Authors/Ockham/Summa Logicae/Book III-3/Chapter 32

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Latin English
[CAP. 32. QUO MODO IN PROPOSITIONIBUS DE INESSE FIT INDUCTIO] [Chapter 32. How induction comes about in assertoric propositions]
His visis videndum est quomodo diversae propositiones universales inducuntur ex suis singularibus et quomodo universales inferunt singulares. Et primo de illis de praesenti et de inesse. Having looked at these things, we should see how diverse universal propositions are induced[1] from their singulars, and how universals imply singulars. And first, of present tense assertoric propositions. 
Et est sciendum quod quandoque talis universalis habet singulares et quandoque non habet singulares. Quando enim subiectum verificatur de aliquo, tunc habet singulares, quando autem non verificatur de aliquo, tunc non habet singulares. And it should be known that sometimes such a universal has singulars and sometimes it does not have singulars. For when the subject is verified of something, then it has singulars, but when it is not verified of something, then it does not have singulars.
Et ideo si nullus homo esset albus, ista `omnis homo albus est homo' non haberet aliquam singularem; quando autem aliquis homo est albus, tunc habet singularem. And therefore if no man were white, the proposition 'every white man is a man' would not have any singular, but when some man is white, then it has a singular.
Et ita est de aliis. Et ideo aliquando etiam eadem universalis potest inferri ex suis singularibus, quando scilicet habet singulares, et quandoque non potest induci ex suis singularibus, quando scilicet non habet singulares. And so for others. And therefore sometimes also the same universal can be inferred from its singulars, namely when it has singulars, and sometimes it cannot be induced from its singulars, namely when it does not have singulars.
Sunt autem istae regulae. And there are these rules.
Una est quod quaelibet universalis vera, affirmativa, de praesenti, non aequivalens propositioni de futuro, et > de inesse habet aliquam singularem veram. Si autem sit falsa, non oportet quod habeat aliquam singularem falsam, sed sufficit quod nullam singularem habeat, et tamen quod denotetur habere; sicut per istam `omnis chimaera est' denotatur quod habeat aliquam singularem veram, et nullam habet, ideo est falsa. One is that any true affirmative present tense universal proposition, not equivalent to a future tense proposition, and assertoric, has some true singular. But if it is false, it does not have to have any false singular, but it is sufficient that it has no singular, and still it is denoted to have one. For example, by the proposition 'every chimera exists', it is denoted that it has a true singular, and it has none, therefore it is false.
Alia regula est: si omnes singulares alicuius propositionis universalis sint verae, universalis est vera. Another rule is that if all singulars of any universal proposition are true, the universal is true.
Et ista regula est generalis tam de affirmativa quam de negativa. Alia regula est: si universalis negativa sit falsa, oportet quod aliqua singularis sit falsa; sicut si haec sit falsa `nullum animal est asinus', oportet quod aliqua eius singularis sit falsa. And this rule is common to negatives as well as affirmatives. Another rule is that if the universal negative is false, some singular has to be false. For example, if 'no animal is a donkey' is false, it has to be that one of its singulars is false.
Sed ad veritatem universalis negativae non oportet quod aliqua singularis sit vera, quia non oportet quod habeat aliquam singularem; sicut si nihil sit album, haec est vera `nullum album est coloratum', et tamen nulla singularis eius est vera. But for the truth of the universal negative it does not have to be that any singular is true, for it does not have to have any singular. For example, if nothing is white, 'no white thing is coloured' is true, and yet none of its singulars is true.
Si dicatur quod hoc posito haec est vera `hoc album non est coloratum', demonstrato quocumque, dicendum quod quamvis talis sit vera `hoc album non est coloratum', demonstrato quocumque, ista tamen non est singularis huius universalis `nullum album est coloratum'. If it is said that, in that case, 'this white thing is not coloured', pointing to anything, it should be said that such a proposition as 'this white thing is not coloured' is true, pointing to anything, that proposition is not a singular of the universal proposition 'no white thing is coloured'.
Nam ad hoc quod aliqua singularis sit singularis alicuius universalis, requiritur quod subiectum universalis vere praedicetur de subiecto singularis. Sic autem non est in proposito; haec enim non est vera, illo posito, `hoc album est album', demonstrato quocumque. For, in order that any singular proposition is the singular of some universal proposition, it is required that the subject of the universal is truly predicated of the subject of the singular.  But it is not the case here, for given that, 'this white thing is white' is not true - pointing to anything.
Et si dicatur quod quaelibet singularis est singularis alicuius universalis, dicendum quod hoc non est verum. Unde ista `iste homo est animal', demonstrando asinum, non est singularis alicuius universalis. And if it is said that any singular is the singular of some universal, it should be said that this is not true.  Hence 'this man is an animal' - pointing to a donkey - is not the singular of any universal.
Sed quaelibet singularis, in qua non demonstratur aliquid de quo falsificatur terminus communis sibi additus, est singularis alicuius universalis. Non sic autem est hic: hoc album non est coloratum. But any singular in which something is pointed to, of which a common term added to it is not falsified, is the singular of some universal.  But this is not the case with 'this white thing is not coloured'.
Circa universalem de praeterito intelligendae sunt regulae sicut de universali de praesenti. > Sed circa inductionem propositionis universalis de futuro est primo sciendum quod dicendum est eodem modo de inductione propositionis universalis de futuro necessariae et impossibilis sicut de illis de praesenti et de praeterito. Concerning a universal [proposition] in the past tense, the rules are to be understood just as for a universal in the present tense.  But concerning the induction of a future tense universal proposition, it should be known first that we should speak in the same way of the induction of a future tense proposition of the necessary and of the impossible, as of those of past and present tense.
Sed circa inductionem propositionis universalis de futuro in materia contingenti aliter dicendum est secundum veritatem et aliter secundum intentionem Aristotelis. Et oritur ista diversitas ex hoc quod aliter sentiendum est de veritate propositionis contingentis de futuro secundum veritatem et fidem et aliter secundum intentionem Aristotelis. But concerning the induction of a universal proposition in the future tense in contingent material, we must speak in one way according to truth and in another way according to the intention of Aristotle.  And that diversity arises from the fact that we must judge the truth of a future contingent proposition in one way according to truth (and faith), and in another way according to the intention of Aristotle.
Nam Aristoteles ponit quod nulla propositio contingens talis de futuro est vera vel falsa, ita quod secundum intentionem Aristotelis una pars contradictionis in talibus non est magis vera quam alia. For Aristotle proposes that no such future contingent proposition is true or false, so that according to the intention of Aristotle, one part of a contradiction involving such propositions is no more true than the other.
Et propter hoc, secundum eum, una pars contradictionis non est magis scita a quocumque intellectu quam alia, quia quod non est magis verum, non est magis scibile. Et propter hoc Aristoteles non posuisset aliquod futurum contingens esse scitum a Deo, cum nullum tale, secundum eum, sit verum, et nihil est scitum nisi verum. And because of this, according to him, one part of the contradiction is no more known by any understanding than another, because what is not more true, is not more knowable.  And because of this, Aristotle did not suppose that any future contingent proposition is known by God, since no such proposition, according to him, is true. But nothing is known except what is true.
Sed veritas fidei ponit quod futura contingentia sunt scita a Deo, ita quod una pars contradictionis est scita a Deo et alia non est scita a Deo. Sicut Deus ab aeterno scivit istam `Beata Virgo est salvanda' et numquam scivit istam `Beata Virgo non est salvanda', sicut nec unquam scivit istam `Beata Virgo est damnanda'. But the truth of faith supposes that future contingents are known by God, so that one part of a contradiction is known by God, and the other part is not known by God.  For example, God has known from eternity the proposition 'the blessed Virgin is to be saved', and has never known the proposition 'the blessed Virgin is to be damned'
Et propter hoc una pars contradictionis est scita et non alia; ideo una pars est vera, puta illa quae est scita, et alia non est vera, quia non est scita a Deo. Secundum igitur intentionem Aristotelis universalis affirma>tiva de futuro poterit esse vera, quamvis nulla singularis sit vera. And because of this, one part of the contradiction is known, and not the other, therefore one part is true, namely that which is known, and the other is not true, because it is not known by God.  Therefore, according to the intention of Aristotle, a future tense universal affirmative proposition could be true, although no singular is true.
Sicut ista universalis, secundum eum, est vera `omne futurum contingens erit'; immo, secundum eum, est necessaria. Et tamen, secundum eum nulla singularis eius est vera, quia demonstrato quocumque, haec non est vera, secundum eum, `hoc futurum contingens erit', quia infert istam `hoc est futurum contingens', quae nec est vera nec falsa, secundum eum. For example, the universal proposition 'every future contingent will exist' is true, indeed it is necessary. And yet, according to him, none of its singulars is true because demonstra it is not true, according to him 'this future contingent will exist', because it implies 'this is a future contingent', which is neither true nor false, according to him.
Similiter, secundum eum, universalis de futuro poterit esse falsa, quamvis non habeat aliquam singularem falsam. Sicut haec universalis est falsa `nullum futurum contingens erit'; et tamen non habet aliquam singularem falsam, quia quocumque demonstrato, haec non est eius singularis `hoc futurum contingens non erit', secundum eum, propter causam praedictam. Similarly, according to him, a universal future tense proposition could be true, even though it does not have any false singular. For example, the universal 'no future contingent will exist' is false, and yet it does not have any false singular, because whatever is pointed to, 'this future contingent will not exist' is not one of its singulars, according to him, on account of the reason given above.
Et sicut aliquando talis universalis affirmativa est vera, et tamen nulla singularis, ita aliquando particularis affirmativa est vera, et tamen nulla eius singularis est vera, secundum eum. Et per hoc solveret talia argumenta: probatur enim quod haec est vera `Sortes erit cras', sic 'haec est vera: in aliquo instanti Sortes erit'. Et ista propositio debet concedi, secundum eum, si Sortes sit, quia ponit quod non est dare ultimum rei permanentis in esse. And just as sometimes such a universal affirmative is true, and yet no singular is true, so sometimes a particular affirmative is true, and yet none of its singulars is true, according to him. And by this certain arguments would be resolved, for it is proved that 'Socrates will exist tomorrow', thus 'this is true: in some instant Socrates will exist'. And that proposition ought to be conceded, according to him, if Socrates exists, because it is not possible to allow the last instant of a thing in permanent being[2].
Si igitur haec sit vera `in aliquo instanti Sortes erit', sit illud instans a. Tunc haec est vera `Sortes erit in a', et ultra `igitur erit in aliquo instanti post a'. Detur illud et sit b; et ultra arguetur, ut prius, `igitur erit in aliquo instanti post b', quia aliter b esset ultimum eius, quod non est possibile. Detur etiam illud et sit c. Et sic tandem devenietur ad diem crastinum: Diceret ad hoc Philosophus quod haec est vera `in aliquo instanti erit Sortes', sed nulla eius singularis est vera, et ideo non est > dandum illud instans in quo erit Sortes. Unde, secundum eum, ista est vera `in aliquo instanti erit Sortes', et tamen nulla istarum est vera `in a erit Sortes', `in b erit Sortes', et sic de singulis. Et ideo nulla istarum est danda. Therefore, if 'in some instant Socrates will exist' is true, let that instant be A. Then 'Socrates will exist at A' is true, and also 'therefore he will exist in some instant after A'. Grant that, and let it be B, and further let it be argued, as before, 'therefore he will exist in some instant after B', because otherwise B would be his last instant, which is not possible. Grant that, and let it be C. And so at last we would arrive at the next day. The philosopher would say to this that 'in some instant Socrates will exist' is true, but none of its singulars is true, and therefore that instant in which Socrates will exist should not be granted. Hence, according to him, 'in some instant Socrates will exist' is true, and none of the propositions 'Socrates will exist at A', 'Socrates will exist at B' etc is true. And therefore none of those propositions should be granted.
Et eodem modo dicendum est, secundum eum, ad consimilia argumenta. Sed secundum veritatem fidei talis universalis affirmativa, si sit vera et scita a Deo, habet aliquam singularem veram, et hoc quia semper altera pars contradictionis est vera et scita a Deo. Tamen advertendum est quod aliquando aliter est universalis vel particularis vera et aliter singularis. And in the same way it should be replied, according to him, to similar arguments. But according to the truth of faith, such a universal affirmative, if it is true and known by God, has some true singular, and this is because one or the other part of a contradiction is true and known by God. Yet it should be noted that a universal or particular is true in one way, and singular in another way.
Aliquando enim, secundum unam opinionem, universalis est necessaria et tamen nulla singularis est necessaria, immo quaelibet singularis sic est vera quod quaelibet illarum potest esse falsa et potest numquam fuisse vera. For sometimes, according to one opinion, a universal is necessary and yet no singular is necessary, indeed any singular is true in such a way that any of them can be false and can never have been true.
Haec enim est necessaria `quodlibet verum futurum contingens est verum', et tamen nulla singularis est ita vera quin potuit numquam fuisse vera. Similiter poterit esse quod particularis sit inevitabiliter vera et tamen quaelibet singularis sit evitabiliter vera. Et in hoc est aliqualis similitudo inter opinionem Aristotelis et veritatem fidei. For the proposition 'any true future contingent is true' is necessary, and yet none of its singulars is true in such a way that it could never have been true [false?]. Similarly, it could be the case that a particular could be inescapably true, and yet any singular could be escapably true. And in this there is some kind of similarity between the opinion of Aristotle and the truth of faith.
Et sicut dictum est de propositionibus de futuro, ita dicendum est de propositionibus de praeterito et de praesenti, aequivalentibus propositionibus de futuro. Unde sicut ista est vera `iste salvabitur', et tamen possibile est quod numquam fuerit vera, quia sequitur `iste peccabit finaliter, igitur damnabitur'; et ultra `igitur iste non salvabitur'; et ultra `igitur ista numquam fuit vera: iste salvabitur'. And just as was said about future tense propositions, so it should be said about propositions of the past and present, equivalent to future tense propositions. Hence 'that person will be saved' is true, and yet it is possible that it was never true, because he will finally sin, therefore he will be damned', and further more 'therefore that person will not be saved', and further 'therefore it was never true that this person will be saved'
Et antecedens est possibile, manifestum est, igitur consequens est possibile. Ita ista est modo vera `iste fuit praedestinatus ab aeterno', et tamen possibile est quod numquam fuerit praedestinatus; et hoc est, quia ista `iste fuit praedestinatus ab aeterno' aequivalet isti de futuro `iste salvabitur', et ideo sicut una potest numquam fuisse vera, ita possibile est quod alia numquam fuerit vera. And it is manifest that the antecedent is possible, therefore the consequent is possible. So the proposition 'that person was predestined from eternity' is now true, and yet it is possible that he was never predestined, and this is because the proposition 'that person was predestined from eternity' is equivalent to the future tense proposition 'that person will be saved', and therefore, just as one can never have been true, so it is possible that the other was never true.
Et ista est differentia inter veritatem propositionum de futuro et eis aequivalentium et veritatem propositionum de praeterito et de prae>senti, quae non aequivalent illis de futuro: quia si aliqua propositio sit vera de praesenti, necessario semper postea erit verum dicere quod illa propositio fuit vera. Sicut si haec sit modo vera `Sortes sedet', haec semper erit postea necessaria `haec fuit vera: Sortes sedet', ita quod impossibile est quod ista tota propositio `haec fuit vera: Sortes sedet' sit unquam postea falsa. And that is the difference between the truth of future tense propositions and of propositions equivalent to them, and the truth of past and present tense propositions, which are not equivalent to future tense ones. For if some present tense proposition is true, necessarily it will always be true afterwards to say that it was true. For example, if 'Socrates is sitting' is now true, 'this was true: Socrates sits' will always be necessary afterwards, so that it is impossible that the whole proposition 'this was true: Socrates sits', be ever false afterwards.
Et similiter est de propositione de praeterito: nam si haec sit modo vera `Sortes fuit albus', haec semper erit postea necessaria `haec fuit vera: Sortes fuit albus'. Sed secus est de propositione de futuro: nam quantumcumque haec sit modo vera `Ioannes salvabitur', tamen haec erit postea contingens `haec fuit vera: Ioannes salvabitur'. And it is similarly the case with past tense propositions. For if 'Socrates was white' is now true, the proposition 'this was true: Socrtes was white' will always be necessary afterwards. But is a different case with a future tense proposition, for however much 'John will be saved' is now true, still 'this was true: John will be saved' will be contingent afterwards.
Et per hoc potest patere quod praedestinatio vel reprobatio vel aliquid huiusmodi non potest esse relatio realis inhaerens creaturae praedestinatae vel reprobatae, sicut aliqui dicunt. And through this it can be clear that predestination or reprobation or something of that sort cannot be a real relation, inhering in the predestined creature or reprobate, as some say.
Nam si esset talis res, sequeretur quod iste qui est praedestinatus non posset damnari. Nam si praedestinatio sit talis res, tunc ista erit vera `iste est praedestinatus propter talem rem sibi inhaerentem'; sicut ista est vera `Sortes est albus propter albedinem sibi inhaerentem', et per consequens haec erit postea necessaria `ista fuit vera: iste est praedestinatus'. Et si hoc, sequitur quod ista sit modo necessaria `iste salvabitur'. Nam sequitur `ista fuit vera: iste est praedestinatus; igitur ista fuit vera: iste salvabitur'. Et antecedens est necessarium, igitur consequens est necessarium, et ex hoc sequitur quod ista est modo necessaria `iste salvabitur'. For if there were such a thing, it would follow that a person who is predestined [for salvation] could not be damned. For if predestination is such a thing, then 'this person is predestined on account of some thing inhering in him' will be true, just as 'Socrates is white because of whiteness inhering in him', and as a consequence 'this was true: this person is predestined' will be necessary afterwards. And if this is the case, it follows that 'this person will be saved' is now necessary. For 'this was true: this person is predestined; therefore this was true: this person will be saved'. And the antecedent is necessary, therefore the consequent is necessary, and from this it follows that 'this person will be saved' is now necessary.
Per ista etiam potest patere quod propositione aliqua contingente exsistente vera in aliquo instanti, nullo modo potest esse falsa in eodem instanti. Sicut si haec sit modo vera `iste habet actum bonum', impos>sibile est quod in isto instanti sit haec falsa `iste habet actum bonum'. From this it can also be clear that when a contingent proposition is true in some instant, it can in no way be false in the same instant. For example, if 'that person has a good act' is now true, it is impossible that 'that person has a good act' is false in that instant
Cuius ratio est quia propter positionem possibilis in esse numquam negandum est necessarium. Sed posito in esse quod iste peccet, negandum est hoc necessarium post illud instans `ista fuit vera: iste habet actum bonum in a'; et per consequens a exsistente, et illo habente bonum actum in a, haec est impossibilis `iste non habet bonum actum in a', et tamen ante fuit possibilis, sed ex quo positum est in actu non est amplius possibilis. The reason of this is that because of a proposition being posited as possible, a necessary should never be denied. But with it being supposed that this person commits a sin, the necessary proposition 'this was true: that person had a good act at A' should be denied, and as a consequence, with it being at A, and with that person having a good act at A, the proposition 'that person does not have a good act at A' is impossible, and yet it was possible before, sed ex quo positum est in actu non est amplius possibilis.

Notes

  1. I.e. derived by induction
  2. I.e. it is not possible for there to be a limit of an event which is in continuous existence?"Aristotle, and most medievals following him, contended that all motions, as well as the times and distances and the ranges of powers and resistances that minght be involved in them, are absolutely continuous. Science in the Middle Ages, David Lindberg, 1978, p. 241
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