Ockham on Induction
Summa Logicae, part 3-3, chapters 31–36, trans. John P. McCaskey, September 18, 2017
The text here is from Opera Philosophica, vol. I Summa Logicae, ed. Boehner, et al. (St. Bonaventure, N.Y.: Editiones Instituti Franciscani Universitatis S. Bonaventurae, 1974), pp. 708–721. It was copied from the text at Logic Museum, but then paragraph breaks were made to match the Franciscan edition and punctuation of quotations was cleaned up and given an American style.
| Part 3-3 | |
| CAP. 31. DE SPECIE ARGUMENTI QUAE DICITUR INDUCTIO | Chapter 31. On the species of argument that is called “induction” |
| Circa inductionem, quae ponitur una species argumenti sive consequentiae, est primo sciendum quid est inductio. Et est sciendum quod “inductio est a singularibus ad universale progressio.” Ad hoc autem quod fiat inductio requiritur quod tam in singularibus [p. 708] quam in universalibus sit idem praedicatum et solum sit variatio a parte subiectorum. | Regarding the induction that is taken as one species of argument or consequence, it first has to be known what induction is. And it has to be known that “induction is a progression from singulars to a universal.” But for it to be that an induction occurs, it is required that there is the same predicate in the singulars [p. 708] as in the universals, and that the only variation is on the side of the subjects. |
| Potest autem tripliciter fieri variatio a parte subiectorum: uno modo, ponendo praecise pronomen demonstrativum in singularibus a parte subiecti, sic arguendo: iste currit et ille currit, et sic de singulis, igitur omnis homo currit. Aliter fit variatio, ponendo a parte subiecti pronomen demonstrativum cum subiecto propositionis universalis, sic arguendo: hoc album currit et illud album currit, et sic de singulis, igitur omne album currit. Aliter fit variatio, ponendo nomina propria in singularibus pro subiectis, si nomina sint imposita, sic arguendo: Sortes currit, Plato currit, et sic de singulis, igitur omnis homo currit. | Now there can be variation on the side of the subjects in three ways, [1] in one way, by giving, on the side of the subject, just a demonstrative pronoun in the singulars, by arguing like this: “This one here runs, and that one runs, and so on for each, therefore every man runs.” [2] In another way, there is a variation by giving, on the side of the subject, a demonstrative pronoun with the subject of the universal proposition, by arguing like this: “This white one runs, and that white one runs, and so on for each, therefore every white one runs.” [3] In another way, there is a variation by giving proper names in the singulars as subjects, if names are imposed, by arguing like this: “Socrates runs, Plato runs, and so on for each, therefore every man runs.” |
| CAP. 32. QUO MODO IN PROPOSITIONIBUS DE INESSE FIT INDUCTIO | Chapter 32. In what way 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. | These things having been seen, it [now] has to be seen how various universal propositions are induced from their singulars, and how universals infer singulars—and first, about those that are in the present and are assertoric. |
| 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. 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. 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 it has to 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. And so if no man were white, this here—“Every white man is a man.”—would not have any singular, but when some man is white, then it has a singular. And so it is for others. And so 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. Una est quod quaelibet universalis vera, affirmativa, de praesenti, non aequivalens propositioni de futuro, et [p. 709] 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. | And there are these rules here. One is that any universal—true, affirmative, in the present, not equivalent to a proposition in the future, and [p. 709] assertoric—has some true singular. But if it is false, there is no need that it have any false singular. It is instead sufficient that it have no singular and yet that it is indicated to have [one]. For example, by this here—“Every chimera exists.”—it is indicated that it has some true singular, and it has none, so it is false. |
| Alia regula est: si omnes singulares alicuius propositionis universalis sint verae, universalis est vera. Et ista regula est generalis tam de affirmativa quam de negativa. | Another rule is: If all singulars of any universal proposition are true, the universal is true. And this rule here is general—as much for affirmatives as for negatives. |
| 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. 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. | Another rule is: If a universal negative is false, it needs to be that some singular is false. For example, if this is false—“No animal is a donkey.”—it needs to be that some one of its singulars is false. But for the truth of the universal negative it does not need to be that some singular is true, because it does not need to have any singular. For example, if nothing is white, this is true—“No white thing is colored.”—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.” 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. | If it is said that, that being supposed, this is true—“This white thing is not colored.”—something being pointed at, it has to be said that something such as this—“This white thing is not coloured.”—is true, something being pointed at, then that there is not a singular of this universal—“No white thing is colored.” For it to be that some singular is a singular of some universal, it is required that the subject of the universal be truly predicated of the subject of the singular. But this is not so in what is put forward, for this is not true, that being supposed—“This white thing is white.”—something being pointed at. |
| 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. 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. | And if it is said that whatever singular is the singular of some universal, it has to be said that this is not true. Hence this here—“This man here is an animal.”—a donkey being pointed at, is not the singular of any universal. But whatever singular in which something is not pointed at, about which a common term added to it is falsified, is the singular of some universal. But it is not so here—“This white thing is not colored.” |
| Circa universalem de praeterito intelligendae sunt regulae sicut de universali de praesenti. | Concerning a universal in the past, the rules have to be understood just as for a universal in the present. |
| [p. 710] 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. 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. 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. 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. | [p. 710] But concerning the induction of a universal proposition in the future, it has to be known first that induction of a universal proposition in the future of what is necessary and what is impossible has to be spoken of in the same way as those in the present and in the past. But concerning the induction of a universal proposition in the future in a contingent matter, it has to be said in one way according to truth and in another way according to Aristotle’s way of thinking. And this difference here arises from this, that regarding the truth of a contingent proposition in the future, it has to be judged in one way according to truth and faith and in another way according to Aristotle’s way of thinking. For Aristotle supposes that no such contingent proposition in the future is true or false, so that according to Aristotle’s way of thinking, one part of a contradiction in such [propositions] is no more true than the other. And on account of this, according to him, one part of the contradiction is no more known by any intellect than another, because what is not more true, is not more knowable. And on account of this, Aristotle did not suppose that any future contingent is known by God, since no such, according to him, is true, and 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.” 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. | 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, from eternity, God has known this here—“The blessed Virgin is to be saved.”—and has never known this here—“The blessed Virgin is not to be saved.”—just as he has not ever known this here—“The blessed Virgin is to be damned.” And on account of this, one part of the contradiction is known, and the other not; and so one part is true, namely that which is known, and the other is not true, because it is not known by God. |
| Secundum igitur intentionem Aristotelis universalis affirma[p. 711]tiva de futuro poterit esse vera, quamvis nulla singularis sit vera. 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. | Therefore, according to Aristotle’s way of thinking, a universal affirmative [p. 711] in the future could be true, although no singular is true. For example, according to him, this universal here—“Every future contingent will exist.”— is true, and indeed, according to him, is necessary. And yet, according to him, none of its singulars is true, because anything being pointed at, it is not true; according to him, “This future contingent will be,” because it implies this here—“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 in the future could be false, even though it does not have any false singular. For example, this universal is false—“No future contingent will be.”—and yet it does not have any false singular, because whatever is pointed to, this is not [one] of its singulars—“This future contingent will not be.”—according to him, on account of the reason said earlier. |
| 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. | And just as sometimes such an affirmative universal is true, and yet no singular [is], so sometimes a particular affirmative is true, and yet none of its singulars is true, according to him. |
| 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. 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: | And by this he may resolve such arguments as this: it is proved that this is true—“Socrates will exist tomorrow.”—thus—“This is true: In some instant Socrates will exist.” And this proposition here ought to be conceded, according to him, if Socrates exists, because he supposes that there is no end to something in actuality permanent. If, therefore, this is true—“In some instant, Socrates exists.”—let that instant be A. Then this is true—“Socrates will exist at [instant] A.”—is true, and further—“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 end, which is not possible. Grant that again, and let it be C. And so on until we get to the next day. |
| Diceret ad hoc Philosophus quod haec est vera “in aliquo instanti erit Sortes,” sed nulla eius singularis est vera, et ideo non est [p. 712] 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. Et eodem modo dicendum est, secundum eum, ad consimilia argumenta. | The philosopher would say to this that this is true—“In some instant Socrates will exist.”—but none of its singulars is true, and so that [p. 712] instant in which Socrates will exist is not granted. And so, according to him, this here is true—“At some instant, Socrates will exist.”—and yet none of these here is true—“Socrates will exist at [instant] A.” “Socrates will exist at [time] B.” And so on for each.—And so none of those here should be granted. And, according to him, it has to be said in the same way to similar arguments. |
| 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. | But according to the truth of faith, such an affirmative universal, if it is true and known by God, has some true singular, and this because always another part of the contradiction is true and known by God. |
| Tamen advertendum est quod aliquando aliter est universalis vel particularis vera et aliter singularis. 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. 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. | Yet it has to be noted that sometimes the universal or particular is true and other times the singular. For sometimes, according to one opinion, a universal is necessary and yet no singular is necessary, and indeed any singular is true in such a way that any of those there can be false and can never have been true. For this is necessary—“Any true future contingent is true.”—and yet none of its singulars is true in such a way that it could never have been true. Similarly, it could be that a particular be inescapably true, and yet any singular could be escapably true. And in this there is some kind of similarity between Aristotle’s opinion 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.” 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 just as was said about propositions in the future, so it has to be said about propositions in the past and in present, with the same force about propositions in the future. And so for example this here is true—“This one here will be saved.”—and yet it is possible that it was never true, because it follows—“This one here will in the end sin, therefore he will be damned.”— and further—“Therefore this one here will not be saved.”—and further—“Therefore this here was never true: This one here will be saved.” And the antecedent is possible, it is manifest, therefore the consequent is possible. So this here is now true—“This one here was predestined from eternity.”—and yet it is possible that he was never predestined, and this is because this here—“This one here was predestined from eternity.”—has the same force as this here in the future—“This one here will be saved.”—and so 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[p. 713]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 this here is the difference between the truth of propositions in the future (and those with the same force as those) and the truth of propositions in the past and in the present [p. 713] that do not have the same force as those in the future. Because if some proposition is true in the present, necessarily it will afterwards always be true to say that that proposition was true. For example, if this is now true—“Socrates sits.”—this will always be necessary afterwards—“This was true: Socrates sits.”—so that it is impossible that the whole proposition here—“This was true: Socrates sits.”—is ever afterwards false. |
| 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.” | And it is similar with propositions in the past. For if this is now true—“Socrates was white.”—this was ever afterwards necessary—“This was true: Socrates was white.” |
| 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.” | But it is otherwise with a proposition in the future. For however much this is now true—“John will be saved.”—still this will be contingent afterwards—“This was true: John will be saved.” |
| 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. 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.” | And through this it can be clear that predestination or reprobation or something of the sort cannot be a real relation, inhering in the predestined or reprobate creature, as some say. For if there were such a thing, it would follow that this one here who is predestined could not be damned. For if predestination is such a thing, then this here will be true—“This one here is predestined on account of some thing inhering in him.”—just as this here is true—“Socrates is white on account of whiteness inhering in him.”—and as a consequence this will afterwards be necessary—“This here was true: This one here is predestined.” And if this, it follows that this here is now necessary—“This one here will be saved.” For it follows—“This here was true: This one here is predestined. Therefore this here was true: This one here will be saved.” And the antecedent is necessary, therefore the consequent is necessary, and from this it follows that this here is now necessary—“This one here will be saved.” |
| 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[p. 714]sibile est quod in isto instanti sit haec falsa “iste habet actum bonum.” Cuius ratio est quia propter propositionem* 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.
— |
From this here it can also be clear that, some contingent proposition being true in some instant, it can in no way be false in the same instant. For example, if this—“This one here has done a good deed.”—is now true, it is impossible [p. 714] that in that very instant, this is false—“This one here has done a good deed.” The reason for this is because, what is necessary is never to be denied on account of a proposition about what is in actuality possible. But with it being supposed that this one here would in actuality sin, it has to be denied this is necessary after that instant—“This here was true: This one here has done a good deed at [instant] A.”—and as a consequence of [instant] A coming to be, and with that one having done a good deed at [instant] A, this is impossible—“This one here has not done a good deed at [instant] A.”—and although it was possible before, from when it was placed into actuality it is no longer possible. |
| CAP. 33. DE INDUCTIONE PROPOSITIONUM UNIVERSALIUM DE MODO. | Chap. 33. Regarding induction of universal modal propositions |
| Circa inductionem propositionum universalium de modo est primo sciendum quod si propositiones universales accipiuntur in sensu divisionis vel aequivalentes eis, eodem modo inducuntur sicut universales de inesse. Et ideo omnes tales inductiones sunt bonae: iste homo contingenter est animal, et ille homo contingenter est animal, et sic de singulis, igitur omnis homo contingenter est animal; iste homo non de necessitate est animal, ille homo non de necessitate est animal, et sic de singulis, ergo nullus homo de necessitate est animal. | Regarding induction of universal modal propositions, it first has to be known that, if universal propositions are accepted in the sense of division or its equivalents, they are induced in the same way as assertoric universals. And so all inductions such as these are good—“This man here is contingently an animal, and that man is contingently an animal, and so on for each, therefore every man is contingently an animal.” “This man here is not of necessity an animal, that man is not of necessity an animal, and so on for each, therefore no man is of necessity an animal.” |
| Et est aliud intelligendum, quod sicut in illis de inesse, ita in talibus de modo ad veritatem inductionis non refert in singularibus ponere pro subiectis vel pronomina demonstrativa praecise, vel pronomina demonstrativa cum subiecto propositionis universalis, vel nomina propria significatorum illius termini communis. Unde sicut omnes istae tres inductiones sunt bonae: iste homo currit et ille homo currit, et sic de singulis, igitur omnis homo currit; iste currit et ille currit, et sic de singulis, igitur omnis homo currit; Sortes currit, Plato currit, et sic de singulis, igitur omnis homo currit; – et eodem modo est de quacumque universali de inesse –; ita omnes tales inductiones sunt bonae: iste contingenter est animal, denotato aliquo homine, et ille contingenter est [p. 715] animal, et sic de singulis, igitur omnis homo contingenter est animal; iste homo contingenter est animal et ille homo contingenter est animal, et sic de singulis, igitur omnis homo contingenter est animal; Sortes contingenter est animal, Plato contingenter est animal, et sic de singulis, igitur omnis homo contingenter est animal. | And it also has to be understood that just as in those assertoric, so in those modal, for the truth of the induction, it does not matter whether singulars placed in the subject are just demonstrative pronouns or demonstrative pronouns with the subject of the universal proposition or proper names of signs of their common term. And so these three inductions here are all good.—“This man here runs and that man runs, and so on for each, therefore every man runs.” “This one here runs and that one runs, and so on for each, therefore every man runs.” “Socrates runs, Plato runs, and so on for each, therefore every man runs.”—and in the same way for any modal universal. So all inductions such as these are good.—“This one here is contingently an animal (some man being indicated) and that one is contingently [p. 715] an animal, and so one for each, therefore, every man is contingently an animal.” “This man here is contingently an animal and that man is contingently an animal, and so on for each, therefore every man is contingently an animal.” “Socrates is contingently an animal, Plato is contingently an animal, and so on for each, therefore every man is contingently an animal.” |
| Ex isto patet quod omnes tales inductiones sunt bonae: hoc per se est animal, demonstrato aliquo albo, et illud per se est animal, et sic de singulis, igitur omne album per se est animal. | From this it is clear that all inductions such as these are good—“This is per se an animal (some white thing being pointed at), and that is per se an animal, and so on for each, therefore, every white thing is per se an animal.” |
| Et ex isto et ista regula, quae vera est, “quando singulares sufficienter sumptae inferunt aliquam universalem, una singularis per se sumpta infert particularem vel indefinitam illius universalis” sequitur quod omnes tales consequentiae sunt bonae: iste per se aedificat, demonstrato aliquo qui in rei veritate est albus, igitur album per se aedificat; iste, demonstrato Deo, necessario est Deus, igitur creans de necessitate est Deus, et hoc quando Deus est creans; iste, demonstrato Filio Dei, per se est Deus, igitur homo per se est Deus. Immo, generaliter, ex tali singulari in qua subicitur pronomen demonstrativum vel pronomen demonstrativum sumptum cum quocumque termino communi, qui praedicatur de illo pronomine demonstrante illud quod prius, vel etiam in qua subicitur nomen proprium, ad talem particularem est bona consequentia. Et ideo omnes tales consequentiae sunt bonae: haec res per se aedificat, demonstrato aliquo quod in rei veritate est album, igitur album per se aedificat; iste homo non est aggregatum per accidens, demonstrato aliquo homine qui in rei veritate est albus, igitur homo albus non est aggregatum per accidens; iste homo albus est aggregatum per accidens, ergo homo est aggregatum per accidens. Et sic de multis aliis. | And from this here also is there this rule here, which is true.—“When singulars sufficiently gathered infer some universal, one singular taken per se infers a particular or indefinite of the universal.”—It follows that all such consequences are good.—“This one here builds per se (some one being pointed at who in truth of the matter is white), therefore a white one per se builds.” “This one here (God being pointed at) is necessarily God, therefore the one creating out of necessity is God, and this, when God is creating; this one here (the Son of God being pointed at) is per se God; therefore the man is per se God.” And indeed, generally, from such a singular in which a demonstrative pronoun or demonstrative pronoun taken with any common term is proposed, which is predicated of that pronoun, pointing to that which is first, or also in which a proper noun is proposed, to such particular, the consequence is good. And so all such consequences are good—“This thing per se builds (something that is in truth of the matter is white being pointed at), therefore a white thing per se builds.” “This man here is not an aggregate per accidens (some man who in truth of the matter is white being pointed at), therefore a white man is not an aggregate per accidens.” “This white man here is an aggregate per accidens, therefore a man is an aggregate per accidens.” And so on for many others. |
| Hic tamen est advertendum quod tales consequentiae non sunt semper simplices, sed frequenter sunt ut nunc solum. Unde ista consequentia “Sortes per se est animal, igitur album per se est animal” non est consequentia simplex sed tantum ut nunc, quia numquam valet [p. 716] nisi dum Sortes est albus; quando enim Sortes non est albus, tunc non valet consequentia. Similiter ista consequentia “Filius Dei de necessitate est Deus, igitur homo de necessitate est Deus” est solum bona ut nunc, quia non valet nisi dum Filius Dei est homo. Unde ante incarnationem consequentia non valuit; similiter, si Filius Dei deponeret naturam assumptam, non valeret. | Nevertheless it has to be noted here that such consequences are not always simple, but are frequently only as of now. And so these consequences here—“Socrates is per se an animal, therefore white is per se an animal.”—is not a simple consequence but only as of now, because it is never valid [p. 716] except when Socrates is white. For when Socrates is not white then the consequence is not valid. Similarly this consequence here—“The Son of God is by necessity God, therefore a man is by necessity God.”—is only good as of now, because it is not valid except when the Son of God is a man. And so before the incarnation the consequence was not valid. Similarly if the Son of God set aside [his] assumed nature, it would not be valid. |
| Similiter talis consequentia est bona “haec res potest assumi a Verbo, denotando naturam humanam quae est Ioannes, igitur homo potest assumi, immo, igitur suppositum potest assumi,” quia per istam “suppositum potest assumi” non plus denotatur nisi quod illa res, quae est modo suppositum, potest assumi. Et hoc est verum, sicut est verum quod “album potest esse nigrum.” Et ideo sicut haec est vera “album potest esse nigrum,” non obstante quod haec sit impossibilis “album est nigrum,” sic haec est vera “suppositum potest assumi,” non obstante quod haec sit impossibilis “suppositum assumitur”; ita si haec sit vera “aedificator per se aedificat,” haec est vera “album per se aedificat,” si idem sit aedificator et albus, non obstante quod haec esset per se “aedificator aedificat” et haec per accidens “album aedificat.” | Similarly, a consequence such as this is good—“This thing can be assumed by the Word (the natural person who is John being indicated), therefore a man can be assumed, and indeed therefore what is supposed can be assumed.”—because by this here—“What is supposed can be assumed.”—is no longer indicated except that this thing, which is now supposed, can be assumed. And this is true, just as it is true that—“White can be black.” And so just as this is true—“White can be black.”—not opposing that this is impossible—“White is black.”—so this is true—“What is supposed can be assumed.”—notwithstanding that this is impossible—“What is supposed is assumed.” Thus if this is true—“A builder per se builds.”—this is true—“A white thing per se builds.”—if the same thing is builder and white, notwithstanding that this may be per se—“A builder builds.”—and this per accidens—“A white thing builds.” |
| Aliud etiam est advertendum quod omnes praedictae consequentiae et consimiles sunt verae quando termini accipiuntur personaliter et significative; quia si aliquis terminus acciperetur simpliciter vel materialiter, possent deficere, sicut frequenter dictum est prius de aliis regulis. Et ideo tales consequentiae non valent “iste homo albus significat aggregatum per accidens, igitur homo significat aggregatum per accidens,” quia antecedens non est verum nisi sumpto subiecto antecedentis materialiter vel simpliciter. Similiter non sequitur “de isto albo praedicatur per accidens aedificare, igitur de homine vel de aedificatore praedicatur per accidens aedificare.” Et ita est de multis aliis. | Something else also has to be noted, that all previously said consequences, and the like, are true when the terms are taken personally and significatively, because if any term is taken simply or materially, they cannot fail, just as frequently what is said is first by another rule. And so consequences such as these are not valid—“This white man here signifies an aggregate per accidens, therefore man signifies an aggregate per accidens.”—because the antecedent is not true unless taken as the subject of the antecedent materially or simply. Similarly, it does not follow—“To build is predicated about this white thing per accidens, therefore to build is predicated per accidens either about man or about builder.” And so on for many others. |
| Et ista de inductione propositionum universalium de modo sumptarum in sensu divisionis et eis aequivalentium ad praesens sufficiant. | And these things here about induction of universal propositions modal in the sense of division or its equivalent are enough for now. |
| [p. 717] CAP. 34. QUOMODO SINGULARES DE MODO IN SENSU COMPOSITIONIS SE HABENT AD UNIVERSALES DE MODO IN SENSU COMPOSITIONIS. | [p. 717] Chap. 34. How modal singulars in the sense of composition relate to modal universals in the sense of composition. |
| His visis videndum est quomodo singulares de modo sumptae in sensu compositionis et eis aequivalentes se habent ad universales de modo sumptas in sensu compositionis et eis aequivalentes. Et quia aliter est de diversis, ideo dicendum est de eis separatim. Et primo circa illas de necessario. | These things having been seen, it [now] has to be seen how modal singulars taken in the sense of a composition, and their equivalents, relate to modal universals taken in the sense of a composition, and their equivalents. And because it is different with various things, they have to be spoken about separately—and first regarding those out of necessity. |
| Et est sciendum quod non semper singulares de necessario tales inferunt tales universales de necessario, nisi in singularibus subiciantur pronomina demonstrativa sumpta cum subiecto propositionis universalis. Unde posito quod quaelibet persona divina assumpsisset naturam humanam et quod nullus alius homo esset exsistens, ista consequentia non valeret “istum esse Deum est necessarium, demonstrando Patrem, qui in rei veritate esset homo; et illum esse Deum est necessarium, demonstrando Filium; et illum esse Deum est necessarium, demonstrando Spiritum Sanctum; igitur omnem hominem esse Deum est necessarium,” quia antecedens esset verum, illo casu posito, et consequens falsum. Et tamen, illo posito, ista consequentia esset bona “istum hominem esse Deum est necessarium,” denotando Patrem; “et illum hominem esse Deum est necessarium,” denotando Filium; “et illum hominem esse Deum est necessarium,” denotando Spiritum Sanctum; “igitur omnem hominem esse Deum est necessarium,” ex inductione. Et hoc, si non possent esse plures homines. Quandocumque enim possunt plura contineri sub subiecto universalis quam continentur in inductione, non valet talis consequentia virtute talis inductionis. | And it has to be known that such singulars do not always imply such universals of necessity, unless in the singulars demonstrative pronouns taken with the subject of the universal proposition are made subjects. And so in the case that any divine person were to assume a human nature and that no other man is existing, this consequence here would not be valid—“For this here to be God is necessary (the Father being pointed at), who in the truth of the matter is a man; and for that to be God is necessary, (the Son being pointing at); and for that to be God is necessary, (the Holy Spirit being pointed at); therefore for every man to be God is necessary.”—because the antecedent is true, in that case, and the consequence false. And nevertheless, that being the case, this consequence here would be good—“For this man here to be God is necessary (the Father being indicated) and for this man to be God is necessary (the Son being indicated) and for this man to be God is necessary (the Holy Spirit being indicated), therefore for every man to be God is necessary.”—by induction. And this is so if it is not possible for there to be more men. For when it is possible for more to be contained under the subject of the universal than is contained in the induction, such a consequence is not, by virtue of that induction, valid. |
| Sic igitur patet quod raro vel numquam singulares de necessario, habentes praecise pronomina demonstrativa pro subiectis, sumptae in sensu compositionis, inferunt universalem sumptam in sensu compositionis. Et hoc, quia ista regula non est generaliter vera “omnes singulares sunt necessariae, igitur universalis est necessaria.” Similiter, talis universalis de necessario non infert tales singulares; et hoc, quia ista regula non est generalis “universalis est necessaria, igitur singulares sunt necessariae.” Unde ista universalis est necessaria “omne verum contingens est verum,” et tamen nulla singularis est necessaria, immo quaelibet est contingens, [p. 718] quia quocumque vero contingenti demonstrato haec est contingens “hoc verum contingens est verum,” quia eo ipso quod est verum contingens, potest esse falsum, et per consequens potest non esse verum, et ita non est illa prima necessaria. | So it is therefore clear that of necessity singulars having just demonstrative pronouns as subject, taken in the sense of a composition, rarely or never imply a universal taken in the sense of a composition. And this because this rule here is not generally true—“All singulars are necessary, therefore the universal is necessary.” Similarly, such a universal does not imply of necessity such singulars; and this because this rule here is not general—“The universal is necessary, therefore the singulars are necessary.” And so this universal here is necessary—“Every true contingent is true.”—and nevertheless no singular is necessary, indeed any one is contingent, because whatever true contingent is pointed to, this is contingent—“This true contingent is true.”— [p. 718] because that which itself is a true contingent can be false, and consequently cannot be true, and so that first is not necessary. |
| Similiter, secundum intentionem Philosophi, haec est necessaria “omne album est coloratum,” et tamen quaelibet singularis est contingens; quocumque enim demonstrato haec est contingens “hoc album est coloratum,” quia poterit esse falsa illo destructo. | Similarly, according to the Philosopher’s way of thinking, this is necessary—“Every white thing is colored.”—and nevertheless, any singular is contingent. For whatever is pointed at, this is contingent—“This white thing is colored.”—because it will be false if that is destroyed. |
| Tamen sciendum est quod aliqualis diversitas est inter universalem affirmativam et negativam, nam ex hoc quod universalis affirmativa est necessaria non potest inferri quod singulares, sive de subiectis quae sunt pronomina demonstrativa sive aliae, sint necessariae. Sed si universalis negativa sit necessaria, quamvis non oporteat quod illae singulares quae habent pro subiectis pronomina demonstrativa tantum vel nomina propria sint necessariae, tamen oportet quod illae singulares quae habent pro subiectis pronomina demonstrativa sumpta cum subiecto propositionis universalis sint necessariae. Sicut haec est necessaria “nullum album est nigrum,” et tamen nulla talis singularis est necessaria “hoc non est nigrum,” denotato quocumque albo, nec aliqua talis “Sortes non est niger,” “Plato non est niger”; sed quaelibet talis est necessaria “hoc album non est nigrum,” “illud album non est nigrum,” et sic de aliis. | Nevertheless it has to be known that any sort of difference is between an affirmative and a negative universal. For from this, that an affirmative universal is necessary, it cannot be infered that singulars, either regarding subjects that are demonstrative pronouns or others, are necessary. But if a negative universal is necessary, however much it does not need to be that those singulars that have for subjects only demonstrative pronouns or proper nouns are necessary, nevertheless it needs to be that those singulars that have as subjects demonstrative pronouns taken with the subject of the universal proposition are necessary. For example, this is necessary—“No white thing is black.”—and nevertheless no singular such as this is necessary—“This is not black.”—some white thing being indicated, nor any such as—“Socrates is not black.” “Plato is not black.” But any such as these is necessary—“This white thing is not black.” “That white thing is not black.” And so on for each. |
| CAP. 35. DE INDUCTIONE UNIVERSALIUM DE POSSIBILI. | Chap. 35. Regarding induction of universals of the possibile. |
| Circa inductionem universalium de possibili est sciendum quod ex singularibus non sequitur universalis, quia ista regula non valet “omnes singulares sunt possibiles, igitur universalis est possibilis.” Sicut non sequitur “haec est possibilis: haec propositio contingens est vera; et haec est possibilis: ista propositio contingens est vera, et sic de singulis; igitur haec est possibilis: omnis propositio contingens est vera.” Et ita frequen[p. 719]ter universalis est impossibilis, et tamen quaelibet singularis est possibilis. Et ideo talis consequentia non valet “secundum illud signum continuum esse actu divisum est possibile, et secundum illud signum continuum esse actu divisum est possibile, et sic de singulis, igitur secundum omne signum continuum esse actu divisum est possibile.” Et hoc, accipiendo omnes propositiones in sensu compositionis; nam si acciperentur in sensu divisionis, conclusio esset vera, quia ista est vera “secundum omne signum potest continuum dividi.” | Regarding induction of universals of the possibile, it has to be known that from singulars a universal does not follow, because this rule here is not valid—“All singulars are possible, therefore the universal is possible.” For example, it does not follow—“This is possible: this contingent proposition is true. And this is possible: this contingent proposition here is true. And so on for each. Therefore this is possible: every contingent proposition in true.” And so frequently, [p. 719] a universal is impossible and nevertheless some singular is possible. And so such a consequence as this is not valid:—“According to this sign, it is possible for a continuum to be actually divided. According to this sign, it is possible for a continuum to be actually divided. And so on for each. Therefore according to every sign, it is possible for a continuum to be actually divided.” And this by accepting every proposition in the sense of a composition; for if they were accepted in the sense of a division, the conclusion would be true, because this here is true–“According to every sign, a continuum can be divided.” |
| Et si dicatur quod sicut ex possibili non sequitur impossibile, ita ex possibilibus non sequitur impossibile, dicendum est quod ex possibilibus et compossibilibus non sequitur impossibile, tamen ex possibilibus et incompossibilibus bene sequitur impossibile. Et ita est in proposito, quia singulares talium propositionum universalium impossibilium etsi sint possibiles sunt tamen simul cum hoc incompossibiles. | And if it said that, just as impossible does not follow from a possible, so impossible does not follow from possibiles, it has to be said that impossible does not follow from possibles and compossibles, but impossible follows well from possibles and incompossibles. And so it is in what is proposed, because singulars of such universal impossible propositions, although they are possibles, are nonetheless at the same time incompossible with it. |
| Est tamen hic notandum quod quandoque unius universalis sunt infinitae singulares. Et quando sic est, possibile est quod universalis sit impossibilis et quaelibet singularis possibilis, et tamen nullae duae singulares sunt incompossibiles, immo nullae singulares finitae sunt incompossibiles, sed quaelibet una accepta est incompossibilis omnibus aliis simul sumptis. | It is nevertheless to be noted here that whenever of one universal there are infinite singulars—when this is so, it is possible that the universal is impossible and some singular possible, and nonetheless no two singulars are incompossible, indeed no finite singulars are incompossible, but some given one is incompossible with all others given at the same time. |
| Quandoque autem unius universalis singulares sunt finitae; et tunc si universalis sit impossibilis, necesse est quod aliqua singularis sit impossibilis vel quod aliquae singulares in numero certo sint incompossibiles. | But when of one universal the singulars are finite, and then if the universal is impossible, it is necessary that any singular is impossible or that some singulars in a certain number are incompossible. |
| Notandum est etiam quod ista regula non est vera “universalis est possibilis, igitur suae singulares sunt possibiles”; sicut si nullus homo sit albus et multi asini sint albi, haec universalis est possibilis “omne album est homo,” et tamen nulla singularis est possibilis, quia quocumque albo [p. 720] demonstrato haec est impossibilis “hoc album est homo.” Tamen si universalis sit possibilis, oportet quod possit habere omnes singulares possibiles; sicut, illo posito, ista “omne album est homo” nullam habet singularem possibilem, et tamen potest habere, quia posito quod nihil esset album nisi homo, tunc istius “omne album est homo” omnes singulares essent possibiles. | It has to be noted also that this rule here is not true—“The universal is possible, therefore its singulars are possible.”—for example, if no man is white and many donkeys are white, this universal is possible—“Every white thing is a man.”—and yet no singular is possible, because whatever white thing [p. 720] is pointed at this is impossible—“This white thing is a man.” Yet if the universal is possible, it does not need to be that it can have all singulars possible. For example, in that case, this here—“Every white thing is a man.”—has no possible singular, and yet it can have, because it is the case that there is no white thing except a man; then of this here—“Every white thing is a man.”—all singulars are possible. |
| CAP. 36. DE INDUCTIONE ILLARUM DE CONTINGENTI. | Chap. 36. On induction of those of the contingent |
| Circa illas de contingenti est sciendum quod singulares de contingenti non inferunt universalem de contingenti, quia ista regula non valet “singulares sunt contingentes, igitur universalis est contingens”; quaelibet enim singularis istius universalis est contingens “omne verum contingens est verum,” et tamen universalis est necessaria. Similiter ista est impossibilis “nullum verum contingens est verum,” et tamen quaelibet singularis est contingens; et ita talis inductio non valet “hanc propositionem veram contingentem esse veram est contingens, et illam, et sic de singulis, igitur omnem propositionem veram contingentem esse veram est contingens.” Similiter non sequitur e converso, quia haec regula falsa est “universalis est contingens, igitur quaelibet singularis,” sicut prius dictum est. | Regarding those of the contingent, it has to be known that singulars of the contingent do not imply a universal about the contingent, because this rule here is not valid—“Singulars are contingent, therefore the universal is contingent.”—for any singular of this universal here—“Every true contingent is true.”—is contingent and nevertheless the universal is necessary. Similarly, this here is impossible—“No true contingent is true.”—and nevertheless any singular is contingent. And so an induction such as this—“For this true contingent proposition to be true is contingent, and that one, and so on for each, therefore for every true contingent proposition to be true is contingent.”—is not valid. Similarly, it does not follow by conversion, because this rule is false—“The universal is contingent, therefore any singular is.”—just as was said before. |
| Per ista patet quod ambae istarum regularum sunt falsae “omnes singulares sunt impossibiles, igitur universalis est impossibilis”; “universalis est impossibilis, igitur omnes singulares sunt impossibiles,” sicut patet per praedicta. | From this here it is clear that both of these rules here are false—“All singulars are impossible, therefore the universal is impossible.” “The universal is impossible, therefore all the singulars are impossible.”—just as is clear from what was said. |
| Et eodem modo raro aliae propositiones modales sumptae in sensu compositionis inferunt suas singulares sumptas in eodem sensu; sicut non sequitur “omnem hominem esse risibilem est primo verum, igitur hunc hominem esse risibilem est primo verum.” Et tamen frequenter [p. 721] est bona inductio ex singularibus ad universalem; unde bene sequitur “hunc hominem esse animal est per se verum, et illum hominem, et sic de singulis, igitur omnem hominem esse animal est per se verum.” Et ita est de multis aliis. | And for the same reason, other modal propositions taken in the sense of a composition rarely imply their singulars taken in the same sense, for example it does not follow—“For every man to be risible is at first true, therefore for this man to be risible is at first true.” And nevertheless [p. 721] an induction from singulars to universal is frequently good. And so—“For this man to be an animal is per se true, and that man, and so on for each, therefore for every man to be an animal is per se true.”—follows well. And so it is for many others. |
| Quando autem hoc sit et quando non, potest faciliter sciri per ea quae dicta sunt et sciendo quid requiritur ad hoc quod talis propositio modalis sit vera, et ideo ad praesens ista de inductione sufficiant. | Moreover, when this is and when it is not can be easily known through those things that have been said and by knowing what is required for it to be that such a modal proposition is true. And so for now all this here about induction is enough. |
