Authors/Ockham/Summa Logicae/Book III-3/Chapter 8

Latin	English
CAP. 8. DE REGULIS PER QUAS TENENT CONSEQUENTIAE INFERENTES NEGATIVAM EX NEGATIVA.	Chapter 8. Concerning the rules by which the consequences hold that infer the negative from the negative.
Declaratis aliquibus regulis deservientibus consequentiis inferentibus affirmativam ex affirmativa, nunc dicendum est de regulis per quas tenent consequentiae inferentes negativam ex negativa.	Having explained some of the rules that govern consequences inferring the positive from the positive, we must now speak of the rules by which consequences hold that infer the negative from the negative.
Et est una regula complectens multas, quae est talis: a definitione ad definitum, a descriptione ad descriptum, a nominis interpretatione ad interpretatum, ab uno convertibilium ad reliquum, et e converso, tenet consequentia sive praeponatur sive postponatur negatio.	And there is one rule embracing many, which is as follows: from definition to defined, from description to described, from the interpretation of a name to the interpreted, from one convertible to the other, and vice versa, the consequences hold whether the negation is put forward or postponed.
Et sunt istae regulae intelligendae supponentibus omnibus terminis personaliter et nulla alia variatione facta circa propositiones. Et ideo tales consequentiae non valent `homo non est passio hominis, ergo risibile non est passio hominis'; `animal rationale non est definitum, igitur homo non est definitum' et huiusmodi.	And these rules are to be understood supposing all the terms personally and without any other variation made about the propositions. And therefore such conclusions are not valid: `man is not a man's attribute, therefore man's attribute is not laughable'; `a rational animal is not defined, therefore man is not defined' and the like.
Alia regula est: ab inferiori ad superius postposita negatione est ƿ bona consequentia; sicut sequitur `homo non currit, igitur animal non currit'. Sciendum quod quando praedicatio superioris de inferiori est necessaria, tunc est talis consequentia simplex, quando autem talis praedicatio est contingens, tunc dum talis propositio est vera, est bona consequentia, sed ut nunc solum; quando autem talis propositio est falsa, tunc consequentia non valet.	There is another rule: from the inferior to the superior by negation, is a good consequence; as it follows, `a man does not run, therefore an animal does not run'. It should be known that when the predication of the superior from the inferior is necessary, then such a conclusion is simple, but when such a predication is contingent, then while such a proposition is true, it is a good consequence, but for now only; but when such a proposition is false, then the conclusion is invalid.
Unde si nullus homo sit, haec consequentia non valet `homo non currit, ergo animal non currit'. Per istam regulam tenent tales consequentiae `asinus non est homo, igitur animal non est homo'; `fortitudo non est temperantia, igitur virtus non est temperantia', et huiusmodi multae.	Hence, if there is no man, this conclusion does not hold: `a man does not run, therefore an animal does not run.' By this rule hold such conclusions as `an ass is not a man, therefore an animal is not a man'; `fortitude is not temperance, therefore virtue is not temperance,' and many such things.
Alia regula est: a superiori ad inferius praeposita negatione est bona consequentia; sicut sequitur `Sortes non est animal, ergo Sortes non est asinus'. Intelligendum quod talis consequentia semper est simplex, sive descendatur ad inferius per se sive ad inferius per accidens.	There is another rule: from the superior to the inferior, there is a good consequence by negation; as it follows, `Socrates is not an animal, therefore Socrates is not an ass.' It must be understood that such a consequence is always simple, whether it descends to the inferior bessentially or to the inferior by accident.
Et ideo tales consequentiae sunt bonae `aggregatum per accidens non est animal, igitur aggregatum per accidens non est homo albus'; `ens per accidens non est homo, igitur ens per accidens non est homo niger', et sic de aliis.	And therefore such conclusions are good: `accidentally aggregated is not an animal, therefore an accidentally aggregated is not a white man'; `a being by accident is not a man, therefore a being by accident is not a black man', and so on of others.
Sed intelligendum quod tales consequentiae non valent quando aliquod adverbium vel praepositio cum suo casuali vel aliqua determinatio aequivalens tali sequitur negationem in prima propositione.	But it must be understood that such consequences do not apply when some adverb or preposition with its casual or some determination equivalent to such follows a negation in the first proposition.
Et propter hoc tales consequentiae non valent `homo non est necessario corpus, ergo homo non est animal'; `homo non est necessario coloratus, ergo homo non est albus'. Si tamen illa determinatio poneretur uniformiter in antecedente et consequente, frequenter valeret consequentia.	And for this reason such conclusions are not valid: `man is not necessarily a body, therefore man is not an animal'; 'Man is not necessarily colored, therefore man is not white.' If, however, that determination were placed uniformly in the antecedent and the consequent, the consequence would frequently be valid.
Aliquando tamen non valeret; sicut non sequitur `homo non est primo corpus, igitur homo non est primo animal'. Similiter non sequitur `Sortes non est primo animal, ergo Sortes non est primo homo', intelligendo per `primo' quod inter subiectum et praedicatum non sit medium.	Sometimes, however, it would not be valid; just as it does not follow that `man is not first a body, therefore man is not first an animal'. Similarly, it does not follow that `Socrates is not first an animal, therefore Socrates is not first a man', understanding by `first' that there is no middle ground between the subject and the predicate.
Alia regula est: a negatione inferioris ad negationem superioris, sumpti cum signo universali affirmativo, vel stantis immobiliter, est ƿ bona consequentia; sicut sequitur `Sortes non est iste homo, ergo Sortes non est omnis homo'.	Another rule is: from the negation of the inferior to the negation of the superior, taken with the universal affirmative sign, or standing motionless, is a good consequence; as it follows, `This man is not Socrates, therefore not every man is Socrates.'
Sed intelligendum est quod talis consequentia non est semper consequentia simplex; sed quando illud superius praedicatur necessario de illo inferiori, tunc est consequentia simplex; quando contingenter solum, tunc dum illa propositio est vera, est consequentia bona, quando non est vera, consequentia non valet.	But it must be understood that such a consequence is not always a simple consequence; but when that which is superior is necessarily predicated of that which is inferior, then the consequence is simple; when only tangentially, then as long as that proposition is true, the conclusion is good; when it is not true, the conclusion is invalid.
Unde dum Plato est homo, ista consequentia est bona `Sortes non est Plato, igitur Sortes non est omnis homo', sed quando Plato non est homo, tunc non valet consequentia. Ex isto patet quod si `differre', `esse aliud', `distingui' significent idem quod `non esse idem', tales consequentiae valent: `Sortes differt a Platone, ergo Sortes differt ab omni homine'; `Sortes est alius a Platone, igitur Sortes est alius ab omni homine'; `Sortes distinguitur a Platone, igitur Sortes distinguitur ab omni homine', sicut ista consequentia est bona `Sortes non est Plato, ergo Sortes non est omnis homo'.	Hence, while Plato is a man, this conclusion is good: `Socrates is not Plato, therefore not every man is Socrates', but when Plato is not a man, then the conclusion is not valid. From this it is clear that if `to differ', `to be different', `to distinguish' mean the same thing as `not to be the same', the following conclusions are valid: `Socrates differs from Plato, therefore Socrates differs from every man'; `Socrates is different from Plato, therefore Socrates is different from every man'; `Socrates is distinguished from Plato, therefore Socrates is distinguished from every man', just as this conclusion is good `Socrates is not Plato, therefore Socrates is not every man.'
Si autem `differre', `esse aliud', `distingui' significent idem quod `esse non idem', tunc consequentia non valet. Verumtamen potest distingui de `non idem', quia uno modo potest esse terminus relativus, alio modo potest esse terminus mere infinitus.	But if `to differ', `to be different', `to be distinguished' mean the same thing as `to be not the same', then the conclusion does not hold. However, it can be distinguished from 'not the same', because in one way it can be a relative term, in another way it can be a purely infinite term.
Si sit terminus relativus, tunc non valet ista consequentia `Sortes differt a Platone, igitur Sortes differt ab omni homine', sicut non sequitur `Sortes non est idem Platoni, igitur Sortes non est idem omni homini'.	If it is a relative term, then the conclusion that `Lots differs from Plato, therefore Socrates differs from every man,' does not hold, just as it does not follow that `Socrates is not the same as Plato, therefore Socrates is not the same for every man.'
Cuius ratio: quia si `non idem' sit terminus relativus, li non, eo quod est pars dictionis, non habet aliquam vim mobilitandi vel immobilitandi terminum sequentem; et ideo terminus sequens eodem modo stabit mobiliter vel immobiliter sicut si quicumque alius terminus relativus sibi adderetur.	The reason for this: because if `not the same' is a relative term, or not, because it is part of a sentence, it does not have any power to move or immobilize the following term; and therefore the following term will stand mobile or immovable in the same way as if any other relative term were added to it.
Et ideo sicut in ista `Sortes est idem omni homini', li homini stat mobiliter, ita quod sub ipso contingit descendere, sic in ista `Sortes est non idem omni homini' stabit `homini' mobiliter et contingit sub eo descendere, et ita sequitur `Sortes est non idem omni homini, ergo Sortes est non idem Sorti'.	And therefore, just as in that `Socrates is the same as every man', it stands mobilely for man, so that it may descend under that, so in that `Socrates is not the same as every man, `Socrates' stands mobilely for man and happens to descend under it, and so it follows that `Socrates is not the same as every man, therefore Socrates is not identical with Socrates.'
Si autem `non idem' sit terƿ minus mere infinitus, tunc vel talis propositio erit impropria `Sortes est non idem omni homini', pro eo quod casus dativus sequitur nomen non relativum, vel si sit propria, negatio --- cum sit pars termini --- non habet virtutem super terminum sequentem ad mutandum eius suppositionem.	But if `not the same' is a merely infinite term, then either such a proposition as `Socrates is not the same as every man' will be improper, because the dative case follows a non-relative noun, or if it is proper, the negation --- since it is part of the term --- has no power over the following term to change its supposition.
Et per consequens li homini stabit mobiliter, et tunc erit haec falsa `Sortes est non idem omni homini', quia infert istam `Sortes est non idem Sorti'. Et tunc talis consequentia non valebit `Sortes est alius a Platone, igitur Sortes est alius ab omni homine'; nec infertur negativa ex negativa sed affirmativa ex affirmativa.	And as a result, that person will stand immovably, and then this statement will be false, ``Lots are not the same for every man, because it implies that ``Lots is not the same for Lot. And then such a conclusion will not be valid: `Socrates is different from Plato, therefore Socrates is different from every man'; nor is the negative derived from the negative, but the positive from the positive.
Et si quaeratur, quis sensus est magis de virtute sermonis, dicendum quod dialectici magis utuntur primo. Et ideo omnes tractantes sophismata, quos ego vidi, dicunt tales consequentias esse bonas `Sortes distinguitur a Platone, ergo Sortes distinguitur ab omni homine'; `Sortes differt ab asino, ergo Sortes differt ab omni animali'.	And if it be asked, which sense is more powerful in speech, it must be said that the dialecticians make more use of the former. And therefore all the treaters of sophistry, whom I have seen, say that such conclusions are good: 'Socrates is distinguished from Plato, therefore Socrates is distinguished from every man'; `Socrates is different from an ass, therefore Socrates is different from every animal.'
Et similiter tales `Sortes differt ab animali, igitur Sortes differt ab homine'; `Sortes est alius ab homine, igitur Sortes est alius a Sorte' et huiusmodi. Et super istum sensum dant regulas suas, videlicet quod ad alietatem vel differentiam superioris sequitur alietas et differentia inferioris; et quod isti termini `differre', `esse aliud', `distingui' et huiusmodi, habent naturam confundendi terminum sequentem confuse et distributive, si prius stetit immobiliter, et quod habent vim immobilitandi terminum sequentem, si prius stetit mobiliter, et huiusmodi, quae omnes ad istas reduci possunt.	And likewise such as `Socrates differs from an animal, therefore Socrates differs from man'; `Socrates is different from man, therefore Socrates is different from Socrates' and the like. And on this meaning they give their rules, namely, that to the distinction or difference of the superior follows the distinction and difference of the inferior; and that these terms 'to differ', 'to be different', 'to distinguish', and the like, have the nature of confusing the following term in a confused and distributive manner, if it previously stood immobile, and that they have the power of immobilizing the following term, if it previously stood mobile, and the like, all of which can be reduced to these.
Sed alii ab istis communiter utuntur alio modo.	But others of these generally use another mode.
Et secundum istas diversas significationes istorum terminorum debet de consequentiis multis diversimode dici. Unde primi, qui dicunt quod `differre', `esse aliud', `distingui' significant idem quod `non esse idem', debent negare multas consequentias in quibus arguitur ab aliquo istorum, sumpto cum determinatione adverbiali sequente vel aequivalente, ad ipsum sine tali determinatione sumptum.
Et tamen si talis determinatio praeponeretur, esset consequentia bona. Unde tales consequentias habent negare `hoc distinguitur ƿ formaliter ab hoc', puta `essentia divina distinguitur formaliter a paternitate, ergo essentia divina distinguitur a paternitate'; `hoc per accidens distinguitur ab hoc, ergo hoc distinguitur ab hoc'. Nam haec est vera `essentia divina non est formaliter paternitas' et tamen haec est falsa `essentia divina non est paternitas', et per consequens antecedens primae consequentiae est verum, et tamen consequens falsum, secundum eos, si illae duae aequipolleant istis duabus.
Similiter haec est vera `Deus non est per accidens idem Deo' et tamen haec est falsa `Deus non est idem Deo', ergo secunda consequentia non valet si istae duae aequivaleant istis duabus.
Et tamen istae consequentiae sunt bonae `essentia divina formaliter distinguitur a paternitate, ergo essentia divina distinguitur a paternitate'; `Deus per accidens distinguitur a Deo, ergo Deus distinguitur a Deo', sicut istae sunt bonae `essentia divina formaliter non est paternitas, igitur essentia divina non est paternitas'; `Deus per accidens non est Deus, igitur Deus non est Deus'.
Et ideo illi qui dant regulas praedictas sophisticas quod `ad alietatem superioris' etc., et negant tales propositiones `homo distinguitur per accidens ab homine', `essentia divina distinguitur formaliter a paternitate', `homo est aliud per accidens ab animali', non dicunt consequenter.
Alii autem tales consequentias `a distinguitur formaliter a b, igitur a distinguitur a b'; `a distinguitur per accidens a b, igitur a distinguitur a b', habent concedere, sicut sequitur `a non est idem formaliter b, igitur a non est idem b'; `a non est idem per accidens b, igitur a non est idem b'.
Et tunc haec est falsa `essentia divina distinguitur formaliter a paternitate' et ista similiter `essentia divina distinguitur per accidens a paternitate', sicut utraque istarum est falsa `essentia divina est non eadem formaliter paternitati', `essentia divina est non eadem per accidens paternitati'.
Sed ista est concedenda `essentia divina non est eadem formaliter paternitati'. Et tunc de istis propositionibus est proportionaliter dicendum sicut de istis `Deus est non idem per accidens Deo', `Deus est per accidens idem Deo', `Deus non est per accidens idem Deo', ƿ `Deus distinguitur per accidens a Deo', `Deus per accidens distinguitur a Deo', quia omnes sunt falsae praeter istam `Deus non est per accidens idem Deo'. Ita omnes aliae sunt falsae praeter istam `essentia divina non est eadem formaliter paternitati', secundum istam opinionem. Et ideo utraque istarum est neganda, secundum istam opinionem, `essentia divina est eadem formaliter paternitati', `essentia divina distinguitur formaliter a paternitate', sicut utraque istarum est neganda `Deus est idem per accidens Deo', `Deus distinguitur per accidens a Deo'.
Alia regula est: a negatione alicuius ad negationem eiusdem cum aliqua determinatione est bona consequentia; sicut sequitur `Sortes non est homo, igitur Sortes non est per accidens homo'; `Sortes non currit, igitur Sortes non currit velociter'. Et ideo tales consequentiae sunt bonae `grammaticus non distinguitur a clerico, ergo grammaticus non distinguitur a clerico in quantum logicus'; `natura specifica non est differentia individualis, igitur natura specifica non est realiter differentia individualis'; `homo non est humanitas, igitur homo non est realiter humanitas'; `entitas non est unitas, igitur entitas non est realiter unitas'.
Et si dicatur quod tunc sequeretur `homo non est asinus, ergo homo non est idem specie asino', dicendum quod regula est intelligenda quando nulla fit variatio circa alios terminos propositionum nisi appositio talis determinationis vel ablatio.
Nunc autem in proposito `asinus' in antecedente accipitur in recto et in consequente in obliquo, ideo non valet `homo non est asinus, ergo homo non est idem specie asino', sed sequitur `ergo homo non est specifice asinus'.
Sciendum quod quando illa determinatio est adverbium vel aequivalens adverbio, semper est regula bona. Si autem sit adiectivum vel praepositio cum suo casuali, de quo illud determinabile non oportet quod praedicetur, quamvis de utroque aliquid verificetur, tunc non valet.
ƿ Et ideo non sequitur `Sortes non est homo, igitur Sortes non est homo mortuus'; nec sequitur `Sortes non est albus, igitur Sortes non est albus secundum dentes'.
Intelligendum etiam est quod regula est vera quando negatio praecedit tam determinans quam determinabile.