Works › Prior Analytics, Books I–II
Volume 1 · pp. 653–655
Chapter II. On the reduction of speech into syllogism through inspection of propositions.
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CAPUT II. De reductione orationis in syllogismum per inspectionem propositionum.
In reductione autem orationis ad formam syllogismi quae disputata est sine ordine syllogismi, oportet tentare primo (hoc est, tentando inspicere) duas propositiones praemissas excipere (hoc est, extra capere de ipsa disputata sic oratione), et hoc antequam in terminos in ipsa oratione positos inspiciatur, ita quod prima resolutio illius orationis fiat in propositiones prius quam resolvatur in terminos. Et hujus ratio est, quia a facilioribus est inchoandum in omni arte: facilius autem est omne compositum in majora dividere, quam in minora: quia majora propinquiora sunt composito quam minora: composita autem sunt majora, quam ea ex quibus componuntur: sicut propositiones majores sunt, quam termini ex quibus fiunt propositiones: et ideo oratione propter formam syllogismi disputata, prius resolvenda est in propositiones quam in terminos, et prius consideranda est habitudo propositionum quam terminorum.
Consideratis et exceptis propositionibus de ipsa disputata oratione, oportet considerare propter dici de omni et dici de nullo, quae sunt principia decursus syllogistici necessaria illarum propositionum, quae de oratione exceptae sunt quae sit in toto, hoc est, universalis et necessaria, et quae sit in parte sive particularis. Et si in oratione disputata non ambae positae sunt explicite propositiones praemissae, oportet considerare eum qui in oratione disputat alteram illarum praemissarum: et alia sumenda est quae clauditur in intellectum sicut in enthymemate fit: aliquoties enim tales orationes disputantes proponunt universalem statim ex illa inferentes, et alteram propositionem (quae per intellectum est in universali proposita) explicite non ponunt, neque scribentes, hoc est, describentes lineas et figuras quas demonstrare intendunt, ut in geometricis, arithmeticis, musicis, et astronomicis, in omnibus enim his per figuras descriptas fit demonstratio: neque etiam interrogantes (hoc est, interrogativas orationes disputantes) sicut in probabilibus dialecticis et aliis scientiis talibus: et hoc quidem faciunt in ipsis principalibus syllogismis. Aliquando etiam has quidem propositiones explicite proponunt, ex quibus concluditur in principali syllogismo: et tamen quantum ad prosyllogismos omittunt illas propositiones per quas illae (quae sunt principalis syllogismi propositiones) concludi et probari debent: alia vero quaedam nec ad syllogismum nec ad prosyllogismum facientia vane assumunt. Dico autem vane, quia nec faciunt ad propositum, nec ad propositi declarationem.
Considerandum ergo primo si quid (hoc est, si aliquid) in ipsa oratione taliter disputata superfluum sit et vane appositum, et si aliquid de necessariis sit omissum tam ad syllogismum quam ad prosyllogismum. Et si est aliquid de necessariis sic omissum, illud ponendum est ex intellectis in oratione disputata: et si aliquid est superflue et vane positum, illud est auferendum: et hoc continue faciendum est donec sic resolvens orationem disputatam aliquis veniat ad duas propositiones syllogismi vel prosyllogismi, in cujus formam intendit reducere orationem: sine his enim propositionibus (ex quibus fit syllogismus) non potest aliquis reducere in formam syllogismi sic interrogatas sive disputatas orationes quae sine forma syllogistica disputantur.
CHAPTER II. On the reduction of speech into syllogism through inspection of propositions.
But in the reduction of speech, which has been disputed without the order of syllogism, to the form of syllogism, one must first try, that is, inspect by trying, to take out the two premised propositions, that is, to take them out from that very disputed speech; and this before one looks into the terms posited in that speech, so that the first resolution of that speech is made into propositions before it is resolved into terms. And the reason for this is that in every art one must begin from easier things. But it is easier to divide every composite into greater parts than into lesser, because the greater parts are nearer to the composite than the lesser; but composites are greater than the things from which they are composed, just as propositions are greater than the terms from which propositions are made. And therefore, when speech has been disputed on account of the form of syllogism, it must first be resolved into propositions rather than into terms, and the relation of propositions must be considered before the relation of terms.
When the propositions have been considered and taken from the disputed speech itself, one must consider, because of being said of every and being said of none, which are necessary principles of the syllogistic course of those propositions that have been taken from the speech, which proposition is in the whole, that is, universal and necessary, and which is in a part or particular. And if in the disputed speech both premised propositions have not been posited explicitly, one must consider the one who disputes in the speech as having one of those premises; and the other must be taken, which is enclosed in the understanding, as happens in an enthymeme. For sometimes such disputing speeches propose the universal and immediately infer from it, and do not explicitly posit the other proposition, which through understanding is proposed in the universal; neither do those writing, that is, describing the lines and figures which they intend to demonstrate, as in geometrical, arithmetical, musical, and astronomical matters, for in all these demonstration is made through described figures; nor even those questioning, that is, disputing interrogative speeches, as in probable dialectical matters and other sciences of this kind. And indeed they do this in the principal syllogisms themselves. Sometimes they explicitly propose the propositions from which the conclusion is reached in the principal syllogism, and nevertheless with respect to prosyllogisms they omit those propositions through which those propositions which belong to the principal syllogism ought to be concluded and proved; but certain other things which make neither for the syllogism nor for the prosyllogism they assume vainly. But I say vainly, because they make neither for the proposed point nor for the declaration of the proposed point.
Therefore one must first consider whether anything, that is, if anything, in that speech disputed in this way is superfluous and vainly added, and whether any of the necessary things has been omitted both for the syllogism and for the prosyllogism. And if something necessary has thus been omitted, it must be posited from the things understood in the disputed speech; and if something has been posited superfluously and vainly, it must be removed. And this must be done continuously until someone, thus resolving the disputed speech, comes to the two propositions of the syllogism or prosyllogism into whose form he intends to reduce the speech. For without these propositions, from which the syllogism is made, no one can reduce into the form of syllogism speeches that have been questioned or disputed in this way and are disputed without syllogistic form.
In aliquibus autem talibus orationibus facile est videre quod minus est, et aliquid omissum ad propositiones pertinens. Aliquando autem aliquid esse omissum latet: et tales orationes sine forma syllogismi disputatae videntur syllogizatae: eo quod per eas aliquid (quod est conclusio) ex necessitate inferentiae accidit sive sequitur sicut in syllogismo: sequitur enim conclusio ex his quae posita sunt in oratione, et ideo videntur esse syllogisticae: quia syllogismus est oratio in qua quibusdam positis aliquid accidit ex necessitate ex his quae posita sunt in syllogismo, cum tamen non sint syllogizatae, nec habeant formam syllogismi; quamvis in hoc similitudinem habeant cum syllogismo, eo quod formam syllogismi in complexione propositionum habeant. Cujus exemplum est in hac oratione, ut si sumatur non substantia interempta substantiam non interimi, et ex quibus est compositum aliquod interemptis, etiam corrumpi compositum quod est ex ipsis: haec enim oratio sine forma syllogismi est, et tamen infert de necessitate: necessario enim sequitur quod non substantia interempta, non interimatur substantia: quia substantia non componitur nisi ex substantiis. Similiter necessario sequitur quod corruptis his ex quibus substantialiter est aliquid, quod et ipsum corrumpatur et interimatur. His enim sic positis in oratione praedicta, sequitur quod necessarium est quod substantiae partes sint substantiae: quia interemptis eis interimitur substantia ex eis composita. Haec tamen oratio non est syllogizata, quia ad formam syllogismi non est reducta, cum propositionem primam habeat negativam et conclusionem affirmativam, quod nunquam contingit in syllogismo, et debitam non habeat in propositionibus complexionem et ordinem: et ideo per ea quae in tali oratione sumpta sunt hoc modo oratio illa non est syllogizata: sed debitae ad syllogismum et prosyllogismum desunt propositiones. Si autem suppleri debeat quod deest ad syllogismum istius conclusionis (qua concluditur partes substantiae esse substantias) oportet sic proponere: quibus interemptis interimitur substantia sunt, substantiae: sed partibus substantiae interemptis interimitur substantia: ergo partes substantiae sunt substantiae. Et prima quidem hujus syllogismi intelligitur in prima inductae orationis, minor autem in secunda. Adhuc autem ex hoc arguitur per prosyllogismum sic, quae sunt et non sunt non substantia, sunt substantiae: partes substantiae sunt et non sunt non substantiae: ergo sunt substantiae. Et sic oratio illa ad formam syllogismi reducta est.
But in some such speeches it is easy to see what is lacking and what, pertaining to the propositions, has been omitted. Sometimes, however, it is hidden that something has been omitted, and such speeches disputed without the form of a syllogism seem to have been syllogized, because through them something, which is the conclusion, happens or follows from necessity of inference as in a syllogism. For the conclusion follows from the things posited in the speech, and therefore they seem to be syllogistic, because a syllogism is speech in which, when certain things have been posited, something follows from necessity from the things which have been posited in the syllogism; although nevertheless they have not been syllogized and do not have the form of syllogism, even though in this they have likeness with syllogism, because they have the form of syllogism in the complexing of propositions. The example of this is in this speech: if it is taken that when non-substance has been destroyed, substance is not destroyed, and that when the things from which something composite exists have been destroyed, the composite which is from them is also corrupted; for this speech is without the form of syllogism, and nevertheless it infers of necessity. For it follows necessarily that when non-substance has been destroyed, substance is not destroyed, because substance is composed only from substances. Similarly it follows necessarily that, when those things from which something substantially exists have been corrupted, that thing itself is also corrupted and destroyed. For when these things have been posited thus in the aforesaid speech, it follows that it is necessary that the parts of substance are substances, because when they have been destroyed, the substance composed from them is destroyed. Yet this speech has not been syllogized, because it has not been reduced to the form of syllogism, since it has the first proposition negative and the conclusion affirmative, which never happens in a syllogism, and it does not have the due complexing and order in the propositions. And therefore through the things which are taken in such a speech in this way, that speech has not been syllogized; but the due propositions for the syllogism and prosyllogism are lacking. But if what is lacking for the syllogism of this conclusion, by which it is concluded that the parts of substance are substances, ought to be supplied, one must propose thus: those things by whose destruction substance is destroyed are substances; but when the parts of substance have been destroyed, substance is destroyed; therefore the parts of substance are substances. And the first proposition of this syllogism is understood in the first speech introduced, but the minor in the second. Again, from this it is argued through a prosyllogism thus: the things which are and are not non-substance are substances; the parts of substance are and are not non-substances; therefore they are substances. And thus that speech has been reduced to the form of syllogism.
Si quis autem objiciat quod diffinitio syllogismi dictae orationi videtur convenire, et ita videtur esse syllogismus: est enim oratio in qua quibusdam positis aliud ex necessitate accidit, Dicendum quod habitudinem habet ex materia et locali habitudine, sed non habet formam syllogismi in modo et figura: et ideo non est syllogismus, nec infert ex forma syllogismi. Adhuc autem in syllogismo quidquid est in praemissis, est in conclusione praeter medium: et hoc non est hic: ergo non est syllogismus; desunt enim propositiones, quarum una se deberet habere ut totum, et altera ut pars, et quarum termini duo constituere deberent conclusionem.
Rursum aliud exemplum orationis absque forma syllogismi disputatae est, si sic aliquis ratiocinetur ex syllogismo hypothetico: cum est homo, necesse est esse animal: et cum est animal, necesse est esse substantiam: ergo a primo ad ultimum, cum est homo, necesse est esse substantiam. Haec enim oratio non habet formam syllogismi ostensivi, de cujus forma hic intendimus: quia ille simpliciter est unus et unius formae: de forma enim hypothetici syllogismi in proprio libro de hypotheticis syllogismis habet determinari. Istae enim propositiones sic a primo ad ultimum concludentes, non se habent ad invicem secundum figuram et modum, ut diximus se eas habere debere in syllogismo ostensivo.
Fallimur enim in talibus putantes tales orationes esse syllogisticas: eo quod necessarium inferre in eis accidit ex his quae posita sunt in ipsis, sicut in syllogismo: quia etiam syllogismus necessarium tale quoddam est quod est necessarium necessitate consequentiae ex his quae in oratione syllogistica posita sunt: tale autem consequentiae necessarium in pluribus est quam syllogismus. Et hoc patet: quia consequentia non convertitur inter syllogismum et tale necessarium: nam omnis syllogismus necessarium tale est: non est autem e converso omne tale necessarium syllogismus. Propter quod si quid accidit ex necessitate ex quibusdam positis in oratione, non statim quidem tentandum est reducere: sed primum sumendum est duas propositiones debito modo ordinatas, sicut diximus, sic, omnis homo est animal: omne animal substantia: ergo omnis homo substantia: hic enim non est peccatum nisi in ordine propositionum, quod statim corrigitur, sic, omne animal substantia: omnis homo animal: ergo omnis homo substantia: et tunc reducta est oratio in formam veram syllogismi. Talis igitur est reductio orationis non syllogizatae in propositiones in quibus stat forma actualis syllogistica, sicut cuilibet patet inspicienti.
But if someone objects that the definition of syllogism seems to fit the said speech, and thus it seems to be a syllogism, for it is speech in which, when certain things have been posited, another follows from necessity, it must be said that it has a relation from matter and local relation, but it does not have the form of syllogism in mode and figure; and therefore it is not a syllogism, nor does it infer from the form of syllogism. Again, in a syllogism whatever is in the premises is in the conclusion except the middle; and this is not here; therefore it is not a syllogism. For the propositions are lacking, of which one ought to have itself as whole and the other as part, and of which two terms ought to constitute the conclusion.
Again, another example of speech disputed without the form of syllogism is if someone reasons in this way from a hypothetical syllogism: when there is man, it is necessary that there be animal; and when there is animal, it is necessary that there be substance; therefore from the first to the last, when there is man, it is necessary that there be substance. For this speech does not have the form of an ostensive syllogism, about whose form we are treating here, because that syllogism is simply one and of one form. For the form of a hypothetical syllogism has to be determined in the proper book on hypothetical syllogisms. For these propositions, concluding in this way from first to last, do not have themselves to one another according to figure and mode, as we have said they ought to have themselves in the ostensive syllogism.
For we are deceived in such matters, thinking that such speeches are syllogistic, because necessary inference happens in them from the things which are posited in them, as in syllogism. For syllogism also is a certain necessary thing of this sort, which is necessary by necessity of consequence from the things posited in syllogistic speech; but such a necessity of consequence is in more things than syllogism. And this is plain, because consequence is not converted between syllogism and such a necessary thing. For every syllogism is such a necessary thing, but conversely not every such necessary thing is a syllogism. On account of this, if something follows from necessity from certain things posited in speech, one must not immediately try to reduce it; rather first two propositions ordered in the due way must be taken, as we said, thus: every man is animal; every animal is substance; therefore every man is substance. For here there is no fault except in the order of propositions, which is at once corrected thus: every animal is substance; every man is animal; therefore every man is substance. And then the speech has been reduced into the true form of syllogism. Such, therefore, is the reduction of speech not syllogized into propositions in which actual syllogistic form stands, as is plain to anyone inspecting.
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