclusive, as do such words as “alone”, “single”, “only”, “merely”, “precisely”, and so on. These signs sometimes exclude on account of otherness, sometimes on account of plurality; sometimes they are placed in a proposition without negation, sometimes with a negation preceding or following. We now offer certain rules respecting them.
Prima est quod propositio exclusiva sine negatione exponitur per copulativam affirmativam cuius prima pars est praeiacens exclusivae, et secunda pars est negativa importans negationem praedicati de omnibus aliis a subiecto; ut "Tantum homo est rationalis", id est, "Homo est rationalia et nihil aliud ab homine est rationale"; vel "Tantum duodecim sunt apostoli dei", id est, "Apostoli dei sunt duodecim et non plures quam duodecim sunt apostoli dei". The first rule is that an exclusive proposition without negation is expounded through an affirmative copulative proposition whose first part is that to which the exclusive sign was prefixed, and whose second part is a negative proposition denying the predicate of all others apart from the subject; thus “Only man is rational” is equivalent to “Man is rational and nothing other than man is rational”; or “Only twelve are the apostles of God” is equivalent to “The apostles of God are twelve and not more than twelve are apostles of God”.
Secunda regula est quod propositio exclusiva huius generis infert copulativam compositam ex duabus exponentibus sive componentibus, et quamlibet earum seorsum sed non e contra; ut "Tantum homo currit", ergo "Homo currit et nihil aliud ab homine currit". The second rule is that an exclusive proposition of this kind implies a copulative compounded of two exponents or components, and it implies either one of these singly but not conversely; as in the case of: “Only man runs”, therefore “Man runs and nothing other than man runs”.
Tertia regula est quod ab exclusiva affirmativa ad universalem de terminis transpositis est bona consequentia si fiat exclusio gratia alietatis, et non e contra; ut "Tantum animal est homo ergo omnis homo est animal". The third rule is that a valid consequence is had in reasoning from an exclusive affirmative proposition to a universal proposition with transposed terms, if the exclusion is the result of otherness, but not conversely; as “Only animal is man therefore every man is an animal”.
Quarta regula est quod exclusiva contradictoria prioris exponitur per disiunctivam affirmativam de partibus contradicentibus prions copulativae; ut ista: "Non tantum > homo currit". id est, "Nullus homo currit vel aliud ab homine currit". Patet ex virtute contraditionis, quia utrobique servatur oppositio contradictionis. Ex hoc etiam patet qualiter in eis valeat consequentia. The fourth rule is that an exclusive proposition contradictory of a previous [statement] is expounded through an affirmative disjunctive proposition whose parts contradict the previous copulative proposition; as “Not only man runs” is equivalent to “No man runs or another than man runs”. This is clear from the force of the contradiction, because the opposition of contradiction is preserved in both. From this also it is clear how the consequence is valid in such propositions.
Quinta regula est quod exclusiva, in qua ponitur una negatio sequens exclusionem, exponitur per unam copulativam affirmativam cuius prima pars est negativa praeiacens et secunda pars est affirmativa in qua praedicatum affirmative enunciatur de quolibet alio subiecto; ut "Tantum accidens non est substantia", id est, "Accidens non est substantia et omne aliud ab accidente est substantia". Et ex hoc patet qualiter contraditoria eius est exponenda et qualiter valeat conseqeuntia in exclusivis. The fifth rule is that an exclusive proposition in which the negation is placed after the exclusive sign, is expounded through an affirmative copulative whose first part is the preceding negative proposition and whose second part is an affirmative in which the predicate is asserted affirmatively of any other subject you please; as “Only an accident is not a substance” is equivalent to “An accident is not a substance and everything other than an accident is a substance”. From this it is clear how its contradictory should be expounded and how the consequence is valid in the case of exclusive propositions.
Sequitur de dictionibus exceptivis. Dicuntur autem dictiones exceptivae quae significant exceptionem alicuius contenti sub aliquo distributo, ut "praeter", "praeterquam", et sic de aliis. De quibus dantur quaedam regulae. We now discuss exceptive words. Exceptive words are those which signify the exception of something which is contained under anything distributed, as “with the exception of, “except”, and so on. Certain rules concerning them follow.
Prima est quod omnis exceptio fit a toto in quantitate seu a termino sumpto sub signo universal!. Est autem totum in quantitate terminus communis sumptus cum signo universal, ut "Omnis homo praeter Sortem currit". The first is that every exception occurs in relation to a quantitative whole or in relation to a term with a universal sign attached. But a general term with a universal sign attached is a quantitative whole, as in the case of: “Every man except Sortes is running”.
Secunda regula est quod dictio exceptiva, non impedita, facit terminum communem super quem cadit immediate supponere simpliciter, ut "Omne animal praeter hominem est irrationale". Ibi "hominem" supponit simpliciter. The second rule is that an exceptive word, unless prevented, causes the general term to which it is immediately attached to have simple supposition, as in the case of: “Every animal except man is irrational”. Here, “man” has simple supposition.
Tertia regula est quod universalis affirmativa exceptiva exponitur copulative per tres categoricas exponentes, qua>rum prima affirmat praedicatum de subiecto sumpto cum "aliud ab"; in secunda enunciatur affirmative terminus, a quo fit exceptio, de termino qui excipitur; tertia est negativa in qua praedicatum negatur de termino excepto. Ut si dicatur "Omne animal praeter hominem est irrationale", ista exponitur sic: "Omne animal aliud ab homine est irrationale, et homo est animal, et homo non est irrationalis". The third rule is that an affirmative exceptive universal proposition is expounded copulatively by three categorical exponents, of which the first affirms the predicate of the subject taken with “other than”; in the second, the term from which the exception is made is asserted affirmatively of the term which is excepted; the third is a negative proposition in which the predicate is denied of the excepted term. If for example we say “Every animal except man is irrational”, this proposition is expounded thus: “Every animal other than man is irrational, and man is an animal, and man is not irrational”.
Quarta regula est quod universalis negativa exceptiva exponitur copulative per tres propositiones exponentes, in quarum prima praedicatum negatur de subiecto sumpto cum li "aliud ab"; secunda est affirmativa in qua terminus a quo fit exceptio affirmatur de termino qui excipitur; in tertia affirmatur universaliter praedicatum de termino excepto; ut hic: "Nullum animal praeter hominem est rationale" exponitur sic: "Nullum animal aliud ab homine est rationale, et homo est animal, et omnis homo est rationalis". Ex his patet qualiter suae contradictoriae sunt exponendae et qualiter valeat consequentia in ipsis. The fourth rule is that a negative exceptive universal proposition is expounded copulatively by three exponents, in the first of which the predicate is denied of the subject taken with “other than”; the second is an affirmative proposition in which the term from which an exception is made is asserted of the term which is excepted; in the third, the predicate is affirmed universally of the excepted term. For example: “No animal except man is rational” is expounded thus: “No animal other than man is rational, and man is an animal, and every man is rational”. From this it is dear how their contradictories should be expounded and how the consequence is valid in them.
Sequitur de dictionibus reduplicativis. Dicuntur autem dictiones reduplicativae quae important rationem secundum quam aliquid alteri attribuitur, ut "inquantum", "secundum > quod", "ea ratione qua", et sic de aliis. De quibus tales dantur regulae. We now discuss reduplicative signs. Reduplicative signs are those which imply the reason according to which something is attributed to another, as “insofar as”, “according as”, “by reason of the fact that”, and so on. Concerning these the following rules are offered.
Prima est quod dictio reduplicativa praesupponit aliquod praedicatum inesse alicui subiecto et denotat quod illud super quod cadit immediate sit causa inhaerentiae illius. The first rule is that a reduplicative word presupposes a certain predicate to be in a certain subject and denotes that that to which it is immediately attached is the cause of that inherence.
Secunda est quod dictio reduplicativa semper fertur ad praedicatum et nunquam reduplicat ipsum. The second is that a reduplicative word alwayt refers to the predicate and never reduplicates it
Tertia est quod propositio reduplicativa in qua nulla ponitur negatio exponitur per quatuor exponentes affirmativaa, quarum prima affirmat praedicatum principale de subiecto; secunda autem affirmat reduplicatum de subiecto; tertia vero affirmat praedicatum principale de reduplicato; quarta est una causalis, in cuius antecedente praedicatur dictio supra quam cadit reduplicatio, et in consequente praedicatur praedicatum principale; ut hic: "Homo inquantum rationalis est flebilis", id est, "Homo est flebilis", et "Homo est rationalis", et "Omne rationale est flebile", et "Quia aliquid est rationale, illud est flebile". The third is that a reduplicative proposition in which there is no negation ia expounded through four affirmative exponents, of which the first affirms the principal predicate of the subject; the second asserts the reduplicate of the subject; the third asserts the principal predicate of the reduplicate; the fourth is a causal proposition, in whose antecedent the reduplicate is predicated, and in whose consequent the principal predicate is asserted. For example: “Man in so far as he is rational is tearful” is equivalent to “Man is tearful”, and “Man is rational”, and “Every rational [thing] is tearful”, and “Because something is rational, it is tearful”.
Quarta regula est quod propositio reduplicativa in qua ponitur negatio post dictionem reduplicativam exponitur > copulative per quatuor exponentes, quarum prima negat praedicatum principale de subiecto; secunda affirmat reduplicatum de subiecto; tertia negat universaliter praedicatum principale de reduplicato; quarta est una causalis, in cuius antecedente affirmatur dictio supra quam cadit reduplicatio, et in consequente negatur praedicatum principale; ut hic: "Homo inquantum rationalis non est rudibilis", id est, "Nullus homo est rudibilis, et omnis homo est rationalis, et nullum rationale est rudibile, et quia aliquid est ratoniale, ipsum non est rudibile". Ex quo patet per legem contradictionis qualiter exponendae sunt contradictoriae istarum et qualiter valet consequentia in ipsis. The fourth rule is that a reduplicative proposition in which a negation follows the reduplicative word is expounded copulatively through four exponents, of which the first denies the principal predicate of the subject; the second asserts the reduplicate of the subject; the third universally denies the principal predicate of the reduplicate; the fourth is a causal proposition, in whose antecedent the reduplicate is asserted, and in whose consequent the principal predicate is denied. For example: “Man in so far as he is rational is not capable of braying” is equivalent to “No man is capable of braying, and every man is rational, and no rational [thing] is capable of braying, and because something is rational, it is not capable of braying”. From this it is clear through the law of contradiction how the contradictories of these should be expounded and how the consequence is valid in them.
Sequitur de "incipit" et "desinit" pro quorum expositione notandum est quod rerum quaedam sunt quarum totum esse acquiritur totum simul in instanti, ut "homo" vel "binarius", give hoc sit, mediante aliqua transmutatione successiva praecedente, ut in productione naturali, sive nulla transmutatione praecedente, ut in creatione angeli; alia vero sunt quarum esse acquiritur succesive et pars post partem, > ut sunt res naturae permanentis quarum denominatio dependet a dominio contrarii supra contrarium, sicut album, nigrum, frigidum, calidum, et etiam res naturae successivae, ut motus et tempus. Et similiter aliquarum rerum quarum esse deperditur totum simul et in instanti; aliarum autem successive. Et secundum has differentias ponuntur quatuor regulae. We now treat of “begins” and “ends” in whose exposition it must be noted that there are some things whose whole being is acquired all at once in an instant, as “man” or “double”, whether this is effected with a certain successive preceding transmutation intervening, as in natural production, or with no preceding transmutation, as in the creation of an angel; but there are other things whose being is acquired successively and part after part, as things of a permanent nature whose denomination rests upon the domination of one contrary over another, such as white, black, cold hot, and also things of a successive nature, such as motion and time. In like manner, there are some things whose being is lost all at once and in an instant; and others, successively. In accordance with these differences, four rules are offered.
Prima est quod propositiones de incipit rerum quarum esse totum simul acquiritur, exponuntur per unam copulativam, cuius prima pars est affirmtiva de praesenti et secunda negativa de praeterito; ut hic: "Homo incipit esse", id est, "Homo nunc est et immediate ante hoc non fuit". The first rule is that propositions which deal with the beginning of things whose being is acquired all at once, are expounded through a copulative proposition, of which the first part is an affirmative in the present and the second a negative in the past; as “Man begins to be” is equivalent to “Man now is but immediately prior to this was not”.
Secunda regula est quod propositiones de incipit rerum quarum esse acquiritur successive, exponuntur per unam copulativam, cuius prima pars est negativa de praesenti et secunda affirmativa de futuro; ut hic: "Sortes incipit esse albus", id est, "Sortes nunc non est albus et immediate post hoc erit albus"; vel sic: "Motus incipit esse", id est, "Motus non est et immediate post hoc erit". The second rule is that propositions which deal with the beginning of things whose being is acquired successively, are expounded through a copulative, of which the first part is a negative in the present and the second an affirmative in the future; as “Sortes begins to be white” is equivalent to “Sortes now is not white but immediately after this will be white”; or thus: “Motion begins to be” is equivalent to “Motion is not but immediately after this will be”.
Tertia regula est quod propositiones de desinit rerum quarum esse deperditur totum simul, exponuntur per unam copulativam, cuius prima pars est affirmativa de praesenti et secunda negativa de futuro; ut hic: "Sortes desinit esse homo", id est, "Sortes nunc est homo et immediate post hoc non erit homo". The third rule is that propositions which deal with the ending of things whose being is lost all at once, are expounded by a copulative, of which the first part is an affirmative in the present and the second a negative in the future; as “Sortes ceases to be man” is equivalent to “Sortes now is a man but immediately after this will not be a man”.
Quarta regula est quod propositiones de desinit rerum quarum esse deperditur successive, exponuntur copulative > per unam negativam de praesenti et aliam afnrmativam de praeterito; ut hic: "Sortes desinit esse albus", id est, "Sortes nunc non est albus et immediate ante hoc fuit albus". Ex praedictis, patet qualiter contraditoriae istarum sunt exponendae et qualiter valeat consequentia in ipsis. The fourth rale is that propositions dealing with the ending of things whose being is lost successively, are expounded copulatively through a negative in the present and an affirmative in the past; as “Sortes ceases to be white” is equivalent to “Sortes now is not white but immediately before this was white”. From what has been said, it is apparent how the contradictories of these should be expounded and how the consequence is valid in them.
Sequitur de nomine "infinito", cuius solent assignari quaedam distinctiones. Prima est quod "infinitum" quandoque sumitur negative, et est illud quod non est finitum neque aptum natum finiri; ut punctus vel Deus. Alio modo sumitur privative, et est illud quod non est finitum sed aptum natum finiri; ut motus, nondum perfectus, est infinitus. Et illud est triplex, scilicet, infinitum per appositionem tantum, ut numerus; infinitum per divisionem tantum, ut continuum ; et infinitum per appositionem et divisionem simul, sicut est tempus. We now treat of the adjective “infinite”, with* respect to which certain distinctions are usually made. The first is that infinite sometimes is taken negatively, and in this sense it is that which is not finite nor is its nature such as to be finite; as a point or God. In another way it is taken privately, and in this sense it is that which is not finite but whose nature is such as to be finite; as motion, not yet perfected, is infinite. This [sense of “infinite”] is threefold, viz., infinite through addition only, as number; infinite through division only, as a continuum; and infinite through addition and division simultaneously, as time.
Secunda distinctio est infinitum qua dividuntur omnes modi praecedentes, quorum aliud dicitur infinitum in actu, quod est quantum non terminatum; aliud est infinitum in potentia, ut sunt continua; aliud est infinitum quoad nos tantum et non secundum rem.


There is a second distinction of infinite applicable to any one of the preceding modes, for one thing is said to be infinite in act, as is quantity not terminated; another is infinite in potency, as are the continua; a third is infinite only with respect to us and not in reality.
Tertia distinctio est quod "infinitum" capitur dupliciter: uno modo capitur categorematice, significative ut est terminus communis, et sic significat quantitatem rei subiectae vel praedicatae, ut cum dicitur: "Mundus est infinitus"; alio modo capitur syncategorematice, non prout dicit quan>titatem rei subiectae vel praedicatae, sed inquantum se habet subiectum in ordine ad praedicatum, et sic est distributio subiecti et signum distributivum. Et de his dantur quaedam regulae. The third distinction is that “infinite” is taken in two ways: in one way it is taken categorematically, significatively as a general term, and thus it signifies the quantity of the thing which is subject or predicate, as when one says: “The world is infinite”; in another way it is taken syncategorematically, not insofar as it indicates the quantity of the things which is subject or predicate, but insofar as the subject is related to the predicate, and in this way there is distribution of the subject and [it is] a distributive sign. We [now] offer some rules concerning these distinctions.
Prima est quod "infinitum", syncategorematice captum, positum in subiecto, facit terminum communem sequentem stare confuse tantum ut hic: "Infiniti homines currunt". Ibi "homines" supponit confuse, non tamen mobiliter. The first rule is that “infinite”, taken syncategorematically and placed in the subject, causes the following general term to have indeterminate supposition only, as “Infinite men run”. In this case, “men” has indeterminate but not movably indeterminate supposition.
Secunda regula est quod propositio de infinite, syncategorematice capto, exponitur per unam copulativam, cuius prima pars affirmat praedicatum de subiecto sumpto sub aliqua quantitate, continua vel discreta, et secunda negat praedicatum inesse tali subiecto secundum determinatam quantitatem; ut ista: "Infiniti homines currunt", quae sic exponitur: "Aliqui homines currunt et non tot quin plures duobus vel tribus", vel sic: "Homines aliqui currunt et quotlibet plures". The second rule is that a proposition concerning the infinite, taken syncategorematically, is expounded by a copulative whose first part affirms the predicate of the subject taken according to some quantity, continuous or discrete, and whose second part denies that the predicate is in such a subject according to a determined quantity: as “Infinite men run”, which is expounded thus: “Some men run and not so few that they will not be more than two or three”, or thus: “Some men run and as many more as you please”.
Tertia regula est quod propositio de infinito, capto categorematice sive significative, exponitur per unam copulativam, cuius prima pars affirmat quantitatem de subiecto et secunda negat terminum illius quantitatis; ut hic: "Linea est infinita", id est, "Linea est quanta et non habet terminum suae quantitatis". Et hoc est si "infinitum" sit in praedicato. Sed si sit in subiecto, prima affirmat praedicatum de subiecto et secunda negat terminum illius quantitatis ; ut hic: "Aliquod corpus infinitum est album", id est, "aliquod corpus quantum est album et idem corpus non habet terminus suae quantitatis". Et note quod oportet > negare terminum illius quantitatis secundum quod dicitur infinitum, ita quod si sit infinitum in actu, negandus est terminus illius quantitatis actualis; et si sit in potentia, ita quod sit infinitum secundum potentialem quantitatem et non secundum actualem, negandus est terminus quantitatis potentialis et non quantitatis actualis, sive sit infinitum secundum appositionem vel divisionem. The third rule is that a proposition concerning the infinite, taken categorematically or significatively, is expounded through a copulative whose first part asserts quantity of the subject and whose second part denies the terminus of that quantity; as “A line is infinite” is equivalent to “A line is long and does not have any end of its quantity”. This is the case if “infinite” is in the predicate. But if it is in the subject, the first part asserts the predicate of the subject and the second part denies the terminus of that quantity; as “Some infinite body is white” is equivalent to “Some great body is white and the same body does not have any end of its quantity”. Note that it is necessary to deny the terminus of that quantity according to the way the infinite is spoken of, so that if the infinite in act is spoken of, the terminus of that actual quantity must be denied; and if the infinite in potency is spoken of. whether according to addition or division, ao that the infinite according to potential quantity and not according to actual quantity is spoken of, the terminus of potential quantity and not of actual quantity must be denied.
Sequitur de comparativis et superlativis de quibus tales dantur regulae. Prima est quod propositio habens comparativum, proprie captum et non abusive, exponitur copulative per tres exponentes, quarum prima affirmat positivum de re excedente; secunda affirmat eundem de re excessa; et tertia affirmat excessum de re excedente respectu rei excessae—ut hic: "Sortes est albior asino", id est, "Sortes est albus, et asinus est albus, et Sortes est magis albus quam asinus"—vel negando aequalitatem formae inesse excesso respectu excedentis—ut hic: "Sortes est albus, et asinus est albus, sed asinus non est aeque albus sicut Sortes". We now discuss comparatives and superlatives and offer some rules concerning them. The first rule is that a proposition containing a comparative, taken properly and not pervertedly, is expounded copulatively by three exponents, the first of which asserts the positive degree of the thing exceeding; the second asserts the same [positive] of the thing exceeded; and the third asserts an excess of the thing exceeding in relation to the thing exceeded—as “Sortes is more white than the ass” is equivalent to “Sortes is white, and the ass is white, and Sortes is more white than the ass” —or [it asserts an excess of the thing exceeding] by denying that there ifl an equality of form in the thing exceeded in relation to the thing exceeding—as “Sortes is white, and the ass is white, but the ass is not equally as white as Sortes”.
Secunda regula est quod superlativus distribuit terminum communem sequentem qui significat rem excessam; ut "Leo est fortissimus animalium". Ibi "animalium" distribuitur. The second rule is that a superlative distributes the general term following it, which signifies the exceeded thing; as “The lion is the bravest of animals”. In this case “animals” is distributed.
Tertia regula est quod superlativus, proprie tentus, denotat rem excessam convenire rei excedenti. Patet, quia haec est impropria locutio: "Leo est fortissimus lyncum". The third rule is that a superlative, properly taken, denotes that the thing exceeded agrees with the thing exceeding. The rale is evident, for this is an improper statement : “The lion is the bravest lynx”.
Quarta regula est quod propositio de superlativo, proprie > capto, exponitur copulative per tres exponentes, quarum prima affirmat positivum de re excedente; secunda affirmat eundem de re excessa; et tertia universaliter negat excessum de re excessa per respectum ad rem excedentem: ut hic: "Rosa est pulcherrima florum", id est, "Rosa est pulchra, et omnis flos est pulcher, et nullus flos est pulchrior rosa". Si vero superaltivus teneatur affirmative, tertia exponens debet esse affirmativa affirmans excessum de re excedente per respectum ad rem excessam acceptam universaliter, ut dicendo: "Rosa est pulchrior omni flore". Et omnes propositiones de maximo et minimo, et sic de aliis superlativis, his duobus modis possunt exponi dummodo ponatur genitivus importans rem excessam; et si non ponitur ille genitivus, debet omitti secunda exponens—ut hic: "Sortes est fortissimus homo", id est, "Sortes est fortis et nullus homo est fortior ipso". Et contradictoriae istarum debent exponi per disiunctivas de partibus contradicentibus. The fourth rule is that a proposition with a superlative taken strictly, is explained copulatively by three exponents, the first of which affirms the positive of the thing exceeding; the second affirms the positive of the thing exceeded; and the third universally denies an excess of the thing exceeded in relation to the thing exceeding. Thus “A rose is the most beautiful of flowers” is equivalent to “A rose is beautiful, and every flower is beautiful, and no flower is irore beautiful than a rose”. But if the superlative is taken affirmatively, the third exponent should be an affirmative proposition asserting an excess of the thing exceeding in relation to the thing exceeded taken universally, as when one says: “A rose is more beautiful than every flower”. All propositions concerned with maximum and minimum, and thus concerning the other superlatives, can be explained in these two ways as long as the genitive denoting the thing exceeded is contained in them; but if that genitive is not included the second exponent should be omitted. For example: “Sortes is the bravest man” is equivalent to “Sortes is brave and no man is more brave than he”. The contradictories of these should be expounded through disjunctive propositions with contradictory parts.
Sequitur de "differt", "aliud ab", de quibus tales dantur regulae. Prima est quod "differt", "aliud ab", et diversum" conveniunt tantum entibus. Nam, ut dicitur quarto Metaphysicae, nec non-ens enti nec ens non-enti est idem vel diversum. We now treat of “differs” and “other than”, and offer some rules concerning them. The first rule is that “differs”, “other than”, and “different” apply only to beings. For, as is said in the fourth book of the Metaphysics,* neither is non-being the same as nor different from being, nor vice versa.
Secunda regula est quod ablativus rectus ab istis dictionibus, mediante "a" vel "ab", distribuitur, si sit distribuibilis, nisi habeat aliud impedimentum. The second rule is that the ablative case dependent on these words through “from” or “than” is distributed, if it can be distributed, unless there is some impediment.
Tertia regula est quod propositio affirmativa de "differt" > exponitur copulative per tres exponentes, in quarum prima affirmatur hoc verbum "est" de eo quod differt; in secunda affirmatur idem de eo a quo differt; in tertia negatur unum illorum de alio; ut "Homo differt ab asino", id est, "Homo est, et asinus est, et homo non est asinus". The third rule is that an affirmative proposition with “differs” is expounded copulatively by three exponents, of which the first affirms the verb “is” of that which differs; the second affirms the same of that from which it differs; the third denies one of the other; as “Man differs from an ass” is equivalent to “A man is, and an ass is, and a man is not an ass”.
Quarto[11] regula est quod propositio negativa de "differt" debet exponi per unam disiunctivam de partibus contradicentibus; ut "Sortes non differt ab asino", id est, "Sortes non est vel asinus non est vel Sortes est asinus". Et valent consequentiae in istis, sicut in praecedentibus. A fourth rule is that a negative proposition with “differs” should be expounded by a disjunctive with contradictory parts; as “Sortes does not differ from an ass” is equivalent to “Sortes is not, or an ass is not, or Sortes is an ass”. And the consequences in these are valid, just as in the preceding.
Sequitur de hoc signo "totus" pro quo sciendum est quod hoc syncategorema "totus" potest capi tribus modis. Uno modo proprie pro omni illo quod habet partes ex quibus componitur. Secundo modo capitur magia proprie pro omni illo quod ex omnibus suis particibus est perfectum, sicut domus dicitur tota quando est completa. Et his duobus modis "totus" tenetur significative et categorematice. Tertio modo, capitur syncategorematice prout includit signum distributivum; ut hic: "Totus Sortes est albus". Et sic non dicit quale sit subiectum sed qualiter se habeat ad praedicatum; et hoc modo reddit propositionem exponibilem. De quo dantur duae regulae. We now discuss the sign “whole” concerning which we should know that this syncategorematic word can be taken in three ways. In one way, it is taken properly for everything that has component parts. In a second way, it is taken more strictly for everything that is complete by virtue of all its parts, as a house is said to be whole when it is complete. In these two ways, “whole” is taken significatively and categorematically. In a third way, it is taken syncategorematicaly as equivalent to a distributive sign; as “The whole Sortes is white”. Here it does not assert of what sort the subject is but how the subject is related to the predicate; and in this way the proposition becomes exponible. Concerning this, we offer two rules.
Prima est quod "totus" distribuit terminum cui adiungitur pro qualibet parte integrali eius; ut "Totus Sortes est albus", id est, "Quaelibet pars Sortis est alba". The first [rule] is that “whole” distributes the term to which it is joined for any integral part of it whatsoever; as “The whole Sortes is white” is equivalent to “Any part whatever of Sortes is white”.
Secunda regula est quod propositio affirmativa de "toto" exponitur per unam categoricam transmutando ly "totus" in hoc quod est secundum quamlibet sui partem; ut "Totus > Sortes est minor Sorte", id est, "Sortes, secundum quamlibet sui partem, est minor Sorte". The second rule is that an affirmative proposition with “whole” is expounded through a categorical proposition by altering the term “whole” into that which is so according to any one whatsoever of its parts; as “The whole Sortes is less than Sortes” is equivalent to “Sortes, according to any one whatsoever of his parts, is less than Sortes”.
Praeterea notandum est quod haec signa, "quaelibet", quantum!ibet", non proprie faciunt propositiones exponibiles sed faciunt distributionem, non absolute secundum modum reliquorum signorum, sicut sunt ista signa, "omnis", "quilibet", sed contrahunt ad aliquod determinatum genus praedicamentale; ut "quantumlibet" distribuit pro quantitate continua et tantum valet sicut habens omnem quantitatem continuam, et "qualelibet" distribuit pro omni qualitate et tantum valet sicut habens omnem qualitatem. Et sic dicuntur mentaliter complexa, quorum propositiones fiunt per compositionem. Et haec de exponibilibus dicta sufficiant. Furthermore, it should be noted that these signs, “of whatever quality you please”, “as much as you please”, do not properly make propositions exponible but they effect distribution, not absolute distribution after the fashion of other signs, such as “every”, “any one you please”, but rather they restrict to some determined categorial genus; for example, “as much as you please” distributes in relation to continuous quantity and only has meaning as containing every continuous quantity, and “of whatever quality you please” distributes in relation to every quality and only has meaning as containing every quality. And thus these signs are called mentally complex expressions whose propositions are formed by synthesis. These remarks suffice concerning exponibles.

Notes

  1. I.e. relatives belonging to the category of relation
  2. I.e. relatives which refer back to something mentioned previously
  3. sic
  4. Littus aratur may be translated literally, as The shore is ploughed”; or proverbially, at “It is a vain labor”. Scit saeculum means “He knows [this] generation” or [This] feneration knows [something]”, depending upon whether saeculum is taken as subject or predicate of the statement.
  5. De Interpretatione 6, 17a, 31-82
  6. De Interpretatione 7, 17b, 16-19.
  7. sic
  8. De Interpretatione 10. 19b. 26
  9. Interpolate [But this is false. Therefore, the sophism is false.] This consequence is offered as proving the falsity of the sophism, since it appears to conclude a false consequent, for, on the hypothesis, it is false that the grammarian among the three “other men” knows himself and the the three men to be grammmarians.
  10. Perhaps this refers to Physica. IV, 12, 220A, 30. However, language and context suggest rather Physica III, 7, 207b. 15.
  11. sic
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