Here, from Buridan's Questions in the Posterior Analytics, is the clearest statement that I can find of a kind of medieval logical atomism. Buridan argues for a distinction between connotative terms, which are semantically complex, reducible or analysable into absolute terms that are not complex in this way, and are not further reducible. An absolute term is object dependent: it must stand for something that exists either in the present, the past or the future. A connotative term, by contrast, does not have to stand for anything at all.
Thus he tries to explain how we are able to understand concepts of things that neither have nor will exist. For example (according to Buridan's Aristotelian Physics) the word 'vacuum' does not stand for anything, because there is no such thing as a vacuum. However, the concept of a vacuum is reducible to the concept 'place not filled by a body'.
This appears to have some connection with the traditional doctrine, puzzling to modern logicians, that the A proposition 'every A is B' implies the I proposition 'some A is B'. This will be true, however, so long as 'A' represents an absolute term (like 'man' for example, which Aristotelian logicians regarded as absolute - see the passage by Ockham referred to here).
This was not at all easy, as Buridan uses a number of technical Latin terms in a non-classical sense.
Ockham, Summa Logicae, chapter 10 of Book I.
The Logic Museum, Connotation
|IOHANNIS BURIDANUS: QUAESTIONES IN ANALYTICA POSTERIORA||John Buridan: Questions in the Posterior Analytics|
|Quaestio 4a: UTRUM ANTE CUIUSLIBET CONCLUSIONIS DEMONSTRABILIS NOTITIAM NECESSE SIT PRAECOGNOSCERE DE SUBIECTO QUIA EST||Question 4a: Whether before the knowledge of any demonstrable conclusion, it is necessary to know beforehand of the subject whether it is such-and-such.|
|Consequenter quaeritur, quarto, utrum ante cuiuslibet conclusionis demonstrabilis notitiam necesse sit praecognoscere de subiecto quia est.||Consequently it is asked (four) whether before the knowledge of any demonstrable conclusion, it is necessary to know beforehand of the subject whether it is such-and-such.|
|1. Arguitur quod non: quia quod quaeritur in scientia demonstrativa non praecognoscitur; sed quaeritur si est, et quia est, et quid est et propter quid est, ut patet secundo huius*; igitur nullum illorum praecognoscitur.||1. It is argued that it is not, because what is asked in demonstrative science is not known beforehand, but rather it is asked if it is, if it is such-and-such, what it is, and why it is, as is clear from the second book. Accordingly, none of these is known beforehand.|
|2. Item, quod demonstratur non praecognoscitur; sed si est, quia est, quid est et propter quid est demonstrantur, quoniam illae quattuor quaestiones terminantur per demonstrationem, ut dicit Lincolniensis*, secundo huius; ergo non praecognoscuntur.||2. Likewise, what is demonstrated is not known beforehand, but rather if it is, if it is such-and-such, what it is, and why it is, since these four questions are determined by demonstration, as Lincoln says, in the second book. Therefore they are not known beforehand.|
|3. Item, syllogismus sophisticus ponitur esse subiectum in libro Elenchorum, et tamen in illo libro demonstrat Aristotiles syllogismos sophisticos esse; ergo subiectum in aliqua scientia bene demonstratur esse; ergo non oportet hoc praecognoscere.||3. Likewise, a sophistical syllogism is supposed to be the subject in De Sophisticis Elenchis. And yet in that book Aristotle demonstrates that there are sophistical syllogisms . Therefore the subject in some science is demonstrated well to exist, therefore it is not necessary to know this beforehand.|
|4. Item, non praecognoscitur de passione quia est; ergo nec de subiecto hoc praecognoscitur. Probo consequentiam: quia saepe passiones sunt subiecto notiores; igitur videtur quod magis debeant praecognosci, et non videtur ratio quare magis sit necessarium de passione quam de subiecto.||4. Likewise, it is not known beforehand about an attribute that it is such-and-such, therefore neither is this known beforehand about the subject. I prove the the consequent: because often attributes are better known than the subject. Accordingly it seems that they ought to be better known beforehand, and there does not seem a reason why this is more necessary with an attribute than with the subject.|
|5. Item, quod investigatur in scientia demonstrativa non praecognoscitur; sed quia est investigatur; ergo non praecognoscitur. Minor patet: quia idem est quid est subiecti et quia est subiecti; modo quid est subiecti bene investigatur: verbi gratia, in libro de Anima investigatur definitio animae, id est quid anima est, et in hoc secundo libro declaratur quid est demonstratio, licet tamen demonstratio et anima sint subiecta in scientiis dictorum librorum.||5. Likewise, what is investigated in demonstrative science is not known beforehand, but rather it is investigated whether it is such-and-such . Therefore it is not known beforehand. The minor [premiss]] is clear, because what the subject is, and that it is such-and-such, are the same thing. Now, what the subject is is well investigated. For example, in the De Anima the definition of the soul ia investigated, i.e. what the soul is, and in the second book it is clarified what demonstration is, although, nonetheless, demonstration and the soul are subjects in the science of said books.|
|6. Item, multae conclusiones sunt negativae; sed ad sciendum conclusionem negativam non oportet scire de subiecto quia est, eo quod conclusio negativa esset vera licet pro nullo subiectum supponeret; ideo non oportet in omni scientia demonstrativa praesupponere de subiecto quia est. Confirmatur hoc: quia multas habemus conclusiones demonstrabiles de vacuo et infinito; tamen non supponimus vacuum vel infinitum esse, quia falsum supponeremus; ergo ... et caetera.||6. Likewise, many conclusions are negative. But for the knowledge of a negative conclusion it is not necessary to know of the subject that it is such-and-such, seeing as a negative conclusion would be true even though the subject stood for nothing. For that reason it is not necessary in every demonstrative science to presuppose of the subject that it is such-and-such. This is confirmed, because we have many demonstrable conclusions about a vacuum and the infinite. Yet we do not suppose a vacuum or the infinite to exist, because we would suppose what is false. Therefore &c.|
|Oppositum patet per Aristotilem, prooemio huius, dicentem "dupliciter necessarium est praecognoscere"*, scilicet de subiecto et de dignitate quia est, et de subiecto et de passione quid est; et hoc magis determinat in medio istius primi libri*.||The opposite is clear from Aristotle, in the introduction, saying 'it is necessary to know beforehand in two ways, namely ofthe subject and de dignitate that it is such-and-such, and of the subject and the attribute what it is. and he determines this more in the middle of the first book.|
|Item, secundo Metaphysicae*, dicit Aristotiles quod scientiae nihil dicunt seu inquirunt si est aut non est genus subiectum circa quod versantur.||Likewise, in the second [book] of the Metaphysics, Aristotle says that the sciences say or inquire nothing, about whether the genus is or is not the subject with which they engage.|
|Notandum est quod licet 'subiectum'* multipliciter capiatur, tamen quantum ad propositum non intendimus loqui nisi de duplici acceptione 'subiecti'.||It is to be noted that although 'subject' is taken in many ways, yet as far as what is proposed, we do not mean to speak except about a twofold acceptance of 'subject'.|
|Uno modo 'subiectum' dicitur in relatione ad 'praedicatum'; et sic est subiectum ille terminus alicuius propositionis de quo alter terminus in illa propositione praedicatur.||In one way 'subject' is said in relation to 'predicate', and thus the subject is that term in some proposition of which the other term in that proposition is predicated.|
|Alio modo dicitur 'subiectum' in ordine ad 'passionem', et tunc 'subiectum' et 'passio' sunt termini pro eodem supponentes, quorum tamen unus addit super significationem alterius aliquam extraneam connotationem, sicut isti termini 'homo' et 'risibile'; quoniam iste terminus 'risibile' connotat actum ridendi: dicitur enim 'risibile' quod aptum natum est ridere. Et tunc semper ille terminus qui super alterum addit connotationem dicitur 'passio'* respectu illius, et ille alter terminus, minus connotativus vel omnino absolutus a connotatione, dicitur 'subiectum'.||In another way 'subject' is said in the order of 'attribute', and then 'subject' and 'attribute' are terms standing for the same thing, one of which nonetheless adds the signification of some extraneous connotation, such as the terms 'man' and 'capable of laughter', since the term 'capable of laughter' connotes actual laughing, for 'capable of laughter' is said of what is naturally suited to laugh. And then that term which adds the connotation over and above the other is called the 'attribute' in respect of the other, and that other term, less connotative or altogether free from connotation, is called the 'subject'.|
|Modo, multi* opinantur quod Aristotiles intendit de subiecto conclusionis, scilicet de quo alterum praedicatur, quando dicit quod de subiecto oportet praecognoscere quia est. Quia ipsi* dicunt quod impossibile est demonstrare de aliquo termino hoc verbum 'est' secundum adiacens, ita quod tales propositiones 'deus est', 'prima causa est', sunt omnino indemonstrabiles. Et hoc ipsi nituntur sic probare. Si ista propositio 'deus est' esset demonstrabilis, sequeretur quod hoc esset per aliquod medium quod esset magis notum de deo quam hoc verbum 'est'; consequens est falsum; igitur et antecedens. Falsitas consequentis videtur manifesta propter duo. Primo, quia de nullo ente videtur aliquid notius quam quod ipsum est, cum conceptus entis sit communissimus et notissimus. Secundo, quia in qualibet propositione affirmativa formata de isto subiecto 'deus' includitur ista 'deus est': quia non est verum quod deus sit immobilis nisi deus sit et quod sit prima causa nisi ipse sit; nec est possibile quod tu scias deum esse, nec deum esse bonum, aut primam causam, et sic de aliis, si tu dubitas utrum deus sit. Et sic patet quod de isto termino 'deus', et de quocumque alio termino sumpto pro quolibet ente, impossibile est quod aliquod praedicatum sit notius quam hoc praedicatum 'est'. Et sic patet falsitas consequentis. Sed consequentia principalis est manifesta: quia non potest syllogizari nec probari nisi per medium affirmative coniunctum utrique extremitati, et, per consequens, dictum affirmative de deo.||Now, many think that Aristotle means [to speak of] the subject of the conclusion, i.e. of which the other [term] is predicated, when he says that it is necessary that it is known beforehand of the subject that it is such-and-such. For they say that it is impossible to demonstrate the word 'is' of some term secundum adiacens, so that such propositions as 'God is', 'the first cause is are altogether undemonstrable. And they endeavour to prove this as follows. If the proposition 'God is were demonstrable, it would follow that this were through some medium that were more known than the word 'is'. Consequently it is false; accordingly also the antecedent. The falsity of the consequent seems manifest for two [reasons]. First, because it seems of no existing thing is something more known than that it is , since the concept of an existing thing is the most common and the most known. Second, because in any proposition whatever, the affirmative formed from the subject 'God' includes 'God is'. For it is not true that God is unmoveable unless God is, and because [is not true that] he is the first cause unless he is. Nor is it possible that know that God is, or that God is good, or is the first cause, and suchlike, if you doubt that God is. And thus it is clear that of the term 'God', and of any other term taken for something that exists, it is impossible that some predicate be more known than the predicate 'is'. And thus the falsity of the consequent is clear. But the principal consequence is manifest: because it is not possible to syllogise or prove except through some medium affirmatively joined to each extreme, and, as a consequence, said affirmatively of God.|
|Item, illa opinio confirmatur. Quia nulla demonstratio esset bona in qua peteretur principium. Sed in syllogizando quod deus est aut quod A est peteretur principium: quia una praemissa affirmaret unum praedicatum de isto subiecto 'deus' vel de hoc subiecto 'A', et in hoc statim peteretur principium: quia nullus concedit illam de tertio adiacente si vult negare illam de secundo adiacente: numquam enim concederet deum esse primam causam si negaret deum esse.||Likewise, that view is confirmed. For no demonstration which begged the question would be a good one. But in syllogising that God is, or that A is, we would beg the question, for one premiss would affirm one predicate of the subject 'God' or the subject 'A', and this immediately would beg the question, for no one would concede that [proposition] de tertio adiacente if he wished to deny it de secundo adiacente, for he would never concede that God was the first cause if he were deny that God is [i.e. exists].|
|Sed credo quod haec opinio est falsa. Quia est contra Aristotilem* et Lincolniensem*, secundo huius, qui ponunt quattuor quaestiones demonstrabiles, quae cum sint primo dubiae, tamen bene possunt verificari. Et inter illas enumerant quaestionem si est, in qua hoc verbum 'est' secundum adiacens quaeritur de aliquo subiecto. Aristotiles et Lincolniensis ponunt quod dictae quattuor quaestiones, praeter quaestionem 'quid est', terminantur per demonstrationem.||But I believe this view is false. For it is against Aristotle and Lincoln, in the second book, who suppose four demonstrable questions, which, while they are first able to be doubted, nonetheless can well be verified. And among those they enumerate the question 'if it is', in which the word 'is' is asked of a subject secundum adiacens. Aristotle and Lincoln suppose that the said four questions, besides the question 'what it is', are determined by demonstration.|
|Item, dubitabile est utrum aliquid immobile sit, et tamen per scientiam demonstrativam et per processum demonstrativum in scientia naturali scitur quod aliquod immobile est; modo omne illud est demonstrabile quod ante erat dubium et postea est scitum per processum demonstrativum.||Likwise, it is open to doubt where something is immoveable, and yet it is known through demonstrative science and by demonstrative process in natural science that something is immoveable. Now, all that is demonstrable is what was before open to doubt, and which is known through a process of demonstration.|
|Sed ipsi volunt respondere quod haec non demonstratur 'immobile est', immo haec demonstratur 'aliquid est immobile'. Et quando quaeritur ab eis "quo modo igitur scitur ista 'immobile est'? cum ante dubitabatur", respondent quod scitur per unam consequentiam non syllogisticam, et, per consequens, non demonstrativam: quia quando demonstratum est quod aliquid est immobile, demonstratum est quod immobile est.||But they will reply that 'an immoveable thing is' is not demonstrated. On the contrary, it is 'something is immoveable' that is demonstrated. And when it is asked of them 'in what way then is "an immoveable thing is" known, when before it was open to doubt?', they will reply that it is known by a consequence that is not syllogistical, and, in consequence, not demonstrative. For when it is demonstrated that something is immoveable, it is demonstrated that an immoveable thing is.|
|Sed, sine dubio, sic dicentes concedunt propositum meum; quia quidquid sequitur ad consequens sequitur ad antecedens; ideo ad praemissas demonstrativas ad quas sequitur ista 'aliquid est immobile' sequitur etiam ista 'immobile est'. Et est bonus syllogismus et bona demonstratio: quia est ex praemissis necessariis et notioribus, quia ad bonum syllogismum nihil plus exigitur nisi quod praemissae sint ordinatae in debito modo et figura, et quod conclusio de necessitate sequatur ex eis; ideo in secundo Priorum* habetis potestatem syllogismi quod est posse plura concludere, ita quod syllogistice concluditur quidquid sequitur ad unam conclusionem syllogistice conclusam.||But without a doubt, in saying this, they concede what I have proposed. For whatever follows from the consequent, follows from the antecedent. For that reason, from the demonstrative premisses from which 'something is immoveable' follows, there also follows 'an immoveable thing is'. And it is a good syllogism and a good demonstration, because it is from premisses that are necesary and better known, [and] because for a good syllogism nothing more is needed than that the premisses are ordered in the requisite mode and figure, and that the conclusion follows of necessity from them. For that reason in the second book of the Prior Analytics, you have the power of the syllogism that it can conclude many things, so that whatever follows from a conclusion that is syllogistically concluded, is concluded syllogistically.|
|Igitur, relicta illa opinione, pono conclusionem, cum Aristotile, quod oportet, in omni scientia simpliciter demonstrativa, de subiecto praecognosci quia est, capiendo 'subiectum', prout dicitur, in ordine ad passionem. Tamen illam conclusionem debetis modificare ita quod non intelligamus quia est pro praesenti solum, quia tunc conclusio esset falsa. Nam de rosis posset dari talis scientia demonstrativa licet non praecognosceretur quod aliqua rosa esset in praesenti. Sed debemus capere 'quia est' indifferenter ad praesens, praeteritum et futurum, sic intelligendo quod oportet de quolibet subiecto praecognoscere quia est vel fuit vel erit.||Accordingly, with that view left, I grant the conclusion, along with Aristotle, that it is necessary in every simply demonstrative science, that it is known beforehand that the subject is such-and-such, taking 'subject', as we said, in the order of attribute. Yet you should modify that conclusion so that we do not understand ' that it is such-and-such' for the present only, because then the conclusion would be false. For such demonstrative knowledge could be given of roses, although it were not known beforehand that some rose existed in the present. Rather, we ought to take ' that it is such-and-such' indifferently to present, past or future, by so understanding that it is necessary to know beforehand of a subject that it is – or was, or will be – such-and-such.|
|Hoc probatur. Primo, quia oportet sensum vel intellectum primo moueri ab aliquo ente quod manifeste appareat esse, et non posset evidentius probari quam quia apparet in prospectu sensus; ideo aliquid oportet praecognoscere esse.||This is proved. First, because it is necesary that, either the sense or the intellect is first moved by some existing thing that manifestly appears to exist, and it could not be proved more evidently than that it appeared in the prospect of sense. For that reason, something must be known beforehand.|
|Iterum, impossibile est habere conceptum simplicem purum, et non connotativum, quin ille supponat pro aliquo praesenti, praeterito vel futuro; et hoc est quia nihil intelligitur quod non sit vel fuerit, sicut postea magis videbitur. Igitur, si aliquis terminus pro nullo supponit, hoc est quia est connotativus, vel quia componuntur in se plures conceptus. Sic conceptus vacui pro nullo supponit, quia conceptus vacui componit in se conceptus loci et conceptum corporis, scilicet negative: idem enim significat 'vacuum' quod 'locus non repletus corpore'. Et ita omnes tales termini, pro nullo supponentes, resolvuntur quantum ad quid nominis in alios terminos de quibus manifestum est et praecognitum est quod pro aliquo supponunt; et illi termini sunt subiecta de quibus notum est quia est.||Again, it is impossible to have a pure, simple concept, and not connotative, unless it stands for something present, past or future, and this is because nothing is understood that does not exist, or did exist, as will be seen later. Accordingly, if some term stands for nothing, this is because it is connotative, or because many concepts are brought together in it. Thus the concept of a vacuum stands for nothing, because the concept of a vacuum brings together in it both the concept of place and the concept of body, namely negatively. For 'vacuum' signifies the same as 'a place not filled by a body'. And so such terms, standing for nothing, are resolved, insofar as their nominal definition, into other terms of which it is manifest that they stand for something; and those terms are the subjects of which it is known that it is such and such.|
|Item, in omni quaestione oportet aliquid esse notum et aliquid esse dubium, secundo huius*, et illud quod est primo notum dicitur ipsum subiectum in scientia, de quo, cum sit primo notum, non est dubitatum quin sit vel fuerit.||Likewise, in every question it is necessary that something is known and something is open to doubt, in the second book, and that which is known first is said to be the subject in science of which, since it is known first, is not to be doubted but that it is or was.|
|Ultimo, primus conceptus absolutus est conceptus 'entis', scilicet significatus per hoc nomen 'ens', vel 'aliquid'*, et de illo ab omnibus praecognoscitur hoc verbum 'est' secundum adiacens: omnes enim sciunt aliquid esse. Et ille conceptus est primum subiectum in metaphysica; ideo in metaphysica de subiecto praecognoscitur quia est. Et si in aliis scientiis dubitetur de primis subiectis esse, illud demonstratur per metaphysicam, et sic supponitur in istis scientiis.||Finally, the first absolute concept is the concept of an existing thing, namely signified by the name 'existing thing', or 'something', and concerning that, the word 'is', secundum adiacens, is known beforehand by all, for all know that anything is. And that subject is the first subject in metaphysics. For that reason in metaphysics it is known beforehand of the subject that it is such-and-such. And if in other sciences it is doubted whether its principal subject exists, that is demonstrated by metaphysics, and so it is supposed in these sciences.|
|Per hoc ad rationes.||Replies to arguments.|
|1. Ad primam, dico quod bene quaeritur, et dubitatur, et demonstratur de subiecto quia est, vel etiam si est: demonstratur enim quod immobile est. Sed de primis subiectis in quae passiones scientiarum ultimate resolvuntur non dubitatur si est; et si in aliqua scientia speciali dubitetur, inquiritur per superiorem scientiam.||1. To the first, I say that it is well asked, and doubted, and is demonstrated of the subject that it is such-and-such, or even if it is, for it is demonstrated that an unmoveable thing is. But of the first subjects in which the attributes of sciences are finally resolved it is not doubted whether it is. And if in some specific science it is doubted, it is inquired in some superior science.|
|2. Et sic responsum est ad secundam. Unde conceditur quod non est idem si est et quia est, cuius est praecognitio et cuius est quaestio.||2. And thus is the response to the second argument. Wherefore it is conceded that 'if it is', and 'whether it is such-and-such' are not the same, of which it is something known beforehand, and of which it is a question.|
|3. Ad tertiam, conceditur quod in libro Elenchorum probatur et demonstratur syllogismum sophisticum esse, sed hoc est per habitum scientiae superioris, scilicet per metaphysicam.||3. To the third, it is conceded in the book De Sophisticis Elenchis that it is proved and demonstrated that a sophistical syllogism exists. But this is through something held in a superior science, namely through metaphysics.|
|4. Ad aliam dico quod licet de multis passionibus ad sensum apparentibus praecognoscatur quia est, tamen de multis dubitatur et inquiritur, +ut est simile de subiecto et passione+. Quia subiectum specialiter primum, ut subiectum in metaphysica, est conceptus simplex ad quem movetur intellectus ab ente sibi manifeste apparente; ideo non potest dubitari de illo si est. +Sed de subiecto exsistente noto+ tamen, propter connotationes passionum, potest dubitari an de illo verificetur hoc verbum 'est': quia potest esse dubium utrum dispositio connotata adiaceat rei pro qua subiectum supponit et utrum eodem modo adiaceat quo modo connotatur, quia si non, tunc de illo non verificatur hoc verbum 'est'.||4. To the other I say that although of many attributes appearing to sense, it is known beforehand that it is such-and-such, yet concerning many it is doubted and is investigated, as is similar concerning subject and attribute. For the primary subject in particular, such as the subject in metaphysics, is a simple concept to which the understanding is moved by the existing thing manifestly appearing to it. For that reason it is not possible to doubt of that, that it exists. But of a known existing subject, nonetheless, because of the connotations of the attributes, it can be doubted whether the word 'is' is verified of it, since it can be doubted whether the disposition that is connoted adjoins to the thing for which the subject stands, and whether it adjoins in the same way in which it is connoted, for if not, then the word 'is' is not verified of it.|
|5. Ad aliam, dico quod quid nominis de quolibet termino intrante demonstrationem debet praecognosci. Tamen aliquae definitiones possunt investigari per definitionem dicentem quid nominis praesuppositum. Concedo etiam quod nulla scientia potest investigare definitionem quidditativam sui subiecti primi nisi per habitum superioris scientiae: quia cum subiectum sit adaequatum scientiae, genus subiecti transcendit scientiam, et tamen genus intrat definitionem; ideo nec quid est nec quia est potest investigari de subiecto in scientia aliqua in qua illud est subiectum proprium.||5. To the other, I say that the nominal essence of any term entering a demonstration ought to be known beforehand. Yet some definitions can be investigated by means of the nominal definition being known beforehand. I also concede that no science can investigate the quidditative definition of its primary subject except by what is held of a superior science, since when the subject is adequate of the science, the genus of the subject transcends the science, and yet the genus enters the definition. For that reason neither what a thing is, nor that it is such-and-such can be investigated in some science in which that is the proper subject.|
|6. Ad aliam, quae arguit de conclusionibus negatiuis, dico quod conclusiones negativae indigent praemissis affirmativis, vel saltem praemissa affirmativa, in qua iam oportet de aliquo termino supponere quia est. Et si iste terminus sit passio, oportet quod resolvatur in subiectum prius de quo etiam sit notum quia est. Et quando arguitur de vacuo, dicerem quod de vacuo nullam habemus scientiam (et de hoc post magis quaeretur), sed scientiam magis habemus de loco, per quam scimus quod nullus locus est sine corpore; et per hoc scimus quod vacuum non est, et est illa scientia de loco.||6. To the other, which argues about negative conclusions, I say that negative conclusions require affirmative premisses, or at least an affirmative premiss, in which it is necessary of some term to suppose that it is such-and-such. And if that term is an attribute, it is necessary that it is resolved into a subject of which also it is known that it is such-and-such. And when the argument is about a vacuum, I would say that we have no science of a vacuum (and of this will be asked more later), but we have more science of place, through which we know that no place is without body, and through this we know that a vacuum does not exist, and that is our science of place.|
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