Here, in a new translation, are chapters 12 and 14 of the second part of Ockham's Summa Logicae, where he argues for something that looks very like Russell's theory of descriptions (and for very similar reasons).
Ockham begins with the idea of 'connotative' terms. See here for more on this. Briefly, a connotative term 'an F' is one which we can legitimately unpack into an expression of the form 'a thing which has F-ness'. Ockham, unlike Russell (and other modern logicians) thought that this is only possible for certain terms. 'A man', for example, is not connotative, and Ockham's 'theory of descriptions' does not apply to these.
When a term is connotative, we can unpack any proposition containing it into two separate propositions. Thus the apparently single proposition 'a donkey is a non-man' unpacks into the conjunction 'a donkey is something and it is not the case that a donkey is a man'. The proposition is 'exponible'.
Thus we can solve the problem of whether 'the chimaera is a non-man' is true or false. 'The chimaera is a man' can hardly be true, but then neither can 'the chimaera is a non-man'. Yet one or other of a proposition or its negation must be true or false, as Aristotle (and most logicians before or since) said. (This is exactly the problem that Russell addresses in his famous article 'On Denoting', of course).
Ockham argues that, since 'the chimaera is/is not a man' is really two propositions, namely 'the chimaera is something and it is/is not a man', when 'the chimaera is something' is true, one or the other of 'it is a man' and 'it is not a man' has to be true. So the propositions are contradictory when there are such things as chimaeras. But 'A chimaera is something' is not true (since this is equivalent to 'chimaeras exist'. Hence neither 'the chimaera is a man' (= the chimaera is something and it is a man') nor 'the chimaera is a non-man' (= the chimaera is something and it is not a man') is true.
Thus (chapter 14) we should not imagine that just because such terms as 'man', 'animal', 'hot', 'long', 'short' and suchlike mean something, that there are certain non-entities and impossible things, entirely distinct from beings, signified by terms such as 'chimera', 'goat-stag' and suchlike, 'as if there were one world of impossible things just as there is a world of things'. Finally, what about 'the chimaera is the chimaera'? Boethius says that no proposition is more true than one in which the same term is predicated of itself. Isn't that true? No, says Ockham, because nothing is predicated of anything here. It is not the case that the chimaera is something, so it isn't anything, and so nothing is predicated of anything.
There are a number of familiar ideas here:
1. We can resolve philosophical problems by analyzing potentially misleading propositions into their 'true' logical form.
2. There is a distinction between wide and narrow scope negation ('the king of France is not wise' and 'it is not the case that the king of France is wise'.
3. Existence is not a predicate. To be something, is to exist.
4. Propositions that assert the existence of a thing are false when there is no such thing. Thus a propositions like 'the king of France is not bald' does not say, of some king of France, that he is not bald, but that there is no entity who is both king of France, and bald.
Ockham appears to be missing only the idea that such propositions assert not only existence, but uniqueness. But the narrow formal logic within which he was working did not allow for such statements anyway; another thing he was missing was the predicate calculus in which Russell's theory is formally expressed. But that's another story.
|C.12. DE PROPOSITIONIBUS IN QUIBUS PONUNTUR TERMINI NEGATIVI, PRIVATIVI ET INFINITI||Chapter 12. On propositions in which there occur negative, privative and infinite terms.|
|Non solum autem propositiones in quibus ponuntur termini connotativi vel relativi sunt aequivalentes propositionibus hypotheticis, sed etiam propositiones in quibus ponuntur termini negativi, privativi et infiniti sunt aequivalentes propositionibus hypotheticis, quia etiam omnes tales termini sunt vere connotativi, eo quod in eorum definitionibus exprimentibus quid nominis debet poni aliquid in recto et aliquid in obliquo, vel in recto cum negatione praevia.||Now, not only propositions with connotative or relative terms are equivalent to hypothetical propositions, but also propositions with negative, privative and infinite terms are equivalent to hypothetical propositions, since all such terms also are truly connotative, seeing as in their nominal definitions should be put something in the nominative case and something in an oblique case (or in the nominative case with a previous negation).|
|Sicut definitio huius nominis 'immateriale' est ista 'aliquid quod non habet materiam', et definitio istius termini 'caecum' est ista 'aliquid carens visu quod natum est habere visum', et definitio istius termini 'non-homo' est ista 'aliquid quod non est homo', et sic de aliis.||(As for instance the definition of the name 'immaterial' is 'something which is not material', and the definition of 'blind' is 'something lacking sight which naturally is to have sight, and the definition of 'not a man' is 'something which is not a man', and so on).|
|Et ideo quilibet terminus talis est vere connotativus, quamvis non quilibet talis sit relativus, eo quod aliquando terminus talis potest de aliquo verificari, quamvis terminus obliquus sibi non possit vere et convenienter addi, sicut angelus est immaterialis, et tamen non oportet quod 'alicuius immaterialis' sit nec 'alicui immaterialis', et sic de aliis obliquis.||And for that reason any such term is truly connotative, although not every such term is relative, seeing as sometimes such a term can be truly predicated of something, although an oblique term cannot be added to it truly and consistently, just as an angel is immaterial and yet is not necessary that it is 'immaterial of something' nor 'immaterial to something' and so for other oblique cases.|
|Quaelibet autem propositio talis in qua ponitur terminus talis, duas ad minus habet exponentes, et aliquando habet plures; quod faciliter videri potest videndo definitionem exprimentem quid nominis ipsius termini.||But any such proposition in which such a term is put has at least two exponents, and sometimes more; which can easily be seen by looking at the nominal definition of the term itself.|
|Unde quaelibet propositio in qua ponitur terminus infinitus habet duas exponentes: unam affirmativam, in qua iste terminus 'aliquid' in singulari vel in plurali, vel aliquis alius terminus aequipollens tali, subicitur vel praedicatur.||Wherefore any proposition containing an infinite term has two exponents: one affirmative, in which the term 'something' in the singular or the plural, or some other term equivalent to it, is subject or predicate.|
|Unde ista 'asinus est non-homo' aequivalet isti 'asinus est aliquid et asinus non est homo'.||Wherefore 'a donkey is a non man' is equivalent to 'a donkey is something and it is not the case that a donkey is a man'.|
|Similiter ista 'angelus est immaterialis' aequivalet isti 'angelus est aliquid et angelus non habet materiam'.||Similarly, 'an angel is immaterial' is equivalent to 'an angel is something and an angel has no material'|
|Et hoc est intelligendum quando terminus talis negativus nihil significat negative nisi quod terminus oppositus significat affirmative.||And this is to be understood when such a negative term signifies nothing negatively unless the opposite term signifies affirmatively.|
|Quod dico ad excludendum istam instantiam: ista enim copu- lativa 'essentia divina est aliquid et non est genita' non aequivalet isti 'essentia divina est ingenita'.||Which I say in order to exclude this instance: for the conjunction 'the divine essence is something and it is not begotten' is not equivalent to 'the divine essence is unbegotten'.|
|Ex isto patet quod de virtute sermonis ista est neganda 'chimaera est non-homo', quia habet unam exponentem falsam, scilicet istam 'chimaera est aliquid'.||And from this is is clear that 'a chimera is a non-man' is literally false, because it has one false exponent, namely 'a chimera is something'.|
|Similiter si nullus homo sit albus, haec est neganda de virtute sermonis 'homo albus est non-homo', quia ista exponens est falsa 'homo albus est aliquid'.||Similarly if no man is white, 'a white man is something', taken literally, is to be denied, because 'a white man is something' is false.|
|Et si dicatur quod, secundum Aristotelem, alterum contradictoriorum dicitur de quolibet; si igitur chimaera non sit non-homo, igitur chimaera est homo: Dicendum est, secundum intentionem Aristotelis, quod non de quolibet termino significative sumpto dicitur alterum contradictoriorum incomplexorum, sicut de hoc nomine 'chimaera' significative sumpto nec dicitur 'homo' nec 'non-homo'.||It may be said, according to Aristotle, that one or the other of contradictories is said of anything; if therefore a chimaera is not a non-man, therefore a chimaera is a man. The reply is that, according to the intention of Aristotle, it is not true of any term whatsoever, taken significatively, that one or the other of contradictory terms is said of it; for example, neither man or non-man is said of the name 'chimaera', taken significatively.|
|Tamen de omni termino supponente significative, non includente aequivalenter aliquod syncategorema vel aliam determinationem, de quo praedicatur vere 'ens' vel 'aliquid', dicitur alterum contradictoriorum.||Yet of every term denoting significatively not including some syncategoremata or other determinate term, of which is truly predicated 'being' or 'something', is said one or the other of contradictories.|
|Unde si haec esset vera 'chimaera est aliquid', altera istarum esset vera 'chimaera est homo', 'chimaera est non-homo'.||Wherefore if 'a chimaera is something' were true, one or the other of 'a chimaera is a man' or 'a chimaera is a non-man' would be true.|
|Et ideo concedendum est quod non de quolibet significative sumpto dicitur alterum contradictoriorum, tamen hoc non obstante de quolibet tali quidlibet vere affirmatur vel vere negatur.||And for that reason it is to be granted that not of any [term] taken significatively is said one or the other of contradictories, yet this does not prevent anything being truly affirmed or truly denied of any such term.|
|Et hoc intendit Aristoteles quando dicit : "De quolibet affirmatio vel negatio", et de nullo eorum ambo.||And this is what Aristotle intends when he says 'Of anything either affirmation or negation', and of none of them both.|
|Unde quamvis nec 'homo' nec 'non-homo' dicatur de chimaera, tamen homo vere affirmatur vel negatur de chimaera, unde altera istarum est vera '‚chimaera est homo', 'chimaera non est homo'.||Wherefore although neither 'man' or 'non man' is said of the chimaera, yet 'man' is truly affirmed or denied of the chimaera, wherefore one or the other of 'a chimaera is a man' or 'it is not the case that a chimaera is a man' is true.|
|Similiter altera istarum est vera 'chimaera est non-homo', 'chimaera non est non-homo'.||Similarly one or the other of 'a chimaera is a non-man' or 'it is not the case that a chimaera is a non-man' is true.|
|Et sic de istis 'homo albus est homo', 'homo albus non est homo', 'homo albus est non-homo', 'homo albus non est non-homo'.||And so for 'a white man is a man' and 'it is not the case that a white man is a man', 'a white man is a non-man' and 'it is not the case that a white man is a non-man'|
|Quod autem neutra istarum sit vera 'homo albus est homo', 'homo albus est non-homo', posito quod nullus homo sit albus, potest ostendi: nam si haec sit vera 'homo albus est non-homo', cum sit affirmativa oportet quod subiectum supponat pro aliquo.||However, it can be shown that neither 'a white man is a man' or 'a white man is a non-man' is true, having posited that no man is white: for if 'a white man is a non-man' is true, it must denote something, since it is affirmative.|
|Quo dato quaero: pro quo supponit? Non pro voce nec pro conceptu, cum supponat significative et non materialiter neque simpliciter; igitur supponit pro aliquo alio.||If so, I ask, what does it denote? Not a sound or a concept, since it denotes significatively and not materially or simply, therefore it denotes something else.|
|Et per consequens iste terminus 'homo albus' significative sumptus praedicaretur de pronomine demonstrante illud pro quo supponit, et per consequens haec esset vera 'hoc est homo albus'; quod est manifeste falsum.||And in consequence the term 'a white man' taken significatively would be predicated of a pronoun referring to what it denotes, and in consequence 'this is a white man' would be true, which is manifestly false.|
|Quia si sit vera, aut demonstratur ens aut non-ens.||Because if it is true, it refers to either a being or a non-being.|
|Si ens, ergo aliquod ens esset homo albus, quod est contra positum; si non-ens, igitur aliquod non-ens esset homo albus, et per consequens esset album, quod est manifeste falsum.||If a being - therefore some being – were a white man, that is contrary to what was supposed; if a non-being, then some non-being would be a white man, and in consequence would be white, which is manifestly false.|
|Et ita patet quod haec est falsa 'homo albus est non-homo', si nullus homo sit albus.||And so it is clear that 'a white man is a non-man' is false, if no man is white.|
|Et per eandem rationem possunt consimiles probari esse falsae.||And by the same reason, similar things can be shown to be false.|
|CAP.14. DE PROPOSITIONIBUS IN QUIBUS PONUNTUR FIGMENTA QUIBUS NIHIL CORRESPONDET EX PARTE REI: QUOMODO DEBENT EXPONI?||C. 14 ON PROPOSITIONS IN WHICH OCCUR FIGMENTS TO WHICH NOTHING CORRESPONDS IN REALITY: WHAT SHOULD BE GIVEN AS THEIR EXPONENTS?|
|Sicut propositiones in quibus ponuntur termini negativi et privativi habent plures exponentes, ita propositiones in quibus ponuntur figmenta, hoc est in quibus ponuntur termini ficti quibus nihil correspondet a parte rei tale quale finguntur significare, plures habent exponentes.||Just as propositions with negative and privative terms have more than one exponent, so propositions in which figmenta are posited (that is, propositions in which invented terms are posited, to which nothing corresponds in the world of things such as they are made up to signify) have more than one exponent.|
|Tales enim termini vere sunt connotativi, nec aliquid imaginabile per eos significatur nisi vera res quae est in actu vel esse potest vel saltem potuit fuisse vel fuit in actu.||For such terms are really 'connotative', and it is false that something imaginable is signified by them except a real thing which is actual or could be actual or at least could have been or was actual.|
|Unde sicut termini negativi et privativi nihil significant nisi quod significatur per terminos positivos, quamvis illud idem quod significatur per terminum affirmativum positive et construendo vel affirmative, significetur per terminum negativum vel privativum non construendo sed destruendo vel negando, secundum modum loquendi Anselmi, ita per tales terminos fictos, cuiusmodi sunt 'chimaera', 'tragelaphus', 'vacuum', 'infinitum' et huiusmodi, nihil significatur nisi quod significatur per terminos alios, sicut patet ex definitionibus exprimentibus quid nominis eorum.||Wherefore just as negative and privative terms signify nothing except what is signified by positive terms, even though that same thing which is signified positively by an affirmative term and by constructing or affirmatively, is signified by a negative or privative term that is not by constructing, but by destroying or negating, according to Anselm's way of speaking. Thus by such made up terms, like 'chimera', 'tragelaphus', 'vacuum', 'infinitum' and the like, nothing is signified but what is signified by other terms, such as is clear from their nominal definitions.|
|Tamen non eodem modo significantur res per istos terminos et alios, sed sic significantur per alios quod pro illis rebus alii termini supponere possunt, isti autem termini non possunt pro eis supponere, sicut nec definitiones exprimentes quid nominis eorum.||Yet things are not signified in the same way by these and other terms, rather, they are signified by other terms in such a way that the other terms can denote those things, but those terms cannot denote them, insofar as they are not their nominal definitions.|
|Unde non est imaginandum quod sicut sunt quaedam entia significata per tales terminos 'homo', 'animal', 'album', 'calidum', 'longum', 'breve' et huiusmodi, ita sunt quaedam non-entia et impossibilia, distincta totaliter ab entibus, significata per tales terminos 'chimaera', 'hircoceruus' et huiusmodi, quasi esset unus mundus ex impossibilibus sicut est unus mundus ex entibus.||Wherefore it should not be imagined that just as there are certain entities signified by such terms as 'man', 'animal', 'hot', 'long', 'short' and suchlike, so there are certain non-entities and impossible things, entirely distinct from beings, signified by terms such as 'chimera', 'hircocercus' and suchlike, as if there were one world of impossible things just as there is a world of things.|
|Sed quidquid imaginabile significatur per hoc nomen 'chimaera' significatur per aliquem terminum de quo in propositione de inesse vel de possibili praedicatur esse; tamen hoc nomen 'chimaera' pro illo non potest supponere. Propter quod quaelibet propositio affirmativa, in qua subicitur hoc nomen 'chimaera' significative sumptum vel praedicatur, vel aliquid consimile, est falsa de virtute sermonis, quia habet aliquam exponentem falsam. Ista enim est falsa de virtute sermonis 'chimaera est non-ens' et quaelibet consimilis, quia quaelibet talis habet istas exponentes 'chimaera est aliquid' et 'illud est non-ens' quarum prima falsa est.||But whatever imaginable is signified by the name 'chimera' is signified by some term concerning which an indicative or possible proposition is predicated; yet the name 'chimera' cannot denote that. On account of which any affirmative proposition, in which the name 'chimera' is subject taken significatively or predicated, or something similar, is literally false, because it has some false exponent. For 'a chimera is a non-being' is literally false, and so is anything similar, because whatever of that sort has the exponents 'a chimera is something' and 'that thing is a non-entity', of which the first is false.|
|Et si dicatur: numquid ista est vera 'chimaera est chimaera'? Videtur quod sic, eo quod praedicatur idein de se, et Boethius dicit quod nulla propositio est verior illa in qua idem de se praedicatur.||And if it is objected: whether the proposition "the chimaera is the chimaera" is true? It seems so, seeing as it is predicated of itself, and Boethius says that no proposition is more true [than] that in which the same thing is predicated of itself.|
|Dicendum est quod de virtute vocis ista est falsa 'chimaera est chimaera' si termini supponant significative, eo quod falsum implicatur.||In reply, the proposition "the chimaera is the chimaera" is literally false if the terms denote significatively, in that something false is implied by it.|
|Et ad Boethium dicendum quod Boethius intendit quod nulla propositio in qua aliquid praedicatur de aliquo est verior illa in qua idem praedicatur de se.||And concerning the point about Boethius, it should be said that he meant that no proposition in which something is predicated of something is more true than that in which the same thing is predicated of itself.|
|Quia tamen ista est negativa, cum ista stat quod nulla sit vera: nec illa in qua idem praedicatur de se nec illa in qua praedicatur aliud.||For nevertheless that point is a negative one, since it is consistent with neither proposition being true - neither that in which the same thing is predicated of itself, nor that in which another thing is predicated of that thing.|
|Si tamen illa esset vera in qua de aliquo praedicatur aliquid, illa esset vera in qua praedicatur idem de se. Sicut si haec esset vera 'chimaera est aliquid', haec esset vera 'chimaera est chimaera'.||Still, if it were true where something is predicated of something, it would be true in which the same thing is predicated of itself (for example if "the chimaera is something" is true, "the chimaera is the chimaera" is true).|
|Et ita nulla propositio in qua praedicatur aliquid de hoc nomine 'chimaera', significative sumpto, potest esse verior illa in qua hoc nomen 'chimaera' praedicatur de se ipso. Cum hoc tamen stat quod nec illa nec ista sit vera.||And in this way no proposition in which is predicated something with the name "chimaera", taken significatively, can be more true [than] that in which "chimaera" is predicated of itself. But still, this is consistent with neither one nor the other being true.|
THE LOGIC MUSEUM Copyright (introduction and translation) © E.D.Buckner 2006.