Authors/Ockham/Summa Logicae/Book II/Chapter 12

Latin	English
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 a non-man', 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.	}