Authors/Thomas Aquinas/posteriorum/L1/Lect4

Lecture 4 Nature of the demonstrative syllogism

Latin	English
	Lecture 4 (71b8-72a8) NATURE OF THE DEMONSTRATIVE SYLLOGISM
lib. 1 l. 4 n. 1 Postquam ostendit philosophus necessitatem syllogismi demonstrativi, hic iam incipit de ipso syllogismo demonstrativo determinare. Et dividitur in duas partes: in prima, determinat de syllogismo demonstrativo; in secunda, de medio ex quo syllogismus demonstrativus procedit: et hoc in secundo libro; ibi: quaestiones sunt aequales numero et cetera. Prima dividitur in duas: in prima, determinat de syllogismo demonstrativo absolute; in secunda, comparando demonstrationem demonstrationi; ibi: cum autem demonstratio sit alia quidem universalis et cetera. Prima in duas dividitur: in prima, determinat de syllogismo demonstrativo; in secunda, ostendit quod non sit in demonstrationibus in infinitum procedere; ibi: est autem omnis syllogismus per tres terminos et cetera. Prima dividitur in duas: in prima, determinat de syllogismo demonstrativo per quem acquirimus scientiam: in secunda, ostendit quomodo etiam in nobis per syllogismum acquiritur aliqua ignorantia; ibi: ignorantia autem secundum negationem et cetera. Circa primum tria facit: primo, determinat de syllogismo demonstrativo, ostendendo quid sit; secundo, determinat de materia syllogismi demonstrativi, ostendendo quae et qualia sint, ex quibus est; ibi: quoniam autem impossibile est etc.; tertio, determinat de forma ipsius, ostendendo in qua figura praecipue fiat; ibi: figurarum autem magis faciens scire et cetera. Circa primum tria facit: primo, ostendit de demonstrativo syllogismo, quid est; secundo, notificat quaedam, quae in definitione syllogismi demonstrativi ponuntur; ibi: est autem principium demonstrationis etc.; tertio, excludit quosdam errores, qui ex praemissis circa demonstrationem oriri possunt; ibi: quibusdam quidem igitur et cetera.	After indicating the need for the demonstrative syllogism, the Philosopher now begins to settle questions concerning the demonstrative syllogism itself. And his treatment is divided into two parts. In the first he determines concerning the demonstrative syllogism. In the second he determines concerning the middle from which the demonstrative syllogism proceeds (89b21) [Book II]. The first is divided into two parts. In the first he determines concerning the demonstrative syllogism in itself. In the second he compares demonstration to demonstration (85a12) [L. 37]. The first is divided into two parts. In the first he determines concerning the demonstrative syllogism. In the second he shows that one does not proceed to infinity in demonstrations (81b10) [L. 31] The first is divided into two parts. In the first he determines concerning the demonstrative syllogism through which we acquire science. In the second he shows how we also acquire ignorance through a syllogism (79b23) [L. 27]. Concerning the first he does three things. First, he determines concerning the demonstrative syllogism by showing what it is. Secondly, he determines concerning the matter of the demonstrative syllogism, pointing out the nature and character of the matter out of which it is formed (73a21) [L. 9]. Thirdly, he determines concerning the form of the syllogism, pointing out the figure in which it is chiefly presented (79a17) [L. 26]. Concerning the first he does three things. First, he shows what the demonstrative syllogism is. Secondly, he clarifies certain terms that appear in the definition of the demonstrative syllogism (72a8) [L. 5]. Thirdly, he excludes certain errors that could arise from his doctrine on the nature of demonstration [L. 7].
lib. 1 l. 4 n. 2 Circa primum sciendum est quod in omnibus quae sunt propter finem, definitio quae est per causam finalem, est ratio definitionis, quae est per causam materialem, et medium probans ipsam: propter hoc enim oportet ut domus fiat ex lapidibus et lignis, quia est operimentum protegens nos a frigore et aestu. Sic igitur Aristoteles de demonstratione dat hic duas definitiones: quarum una sumitur a fine demonstrationis, qui est scire; et ex hac concluditur altera, quae sumitur a materia demonstrationis.	In regard to the first it should be noted that in all things which exist for an end, the definition which employs a final cause is both the explanation of the definition which expresses the material cause, and is the middle which proves the latter. For the reason why a house should made of stone and wood is that it is a structure protecting us from the cold and heat. Along these lines, therefore, he gives two definitions demonstration, one of which is expressed in terms of the end of demonstration, which is to know in a scientific manner. And from this one is concluded the other, which is drawn from the matter of a demonstration.
lib. 1 l. 4 n. 3 Unde circa hoc tria facit: primo, definit ipsum scire; secundo, definit demonstrationem per finem eius, qui est ipsum scire; ibi: dicimus autem scire etc.; tertio, ex utraque definitione concludit definitionem demonstrationis, quae sumitur per comparationem materiae demonstrationis; ibi: si igitur est scire ut posuimus et cetera. Circa primum quinque facit. Primo enim, determinat cuiusmodi scire sit, quod definire intendit.	Hence he does three things in regard to this. First, he defines what it is to know in a scientific manner. Secondly, he defines demonstration in terms of its end, which is to know in a scientific manner (71b18). Thirdly, from these two definitions he concludes to that definition of demonstration which is expressed in terms of the matter of demonstration (71b19). Concerning the first he does five things. First (71b8), he determines what the scientific knowing, which he intends to define, bears upon.
lib. 1 l. 4 n. 4 Circa quod sciendum est quod aliquid dicimur scire simpliciter, quando scimus illud in seipso. Dicimur scire aliquid secundum quid, quando scimus illud in alio, in quo est, vel sicut pars in toto, sicut si scientes domum, diceremur scire parietem; vel sicut accidens in subiecto, sicut si scientes Coriscum, diceremur scire venientem; vel sicut effectus in causa, sicut dictum est supra quod conclusionem praescimus in principiis; vel quocunque simili modo. Et hoc est scire per accidens, quia scilicet scito aliquo per se, dicimur scire illud quod accidit ei quocunque modo. Intendit igitur philosophus definire scire simpliciter, non autem scire secundum accidens. Hic enim modus sciendi est sophisticus. Utuntur enim sophistae tali modo arguendi: cognosco Coriscum; Coriscus est veniens; ergo cognosco venientem.	And in regard to this it should be recognized that we are said to know something in a scientific manner absolutely, when we know it in itself. On the other hand, we are said to know something in a scientific manner qualifiedly, when we know it in something else in which it exists either as a part in a whole (as we are said to know a wall through knowing the house), or as an accident in its subject (as in knowing Coriscus we are said to know who is coming toward us), or as an effect in its cause (as in the example given earlier, we know the conclusion in the principles), or indeed in any fashion similar to these. To know in these ways is to know incidentally, because we are said to know that which is somehow accidental to what is known of itself. However, what the Philosopher intends to define here is scientific knowing in the strict sense and not according to an accident. For this form of knowing is sophistical, since Sophists use a form of argument typified by the following: “I know Coriscus; Coriscus is coming toward me: therefore, I know the person coming toward me.”
lib. 1 l. 4 n. 5 Secundo, cum dicit: cum causam arbitramur etc., ponit definitionem ipsius scire simpliciter. Circa quod considerandum est quod scire aliquid est perfecte cognoscere ipsum, hoc autem est perfecte apprehendere veritatem ipsius: eadem enim sunt principia esse rei et veritatis ipsius, ut patet ex II metaphysicae. Oportet igitur scientem, si est perfecte cognoscens, quod cognoscat causam rei scitae. Si autem cognosceret causam tantum, nondum cognosceret effectum in actu, quod est scire simpliciter, sed virtute tantum, quod est scire secundum quid et quasi per accidens. Et ideo oportet scientem simpliciter cognoscere etiam applicationem causae ad effectum. Quia vero scientia est etiam certa cognitio rei; quod autem contingit aliter se habere, non potest aliquis per certitudinem cognoscere; ideo ulterius oportet quod id quod scitur non possit aliter se habere. Quia ergo scientia est perfecta cognitio, ideo dicit: cum causam arbitramur cognoscere; quia vero est actualis cognitio per quam scimus simpliciter, addit: et quoniam illius est causa; quia vero est certa cognitio, subdit: et non est contingere aliter se habere.	Then (71b10) he presents the definition of scientific knowing in the strict sense. Apropos of this it should be noted that to know something scientifically is to know it completely, which means to apprehend its truth perfectly. For the principles of a thing’s being are the same as those of its truth, as is stated in Metaphysics II. Therefore, the scientific knower, if he is to know perfectly, must know the cause of the thing known; hence he says, “when we think that we know the cause” (71b10). But if he were to know the cause by itself, he would not yet know the effect actually—which would be to know it absolutely—but only virtually, which is the same as knowing in a qualified sense and incidentally. Consequently, one who knows scientifically in the full sense must know the application of the cause to the effect; hence he adds, “as the cause of that fact” (71b11). Again, because science is also sure and certain knowledge of a thing, whereas a thing that could be otherwise cannot be known with certainty, it is further required that what is scientifically known could not be otherwise. To repeat: because science is perfect knowledge, lie says, “Men we think that we know the cause”; but because the knowledge through which we know scientifically in the full sense is actual, he adds, “as the cause of that fact.” Finally, because it is certain knowledge, he adds, “and that the fact could not be other than it is (71b11).”
lib. 1 l. 4 n. 6 Tertio, ibi: manifestum igitur etc., manifestat positam definitionem per hoc, quod tam scientes, quam non scientes, existimantes tamen se scire, hoc modo accipiunt scire sicut dictum est: non scientes enim qui existimant se scire, opinantur sic se habere in cognoscendo, sicut dictum est; scientes autem vere sic se habent. Est autem haec recta manifestatio definitionis. Definitio enim est ratio, quam significat nomen, ut dicitur in IV metaphysicae; significatio autem nominis accipienda est ab eo, quod intendunt communiter loquentes per illud nomen significare: unde et in II topicorum dicitur quod nominibus utendum est, ut plures utuntur. Si quis etiam recte consideret, hac notificatione magis ostenditur quid significet nomen, quam directe aliquid significetur: non enim notificat scientiam, de qua proprie posset definitio assignari, cum sit species alicuius generis, sed notificat ipsum scire. Unde et a principio dixit: scire autem opinamur etc., et non dixit: scire est aliquid tale vel tale.	Thirdly (71b12), he explains the definition he laid down, appealing to the fact that both those who know scientifically and those who do not know in that way but believe that they do, take scientific knowing to be as above described. For those who do not know in a scientific manner but believe that they do, are convinced that they know in the manner described, whereas those who know in a scientific manner do know in the manner described. Furthermore, this is the proper way to manifest a definition. For a definition is the notion which a name signifies, as it is stated in Metaphysics IV. But the signification of a name must be based on what is generally meant by those who employ the name. Hence it is stated in Topics II that names must be used as the majority of people use them. Again, careful consideration would indicate that this explanation seems rather to show what the name signifies than to signify something directly. For he does not explain science, concerning which a definition could, properly speaking, be formed, since it is a species of some genus; rather he explains scientific knowing. Hence at the very beginning he said, “We suppose ourselves to possess unqualified scientific knowledge” (71b8) and not that scientific knowledge is such and such.
lib. 1 l. 4 n. 7 Quarto, ibi: quare cuius etc., concludit quoddam corollarium ex definitione posita, scilicet quod illud, de quo simpliciter habetur scientia, oportet esse necessarium, scilicet quod non contingat aliter se habere.	Fourthly (71b14), he draws a corollary from the definition, namely, that that of which there is unqualified scientific knowledge must be something necessary, i.e., which cannot be otherwise.
lib. 1 l. 4 n. 8 Quinto, ibi: si quidem etc., respondet tacitae quaestioni, utrum scilicet sit aliquis alius modus sciendi a praedicto. Quod promittit se in sequentibus dicturum: est enim scire etiam per effectum, ut infra patebit. Dicimur etiam aliquo modo scire ipsa principia indemonstrabilia, quorum non est accipere causam. Sed proprius et perfectus sciendi modus est qui praedictus est.	Fifthly (71b16), he answers a tacit question, namely, whether there is another way of knowing scientifically in addition to the way described here. And he promises to discuss this later. For it is possible to know scientifically through an effect, as will be explained below (cf. L. 23). Furthermore, there is a sense in which we are said to know scientifically the indemonstrable principles to which no cause is ascribed. But the proper and perfect manner of knowing scientifically is the one we have described.
lib. 1 l. 4 n. 9 Deinde, cum dicit: dicimus autem etc., definit syllogismum demonstrativum per comparationem ad finem suum, qui est scire. Circa quod tria facit. Primo, ponit quod scire est finis syllogismi demonstrativi sive effectus eius, cum scire nihil aliud esse videatur, quam intelligere veritatem alicuius conclusionis per demonstrationem.	Then (71b17) he defines the demonstrative syllogism in terms of its end, which is to know in a scientific manner. In regard to this he does three things. First, he asserts that scientific knowing is the end of a demonstrative syllogism or is its effect, since to know scientifically seems to b nothing less than to understand the truth of a conclusion through demonstration.
Secundo, ibi: demonstrationem autem etc., definit syllogismum demonstrativum per huiusmodi finem: dicens quod demonstratio est syllogismus scientialis, idest faciens scire. Tertio, exponit hoc quod dixerat scientialem; ibi: sed scientialem etc., dicens quod scientialis syllogismus dicitur, secundum quem scimus, in quantum ipsum habemus, ne forte aliquis syllogismum scientialem intelligeret, quo aliqua scientia uteretur.	Secondly (71b18), he defines demonstration in terms of the end, saying that a demonstration is a sciential syllogism, i.e., producing scientific knowledge. Thirdly (71b18), he explains, “sciential,” saying that a sciential syllogism is one according to which we know scientifically insofar as we understand it, and not in the sense of a syllogism yielding knowledge to be put to use.
lib. 1 l. 4 n. 10 Deinde, cum dicit: si igitur est scire etc., concludit ex praedictis definitionem syllogismi demonstrativi ex materia sumptam. Et circa hoc duo facit: primo, concludit; secundo, manifestat eam; ibi: verum quidem igitur oportet esse et cetera. Circa primum tria facit. Primo, ponit consequentiam, qua demonstrationis materialis definitio concluditur ex praemissis, dicens quod si scire hoc significat quod diximus, scilicet, causam rei cognoscere etc., necesse est quod demonstrativa scientia, idest quae per demonstrationem acquiritur, procedat ex propositionibus veris, primis et immediatis, idest quae non per aliquod medium demonstrantur, sed per seipsas sunt manifestae (quae quidem immediatae dicuntur, in quantum carent medio demonstrante; primae autem in ordine ad alias propositiones, quae per eas probantur); et iterum ex notioribus, et prioribus, et causis conclusionis.	Then (71b19) he concludes from the foregoing a definition of the demonstrative syllogism that is based on its matter. Concerning this he does two things. First, he concludes it. Secondly, he clarifies it (71b24). Concerning the first he does three things. First (71b20), he sets forth the consequent in which the material definition of demonstration is concluded from the premises laid down above. And he says that if scientific knowing is what we have stated it to be, namely, knowing the cause of a thing, etc., then it is necessary that demonstrative science, i.e., science acquired through demonstration, proceed from propositions which are true, first, and immediate, i.e., not demonstrated by some other mid but clear in virtue of themselves (they are called “immediate,” inasmuch as they do not have a middle demonstrating them, but “first,” in relation to other propositions which are proved through them); and which, furthermore, are better known than, prior to, and causes of, the conclusion.
lib. 1 l. 4 n. 11 Secundo, ibi: sic enim erunt etc., excusat se ab additione alterius particulae, quae videbatur apponenda: quod scilicet demonstratio ex propriis principiis procederet. Sed ipse dicit quod hoc intelligitur per ea, quae dicta sunt. Nam si propositiones demonstrationis sunt causae conclusionis, necesse est quod sint propria principia eius: oportet enim causas esse proportionatas effectibus.	Secondly (71b22), he justifies himself for not adding another element which, it might seem, should be added, namely, that demonstration proceeds from proper principles. But he says that this is understood in virtue of the elements he did state. For since the propositions of a demonstration are causes of the conclusion, they must be its proper principles. For effects require proportionate causes.
lib. 1 l. 4 n. 12 Tertio, ibi: syllogismus quidem etc., manifestat praemissae consequentiae necessitatem, dicens quod licet syllogismus non requirat praemissas conditiones in propositionibus, ex quibus procedit, requirit tamen eas demonstratio: aliter enim non faceret scientiam.	Thirdly (71b23), he manifests the necessity of the aforesaid consequence, saying that although a syllogism does not require these conditions in the premises from which it concludes, a demonstration does require them, for otherwise it would not produce science.
lib. 1 l. 4 n. 13 Deinde, cum dicit: verum quidem etc., manifestat positam definitionem, manifestans etiam quod immediate dixerat, scilicet quod nisi praemissae conditiones demonstrationi adessent, scientiam facere non posset. Primo ergo, ostendit quod semper procedit ex veris ad hoc quod scientiam faciat: quia quod non est, non est scire; sicut diametrum esse symmetrum, idest commensurabilem lateri quadrati (dicuntur enim quantitates incommensurabiles, quarum non potest accipi aliqua mensura communis; et huiusmodi quantitates sunt, quarum non est proportio ad invicem sicut numeri ad numerum; quod de necessitate contingit de diametro quadrati et eius latere, ut patet ex X Euclidis). Quod autem non est verum, non est: nam esse et esse verum convertuntur. Oportet ergo id quod scitur esse verum. Et sic conclusionem demonstrationis, quae facit scire, oportet esse veram, et per consequens eius propositiones: non enim contingit verum sciri ex falsis, etsi concludi possit ex eis, ut infra ostendet.	Then (71b24) he explains this definition as well as the subsequent statement that unless these conditions are fulfilled in a demonstration it cannot beget science. First, therefore, he shows that a demonstration must proceed from true principles in order to beget science, because there cannot be scientific knowledge of that which does not exist, for example, that the diagonal is symmetrical, i.e., commensurable with the side of the square. For those quantities are said to be incommensurable which lack a common measuring unit. These are quantities whose ratio to one another cannot be expressed in terms of one number to another number. That this is the case with the diagonal of a square and its side is plain from Euclid’s sixteenth proposition. Now what is not true does not exist, for to be and to be true are convertible. Therefore, anything scientifically known must be true. Consequently, the conclusion of a demonstration which does beget scientific knowing must be true, and a fortiori its premises. For the true cannot be known in a scientific way from the false, although something true can follow as a conclusion from something false, as he will show later (cf. Lecture 13).
lib. 1 l. 4 n. 14 Secundo, ibi: ex primis autem etc., ostendit quod demonstratio sit ex primis et immediatis, sive indemonstrabilibus. Non enim contingit aliquem habere scientiam, nisi habeat demonstrationem eorum, quorum potest esse demonstratio, et hoc dico per se, et non per accidens. Et hoc ideo dicit, quia possibile esset scire aliquam conclusionem, non habentem demonstrationem praemissorum, etiam si essent demonstrabilia: quia sciret eam per alia principia; et hoc esset secundum accidens.	Secondly (71b27), he shows that the demonstration is composed of first and immediate or indemonstrable principles. For no one can possess scientific knowledge unless he possesses the demonstration of things that can be demonstrated—“and I am speaking per se and not per accidens.” He says this because it would be possible to know some conclusion without having a demonstration of the premises, even were they demonstrable; because one would know it through other principles, and this would be accidental.
Detur ergo quod aliquis demonstrator syllogizet ex demonstrabilibus, sive mediatis: aut ergo habet illorum demonstrationem, aut non habet: si non habet, ergo non scit praemissa, et ita nec conclusionem propter praemissa; si autem habet, cum in demonstrationibus non sit abire in infinitum, ut infra ostendet, tandem erit devenire ad aliqua immediata et indemonstrabilia. Et sic oportet quod demonstratio ex immediatis procedat, vel statim, vel per aliqua media. Unde et in primo libro topicorum dicitur quod demonstratio est ex primis et veris, aut ex his quae per ea fidem sumpserunt.	Suppose, therefore, that a demonstrator syllogizes from demonstrable, i.e., mediate, premises. Now he either possesses a demonstration of those premises or he does not. If he does not, then he does not know the premises in a scientific way; nor consequently, the conclusion because of the premises. But if he does possess their demonstration, then, since one may not proceed to infinity in demonstrations, principles immediate and indemonstrable must be reached. And so it is required that demonstration proceed from principles that are immediate either straightway or through middles. Hence it is stated in Topics I that demonstration is composed of first and true statements or of statements made credible by these.
lib. 1 l. 4 n. 15 Tertio, ibi: causas quoque etc., probat quod demonstrationis propositiones sint causae conclusionis, quia tunc scimus, cum causas cognoscimus. Et ex hoc concludit ulterius quod sint priores et notiores, quia omnis causa est naturaliter prior et notior suo effectu. Oportet autem quod causa conclusionis demonstrativae sit notior, non solum quantum ad cognitionem quid est, sed etiam quantum ad cognitionem quia est. Non enim ad demonstrandum quod eclipsis solis est, sufficit scire quod est lunae interpositio, sed oportet etiam scire quod luna interponitur inter solem et terram. Et quia prius et notius dicitur dupliciter, scilicet quoad nos, et secundum naturam; dicit consequenter quod ea, ex quibus procedit demonstratio, sunt priora et notiora simpliciter et secundum naturam, et non quoad nos.	Thirdly (71b29), he proves that the propositions of a demonstration are the causes of the conclusion, because we know in a scientific manner when we know the causes. And in virtue of this he shows that they are prior and better known, because every cause is by nature prior and better known than its effect. However, the cause of a demonstrated conclusion must be better known not only with respect to the knowledge of what it is, but also with respect to the knowledge that it is. For in order to demonstrate that there is an eclipse of the sun, it is not enough to know, that the moon is interposed; in addition it is necessary to know that the moon is interposed between the sun and the earth. Again, because prior i and better known are taken in two ways, namely, in reference to us and according to nature, he says that the things from which a demonstration, proceeds are prior and better known absolutely and according to nature, and not in reference to us.
Et ad huius expositionem dicit quod priora et notiora simpliciter sunt illa, quae sunt remota a sensu ut universalia. Priora autem et notiora quoad nos sunt proxima sensui, scilicet singularia, quae opponuntur universalibus, sive oppositione prioris et posterioris, sive oppositione propinqui et remoti.	To elucidate this he says that “those things are prior and better known absolutely,” which are farthest from sense, as are universals; but “the prior and better known in reference to us” are nearest to sense, namely, the singulars, which are opposed to universals in the way that the prior and the later are opposite, or in the way that the nearest and the farthest are opposite.
lib. 1 l. 4 n. 16 Videtur autem contrarium huius haberi in I Physic., ubi dicitur quod universalia sunt priora quoad nos, et posteriora secundum naturam. Sed dicendum est quod hic loquitur de ordine singularis ad universale simpliciter, quorum ordinem oportet accipere secundum ordinem cognitionis sensitivae et intellectivae in nobis. Cognitio autem sensitiva est in nobis prior intellectiva, quia intellectualis cognitio ex sensu procedit in nobis. Unde et singulare est prius et notius quoad nos quam universale. In I autem Physic. non ponitur ordo universalis ad singulare simpliciter, sed magis universalis ad minus universale, ut puta, animalis ad hominem, et sic oportet quod quoad nos, universalius sit prius et magis notum.	However, it seems that the contrary of this is found in Physics I where it is stated that universals are prior in reference to us and later according to nature. But it should be said that there [in the Posterior Analytics] he is speaking of the order of singular to universal absolutely; and this order must be taken according to the order of sensitive and intellectual knowledge in us. Now in us sensitive knowledge is prior to intellectual, because intellectual knowledge in us proceeds from sense. For this reason the singular is prior and better known in relation to us than the universal. But in Physics I he is not speaking of the order of the universal to the singular absolutely but of the order of the more universal to the less universal, for example of animal to man. In this case the more universal is prior and better known in reference to us.
In omni enim generatione, quod est in potentia est prius tempore et posterius natura, quod autem est completum in actu est prius natura et posterius tempore. Cognitio autem generis est quasi potentialis, in comparatione ad cognitionem speciei, in qua actu sciuntur omnia essentialia rei. Unde in generatione scientiae nostrae prius est cognoscere magis commune quam minus commune.	For in every instance of generation, that which is in potency is prior in time but is later according to nature; whereas that which is complete in act is prior by nature but later in time. Now one’s knowledge of a genus is, as it were, potential in comparison to one’s knowledge of the species in which all the essentials of a thing are actually known. Hence, too, in the generation of our science, knowledge of the more common precedes knowledge of the less common.
Item, in libro Physic. dicitur quod innata est nobis via ex nobis notioribus; non ergo demonstratio fit ex his quae sunt priora simpliciter, sed quoad nos. Sed dicendum quod hic loquitur secundum quod id quod est in sensu est notius quoad nos, eo quod est in intellectu. Ibi autem secundum quod id quod est notius quoad nos, est etiam in intellectu. Ex singularibus autem quae sunt in sensu, non sunt demonstrationes, sed ex universalibus tantum, quae sunt in intellectu. Vel dicendum quod in omni demonstratione, oportet quod procedatur ex his, quae sunt notiora quoad nos, non tamen singularibus, sed universalibus.	Again, in the Physics it is stated that it is natural for us to proceed from what is better known to us. Therefore, it seems that a demonstration is composed not of things that are prior absolutely but in reference to But it must be said that here he is speaking according to the fact that what is in the sense is better known in reference to us than what is in the intellect; but there he was speaking according to the fact that what is better known in reference to us is also in the intellect. But demonstrations do not proceed from singulars which are in the sense but only from universals, which are in the intellect.
Non enim aliquid potest fieri nobis notum, nisi per id quod est magis notum nobis. Quandoque autem id quod est magis notum quoad nos, est etiam magis notum simpliciter et secundum naturam; sicut accidit in mathematicis, in quibus, propter abstractionem a materia, non fiunt demonstrationes nisi ex principiis formalibus. Et in talibus fiunt demonstrationes ex his quae sunt notiora simpliciter. Item, quandoque id quod est notius quoad nos non est notius simpliciter, sicut accidit in naturalibus, in quibus essentiae et virtutes rerum, propter hoc quod in materia sunt, sunt occultae, sed innotescunt nobis per ea, quae exterius de ipsis apparent. Unde in talibus fiunt demonstrationes ut plurimum per effectus, qui sunt notiores quoad nos, et non simpliciter. Nunc autem non loquitur de hoc modo demonstrationum, sed de primo.	Or it might be said that in every demonstration one must proceed from things better known to us, provided they are not singulars but universals. For something is made known to us only by that which is more known to us. But sometimes that which is more known in reference to us is also more known absolutely and according to nature, as happens in mathematics where on account of abstraction from matter the demonstrations proceed from formal principles alone. In this case the demonstrations proceed from things which are more known absolutely. But sometimes that which is more known in reference to us is not more known absolutely, as happens in natural sciences where the essences and powers of things are hidden, because they are in matter, but are disclosed to us through the things which appear outwardly. Hence in these sciences the demonstrations are for the most part made through effects which are better known in reference to us but not absolutely. But he is not now speaking of this form of demonstration, but of the first.
Quia vero in hac manifestatione hoc etiam omiserat manifestare, quod demonstratio esset ex propriis principiis, consequenter subdit quod hoc habetur etiam ex praemissis. Per hoc enim quod dicitur quod demonstratio est ex primis, habetur quod sit ex propriis principiis, sicut et superius dictum est. Idem enim videtur esse primum et principium: nam primum in unoquoque genere et maximum est causa omnium eorum, quae sunt post, ut dicitur in II methaphysicae.	Finally, because in his explanation he neglected to point out that demonstration should proceed from proper principles, he hastens to add that this fact is easily ascertainable from what he did say. For from the fact that he stated that demonstration is from things which are first, it follows that it is from proper principles, as he stated above. For “first” and “principle” seem to be the same: for that which is first and highest in each genus is the cause of all the things that are after it, as it is stated in Metaphysics II.