50. Ad huius autem divisionis intellectum, sciendum est quod quaelibet propositio cuius praedicatum est in ratione subiecti est immediata et per se nota, quantum est in se. To clarify this division it should be noted that any proposition whose predicate is included within the notion of its subject is immediate and known in virtue of itself as it stands. Sed quarundam propositionum termini sunt tales quod sunt in notitia omnium, sicut ens et unum et alia quae sunt entis in quantum ens: nam ens est prima conceptio intellectus. Unde oportet quod tales propositiones non solum in se, sed etiam quo ad omnes quasi per se notae habeantur; sicut quod non contingit idem esse et non esse, et quod totum sit maius sua parte, et similia. Unde et huiusmodi principia omnes scientiae accipiunt a metaphysica, cuius est considerare ens simpliciter et ea quae sunt entis. However, in the case of some of these propositions the terms are such that they are understood by everyone, as being and one and those other notions that are characteristic of being precisely as being: for being is the first concept in the intellect. Hence it is necessary that propositions of this kind be held as known in virtue of themselves not only as they stand but also in reference to us. Examples of these are the propositions that ‘It does not occur that the same thing is and is not’ and that ‘The whole is greater than its part’, and others like these. Hence all the sciences take principles of this kind from metaphysics whose task it is to consider being absolutely and the characteristics of being. Quaedam vero propositiones sunt immediatae quarum termini non sunt apud omnes noti. Unde, licet praedicatum sit de ratione subiecti, tamen quia definitio subiecti non est omnibus nota, non est necessarium quod tales propositiones ab omnibus concedantur; sicut haec propositio: "Omnes recti anguli sunt aequales", est, quantum est in se, per se nota sive immediata, quia aequalitas cadit in definitione anguli recti: angulus enim rectus est quam facit linea recta super aliam rectam cadens ita quod ex utraque parte anguli reddantur aequales. Et ideo cum quadam positione recipiuntur huiusmodi principia. On the other hand, there are some immediate propositions whose terms are not known by everyone. Hence, although their predicate may be included in the very notion of their subject, yet because the definition of the subject is not known to everyone, it is not necessary that such propositions be conceded by everyone. Thus the proposition, ‘All right angles are equal’, is in itself a proposition which is immediate and known in virtue of itself, because equality appears in the definition of a right angle. For a right angle is one which a straight line form when it meets another straight line in such a way that the angles on each side are equal. Therefore, such principles are received as being posited or laid down. Est et alius modus, quo aliquae propositiones suppositiones dicuntur. Sunt enim quaedam propositiones quae non possunt probari nisi per principia alterius scientiae, et ideo oportet quod in illa scientia supponantur, licet probentur per principia alterius scientiae; sicut a puncto ad punctum rectam lineam ducere supponit geometra et probat naturalis, ostendens quod inter quaelibet duo puncta sit linea media. There is yet another way, and according to it certain propositions are called ‘suppositions’. For there are some propositions which can be proved only by the principles of some other science; therefore, they must be supposed in the one science, although they are proved by the principles of the other science. Thus the geometer supposes that he can draw one straight line from one point to another, but the philosopher of nature proves it by showing that there is one straight line between any two points. 51. Deinde cum dicit: Positionis autem etc., subdividit alterum membrum primae divisionis, scilicet positionem, dicens quod quaedam positio est quae accipit aliquam partem enunciationis, scilicet affirmationem vel negationem, quod significat cum dicit: ut dico esse aliquid aut non esse, et haec positio suppositio dicitur, quia tanquam veritatem habens supponitur. Alia autem positio est quae non significat esse vel non esse, sicut definitio, quae positio dicitur: ponitur enim ab arithmetico definitio unitatis tanquam quoddam principium, scilicet quod unitas est indivisibile secundum quantitatem; sed tamen definitio non dicitur suppositio: illud enim proprie supponitur quod verum vel falsum significat. Et ideo subdit quod non idem est quod quid est unitas, quod neque verum neque falsum significat, et esse unitatem, quod significat verum vel falsum. Then, at: if a thesis assumes one part or the other (72a18) he subdivides a member of the original division, namely, ‘position’, and says that there is one type of position which takes one side of an enunciation, namely, either affirmation or negation. He refers to this type when he says, that is, asserts either the existence or non-existence of a subject. Such a position is called a ‘supposition’ or ‘hypothesis’, because it is accepted as having truth. Another type of position is the one which does not signify existence or non-existence: in this way a definition is a position. For the definition of ‘one’ is laid down in arithmetic as a principle, namely, that one is the quantitatively indivisible. Nevertheless a definition is not called a supposition, for a supposition, strictly speaking, is a statement which signifies the true or the false. Consequently, he adds that the definition of ‘one’, inasmuch as it signifies neither the true nor the false, is not the same as ‘to be one’, which does signify the true or the false. 52. Sed potest quaeri, cum definitio non sit propositio significans esse vel non esse, quomodo ponatur <in> subdivisione immediatae propositionis? Now it might be asked how it is that definition is set down as a member of the subdivision of immediate proposition, if a definition is not a proposition signifying either existence or non-existence. Sed dicendum quod in subdivisione non resumit immediatam propositionem, sed immediatum principium; principium autem syllogismi dici potest non solum propositio, sed etiam definitio. One might answer that in this subdivision he was not subdividing immediate proposition but immediate principle; and the principle of the syllogism can be said to be not only the proposition but also the definition. Vel potest dici quod, licet definitio in se non sit propositio in actu, est tamen in virtute propositio, quia, cognita definitione, apparet definitionem de subiecto vere praedicari. Or one might answer that although a definition as such is not an actual proposition, it is one virtually, because once a definition is known, it becomes clear that it is truly predicated of the subject. Lectio 6 Lecture 6 De immediatorum principiorum cognitione Knowledge of immediate principles 72a25. Quoniam autem oportet credere et scire rem in huiusmodi habendo syllogismum quem vocamus demonstrationem, est autem hoc quidem ea scire ex quibus est syllogismus, necesse est non solum praecognoscere prima, aut omnia aut quaedam, sed et magis. 72a25. Now, since the required ground of our knowledge—that is, of our conviction—of a fact is the possession of such a syllogism as we call demonstration, and the ground of the syllogism is the facts constituting its premises, we must not only know the primary premises—some if not all of them—beforehand, but know them better than the conclusion. 72a29. Semper enim propter quod unumquodque, illud magis est, ut propter quod amamus, illud amicum magis est. Quare, si quidem scimus per prima et credimus, illa scimus et credimus magis, quoniam propter illa et posteriora. 72a29. For the cause of an attribute’s inherence in a subject always itself inheres in the subject more firmly than that attribute; e.g., the cause of our loving anything is dearer to us than the object of our love. So since the primary premises are the cause of our knowledge—that is, of our conviction—it follows that we know them better—that is, are more convinced of them—than their consequences, precisely because of our knowledge of the latter is the effect of our knowledge of the premises. 72a32. Non potest autem credere magis quae scit, quae non contingunt, neque sciens neque melius dispositus quam, si contigerit, sciens. Accidet autem hoc, nisi aliquis praecognoverit per demonstrationem credentium. 72a32. Now, a man cannot believe in anything more than in the things he knows, unless he has either actual knowledge of it or something better than actual knowledge. But we are faced with this paradox if a student whose belief rests on demonstration has not prior knowledge. 72a36. Magis autem necesse est credere principiis aut omnibus aut quibusdam quam conclusioni, magis autem debentem habere scientiam per demonstrationem. 72a36. A man must believe in some, if not in all, of the basic truths more than in the conclusion. Moreover, if a man sets out to acquire the scientific knowledge that comes through demonstration, 72a38. Non solum oportet principia magis cognoscere et magis ipsis credere quam ei quod demonstratur, sed neque aliud ipso credibilius esse neque notius oppositis principiis, ex quibus erit syllogismus contrariae deceptionis, si quidem oportet scientem simpliciter non incredibilem esse. 72a38. He must not only have a better knowledge of the basic truths and a firmer conviction of them than of the connexion which is being demonstrated: more than this, nothing must be more certain or better known to him than these basic truths in their character as contradicting the fundamental premises which lead to the opposed and erroneous conclusion. For indeed the conviction of pure science must be unshakable. 53. Quoniam autem oportet credere et scire etc. Postquam ostendit quae sunt immediata principia, determinat de eorum cognitione. Now, since the required ground of our knowledge. After showing what immediate principles are, the Philosopher now determines concerning our knowledge of them. Et circa hoc duo facit: Apropos of this he does two things. primo ostendit quod immediata principia sunt magis nota conclusione; First, he shows that immediate principles are better known than the conclusion. secundo ostendit quod etiam falsitas contrariorum debet esse notissima, ibi: non solum oportet etc. Second, that the falsity of their contraries ought to be most evident, at: he must not only have a better knowledge (72a38; [59]). Circa primum tria facit. Concerning the first he does three things. 54. Primo proponit intentum, dicens quod, quia nos credimus alicui rei conclusae et scimus eam per hoc quod habemus syllogismum demonstrativum, et hoc quidem est in quantum scimus <ea ex quibus est> syllogismus demonstrativus, necesse est non solum praecognoscere prima principia conclusioni, sed etiam magis ea cognoscere quam conclusionem. First (72a25), he states his proposition and says that because we give our assent to a thing which has been concluded and we know it scientifically precisely because we have a demonstrative syllogism (and this insofar as we know the demonstrative syllogism in a scientific way), it is necessary not only to know the first principles of the conclusion beforehand, but also to know them better than we know the conclusion. Addit autem: aut omnia aut quaedam, quia quaedam principia probatione indigent ad hoc quod sint nota, et, ante quam probentur, non sunt magis nota conclusione; sicut quod angulus exterior trianguli valeat duos angulos intrinsecos sibi oppositos, ante quam probetur, ita est ignotum sicut quod triangulus habeat tres angulos aequales duobus rectis; quaedam vero principia sunt quae, statim proposita, sunt magis nota conclusione.—Vel aliter: quaedam conclusiones sunt quae sunt notissimae, utpote per sensum acceptae, sicut quod sol eclipsetur, unde principium per quod probatur non est simpliciter magis notum, scilicet quod luna interponatur inter solem et terram, licet sit magis notum in via rationis procedentis ex causa in effectum.—Vel aliter: hoc ideo dicit quia etiam supra dixerat quod quaedam principia tempore prius cognoscuntur quam conclusio, quaedam vero simul tempore nota fiunt cum conclusione. He adds, either all or some, because some principles require proof in order to be known; so that before they are proved, they are not better known than the conclusion. Thus the fact that an exterior angle of a triangle is equal to its two opposite interior angles is, until proved, as unknown as the fact that a triangle has three angles equal to two right angles. But there are other principles which, once they are posited, are better known than the conclusion. Or, in another way, there are some conclusions which are most evident; for example, those based on sense perception, as that the sun is eclipsed. Hence the principle through which this is proved is not better known absolutely—the principle being that the moon is between the sun and the earth—although it is better known within the reasoning process that goes from cause to effect. Or, in another way, he says this because he had said above that in the order of time certain principles are known before the conclusion, but others are known along with the conclusion at the same moment of time. 55. Secundo ibi: semper enim propter quod etc., probat propositum dupliciter. Second, at: for the cause of an attribute’s inherence (72a29), he proves his proposition in two ways: Primo ratione ostensiva sic: propter quod unumquodque, illud est magis, sicut si amamus aliquem propter alterum, ut magistrum propter discipulum, discipulum magis amamus; sed conclusiones scimus et eis credimus propter principia; ergo magis scimus principia et magis eis credimus quam conclusioni. First, with an ostensive argument, thus: that in virtue of which something is so, is itself more so; for example, if we love someone because of someone else, as a master because of his disciple, we love the disciple more. But we know conclusions and give our assent to them because of the principles. Therefore, we know the principles with more conviction and give them stronger assent than the conclusion. 56. Attendendum est autem circa hanc rationem quod causa semper potior est effectu; quandoque ergo causa et effectus conveniunt in nomine, et tunc illud nomen magis praedicatur de causa quam de effectu, sicut ignis est magis calidus quam ea quae per ignem calefiunt; quandoque vero causa et effectus non communicant in nomine, et tunc, licet nomen effectus causae non conveniat, tamen convenit ei aliquid dignius, sicut, etsi in sole non sit calor, est tamen in eo virtus quaedam quae est principium caloris. Apropos of this reason it should be noted that a cause is always more noble than its effect. When, therefore, cause and effect have the same name, that name is said principally of the cause rather than of the effect; thus fire is primarily called hot rather than things heated by fire. But sometimes the name of the effect is not attributed to the cause. In that case, although the name the effect has does not belong to the cause, nevertheless, something more noble belongs to it. For example, although the sun does not possess heat, nevertheless, there is in it a certain power which is the principle of heat. 57. Deinde cum dicit: non potest autem credere etc., probat idem ratione ducente ad impossibile. Quae talis est: Principia praecognoscuntur conclusioni, ut supra habitum est, et sic quando principia cognoscuntur, nondum conclusio est cognita; si igitur principia non essent magis nota quam conclusio, sequeretur quod homo vel plus vel aequaliter cognosceret ea quae non novit quam ea quae novit; hoc autem est impossibile; ergo impossibile est quod principia non sint magis nota quam conclusio. Then, at: now, a man cannot believe in anything more (72a32) he proves the same thing with a principle which leads to an impossibility. He reasons thus: Principles are known prior to the conclusion, as has been shown above; consequently, when the principles are known, the conclusion is not yet known. If, therefore, the principles were not more known than the conclusion, it would follow that a man would know things he does not know either as well as or better than the things he does know. But this is impossible. Therefore, it is also impossible that the principles not be better known than the conclusion. Littera sic exponitur: neque sciens neque aliquis melius dispositus in cognoscendo quam sciens, si contigerit aliquem esse talem (quod dicit propter intelligentem principia, de quo adhuc non est manifestum), non potest magis credere quae non contingunt, scilicet sciri ab eo, his quae iam scit. Accidet autem hoc, nisi aliquis de numero credentium conclusionem per demonstrationem praecognoverit, id est magis cognoverit principia. Phrase by phrase this is explained in the following manner: a man who knows scientifically or even one who knows in a way superior to this, if such there be (he says this, having in mind the person who has the intuition of principles, a state he has not yet explained), cannot give more credence to things he does not know than to things he does know. But this will be the case if one who assents to a conclusion obtained through demonstration did not foreknow, that is, did not know the principles better. In Graeco planius habetur sic: non est autem possibile credere magis his quae novit, quae non existit neque sciens neque melius dispositus quam si contigerit sciens. In Greek it is stated more clearly: but no one, whether he has scientific knowledge or that form of knowledge which is better than the scientific (if there be such), can believe anything more firmly than the things he knows. 58. Tertio ibi: magis autem necesse etc., exponit quod dixerat, dicens quod hoc quod dictum est quod magis necesse est credere principiis aut omnibus aut quibusdam quam conclusioni, intelligendum est de illo qui debet accipere scientiam per demonstrationem. Si enim aliunde conclusio esset nota, sicut per sensum, nihil prohiberet principia non esse magis nota conclusione in via illa. Third, at: a man must believe in some (72a36), he clarifies what he had said, saying that his statement to the effect that it is more necessary to believe the principles (either all or some) than the conclusion should be understood as referring to a person who is to acquire a discipline through demonstration. For if the conclusion were more known through some other source, such as sense-perception, nothing would preclude the principles not being better known than the conclusion in that case. 59. Deinde cum dicit: non solum oportet principia . . . credere etc., ostendit quod non solum oportet magis cognoscere principia quam conclusionem demonstrandam, sed etiam nihil debet esse certius quam quod opposita principiis sint falsa, et hoc ideo quia oportet <scientem> non esse incredibilem principiis, sed firmissime assentire eis; quicunque autem dubitat de falsitate unius oppositorum, non potest firmiter inhaerere opposito, quia semper formidat de veritate alterius oppositi. Then, at: he must not only have a better knowledge (72a38) he shows that it is not only necessary to know the principles more than the demonstrative conclusion, but nothing should be more certain than the fact that the opposites of the principles are false. And this because the scientific knower must not disbelieve the principles, but assent to them most firmly. But anyone who doubts the falseness of one of two opposites cannot assent firmly to the other, because he will always fear that the opposite one might be true. Lectio 7 Lecture 7 Duo errores—excluditur primus error Discussion of two errors—exclusion of the first one 72b5. Quibusdam quidem igitur propter id quod oportet prima scire, non videtur scientia esse, quibusdam autem esse quidem, omnium tamen demonstrationes esse; quorum neutrum neque verum neque necessarium est. 72b5. Some hold that, owing to the necessity of knowing the primary premises, there is no scientific knowledge. Others think there is, but that all truths are demonstrable. Neither doctrine is either true or a necessary deduction from the premises. 72b7. Supponentes quidem enim non esse omnino scire, hi in infinitum volunt reduci tanquam non sint utique scientes posteriora propter priora, quorum non esse prima, recte dicentes: impossibile enim est infinita transire. Et si stent et sint principia, haec ignota esse cum demonstratio non sit ipsorum, quod vere dicunt esse scire solum. Si vero non est prima scire, neque quae sunt ex his est esse scire simpliciter neque proprie, sed ex conditione, si illa sint. 72b7. The first school, assuming that there is no way of knowing other than by demonstration, maintain that an infinite regress is involved, on the ground that if behind the prior stands no primary, we could not know the posterior through the prior (wherein they are right, for one cannot traverse an infinite series): if on the other hand — they say — the series terminates and there are primary premises, yet these are unknowable because incapable of demonstration, which according to them is the only form of knowledge. And since thus one cannot know the primary premises, knowledge of the conclusions which follow from them is not pure scientific knowledge nor properly knowing at all, but rests on the mere supposition that the premises are true. 72b15. Quidam autem quod scire quidem ipsum sit confitentur, per demonstrationem enim esse solum; sed omnium esse demonstrationem nihil prohibet: contingit enim circulariter fieri demonstrationem, et hoc ex his quae sunt ad invicem. 72b15. The other party agree with them as regards knowing, holding that it is only possible by demonstration, but they see no difficulty in holding that all truths are demonstrated, on the ground that demonstration may be circular and reciprocal. 72b18. Nos autem dicimus neque omnem scientiam demonstrativam esse, sed immediatorum indemonstrabilem. Et quod hoc necessarium sit, manifestum est; si enim necesse est quidem scire priora ex quibus est demonstratio, stant autem aliquando immediata, haec priora quidem indemonstrabilia necesse est esse. 72b18. Our own doctrine is that not all knowledge is demonstrative: on the contrary, knowledge of the immediate premises is independent of demonstration. The necessity of this is obvious; for since we must know the prior premises from which the demonstration is drawn, and since the regress must end in immediate truths, those truths must be indemonstrable.