Praeterea. Illud quod est commune omnibus scientiis non debet uni appropriari. Sed quaelibet scientia ratiocinando procedit, discurrendo vel ex effectibus in causas, vel ex causis in effectus, vel ex aliquibus signis. Ergo non debet naturali appropriari. Obj. 3: Again, what is common to all the sciences should not be reserved to one. But every science proceeds by reasoning, advancing from effects to causes or from causes to effects or from certain signs. So this method should not be reserved to natural science. Praeterea. Ratiocinativum in VI Ethicorum contra scientificum distinguitur a Philosopho. Sed philosophia naturalis ad scientificum pertinet. Ergo non convenienter attribuitur (ei) rationabiliter procedere. Obj. 4: Again, in the Ethics the Philosopher distinguishes the reasoning part of the soul from the scientific part. But natural philosophy belongs to the scientific part. Therefore it is not appropriately said to proceed according to the mode of reason. Sed contra est quod dicitur in libro De spiritu et anima quod ratio circa formas corporum versatur. Sed considerare corpora maxime pertinet ad naturalem. Ergo convenienter attribuitur ei rationabiliter procedere. On the contrary, the De spiritu et anima says that reason is concerned with the forms of bodies. Now it belongs most especially to natural philosophy to consider bodies. Therefore the rational method is appropriately attributed to it. Praeterea. In V De consolatione Boethius dicit: ratio cum quid universale respicit, nec imaginatione nec sensu utens, imaginabilia tamen et sensibilia comprehendit. Sed imaginabilia et sensibilia comprehendere ad solum naturalem pertinet. Ergo rationalis processus convenienter naturali attribuitur. Moreover, Boethius says: when reason contemplates some universal nature, using neither imagination nor sense, it nevertheless comprehends imaginable and sensible things. Now it belongs to the natural philosopher alone to comprehend what is imaginable and sensible. Therefore the rational method is suitably attributed to natural philosophy. II II Ulterius videtur quod inconvenienter dicatur mathematica disciplinabiliter procedere. Disciplina enim nihil aliud esse videtur quam acceptio scientiae. Sed in qualibet parte philosophiae accipitur scientia; quia omnes demonstrative procedunt. Ergo procedere disciplinaliter est commune omnibus partibus philosophiae, et ita non debet appropriari mathematicae. Obj. 1: In the second place, it seems inappropriate to say that mathematics proceeds according to the mode of learning, for learning seems to be nothing else than the receiving knowledge. But we receive scientific knowledge in all branches of philosophy, because all proceed by means of demonstration. So it is common to all parts of philosophy to proceed according to the mode of learning; and so this procedure should not be made exclusive to mathematics. Praeterea. Quanto aliquid certius, tanto facilius esse videtur ut de eo sit disciplina. Sed naturalia sunt certiora, ut videtur, quam mathematica; quia capiuntur sensu, a quo omnis nostra cognitio ortum habet. Ergo hic modus magis competit naturali quam mathematico. Obj. 2: Again, the more certain something is, the easier it seems to learn it. But natural things seem to be more certain than mathematics because they are apprehended by the senses, from which all our knowledge takes its origin. Therefore this method belongs to the natural philosopher rather than to the mathematician. Praeterea. Ut dicitur in V Metaphysicae, initium in scientiis est a quo fit facilior disciplina. Sed initium addiscendi accipitur a logica, quam oportet praeaddiscere mathematicae et omnibus aliis. Ergo disciplinalis modus magis convenit logicae quam aliis. Obj. 3: Again, as the Metaphysics says, in the sciences we begin at the point from which we learn more easily. But learning begins with logic, which must be mastered before mathematics and all the other sciences. Therefore it belongs to logic rather than to the other sciences to proceed according to the mode of learning. Praeterea. Modus naturalis scientiae et divinae sumitur a potentiis animae, scilicet a ratione et intellectu. Ergo similiter et modus mathematicae ab aliqua animae potentia sumi deberet, et sic non convenienter ponitur eius modus disciplinabiliter versari. Obj. 4: Again, the methods of natural and divine science are taken from powers of the soul, namely from reason and intellect. Therefore in the same way the method of mathematics ought to be taken from some power of the soul. So it is not appropriate to say that its method is to proceed according to the mode of learning. Sed contra. Disciplinaliter procedere est demonstrative procedere et per certitudinem. Sed sicut Ptolemaeus in principio Almagesti, solum mathematicum genus, si quis huic diligentiam exhibeat inquisitionis firmam stabilemque fidem intendentibus notitiam dabit, velut demonstratione per indubitabiles vias facta. Ergo disciplinaliter procedere maxime proprium est mathematici. On the contrary, to proceed according to the mode of learning is to proceed by demonstration and with certitude. But as Ptolemy says, mathematics alone, if one applies himself diligently to it, will give the inquirer after knowledge firm and unshaken certitude by demonstrations carried out with unquestionable methods. Therefore it is most characteristic of mathematics to proceed according to the mode of learning. Praeterea. Hoc patet per Philosophum, qui in pluribus locis suorum librorum scientias mathematicas disciplinas nominat. Moreover, this is evident from the Philosopher who, in several places in his works, calls the mathematical sciences disciplines. III III Ulterius videtur quod non sit conveniens modus divinae scientiae intellectualiter procedere. Intellectus enim secundum Philosophum est principiorum, scientia autem conclusionum. Sed non omnia quae in scientia divina traduntur sunt principia, sed quaedam etiam conclusiones. Ergo intellectualiter procedere non est conveniens scientiae divinae. Obj. 1: In the third place, it seems that it is not appropriate to divine science to proceed according to the mode of intellect, for according to the Philosopher, there is understanding of principles, whereas there is science of conclusions. But principles alone are not considered in divine science; some conclusions are also considered. Therefore to proceed according to the mode of intellect is not appropriate to divine science. Praeterea. In illis quae omnem intellectum excedunt intellectualiter versari non possumus. Sed divina excedunt omnem intellectum, ut Dionysius dicit I c. De divinis nominibus, et Philosophus in libro De causis. Ergo intellectualiter tractari non possunt. Obj. 2: Again, we cannot proceed intellectually with regard to those things that transcend every intellect. But divine things transcend every intellect, as Dionysius and the Philosopher say. Therefore they cannot be dealt with intellectually. Praeterea. Dionysius dicit VII c. De divinis nominibus quod angeli habent intellectualem virtutem in quantum divinam cognitionem non congregant a sensibilibus aut a rebus divisis. Sed hoc est supra animae potestatem, ut ibidem subditur. Cum ergo divina scientia de qua nunc agitur sit scientia humanae animae, videtur quod non sit proprius modus eius intellectualiter tractare. Obj. 3: Again, Dionysius says that angels have intellectual power inasmuch as they do not gather their divine knowledge from what is sensible and divided; but, as he adds, this is beyond the power of the soul. Therefore, since the divine science that is now under discussion is a science belonging to the human soul, it appears that its proper method is not to proceed intellectually. Praeterea. Theologia praecipue videtur esse de his quae fidei sunt. Sed in his quae fidei sunt intelligere est finis; unde dicitur Isa. VII, secundum aliam litteram: nisi credideritis non intelligetis. Ergo intellectualiter versari circa divina non debet poni theologiae modus sed finis. Obj. 4: Again, theology seems particularly concerned with the things of faith. But understanding (intelligere) is the goal of the things of faith. Thus it is said in lsaiah, according to another version, unless you believe, you will not understand. So we should not say that proceeding intellectually about divine things is the method of theology but the goal. Sed contra est quod dicitur in libro de spiritu et anima quod intellectus est spirituum creatorum, intelligentia vero ipsius Dei. De his autem praecipue est scientia divina. Ergo intellectualiter procedere videtur esse ipsius proprium. On the contrary, the De spiritu et anima says that intellect (intellectus) has for its object created spirits, while understanding (intelligentia) has for its object God himself. Now divine science is principally concerned with them. Therefore it seems proper to it to proceed intellectually. Praeterea. Modus scientiae debet respondere materiae. Sed res divinae sunt res intelligibiles per se ipsas. Ergo modus conveniens divinae scientiae est intellectualiter procedere. Moreover, the method of a science must correspond to its subject matter. But divine things are intelligible in virtue of themselves. Therefore the method appropriate to divine science is to proceed intellectually. I I Responsio. Dicendum, ad primam quaestionem, quod processus aliquis quo proceditur in scientiis dicitur rationabilis tripliciter. To the first question I answer that a method of proceeding in the sciences is called rational in three ways. Uno modo ex parte principiorum ex quibus proceditur, ut cum aliquis procedit ad aliquid probandum ex operibus rationis, cuiusmodi sunt genus et species et oppositum, et huiusmodi intentiones quas logici considerant; et sic dicetur aliquis processus esse rationabilis quando aliquis utitur in aliqua scientia propositionibus quae traduntur in logica, prout scilicet utimur logica prout est docens in aliis scientiis. Sed hic modus procedendi non potest proprie competere alicui particulari scientiae, in quibus peccatum accidit nisi ex propriis procedatur: contingit autem hoc proprie et convenienter fieri in logica et metaphysica, eo quod utraque scientia communis est et circa idem subiectum quodammodo. In one way, because of the principles from which we begin; for instance, when we proceed to prove something beginning with mental beings, like genus, species, opposite, and concepts of this sort, which the logicians study. In this sense a method will be called rational when in a science we use the propositions taught in logic; namely, when we use logic as having a teaching function in the other sciences. But this method of proceeding cannot belong properly to any particular science: it will fall into error unless it proceeds from its own proper principles. However, logic and metaphysics may properly and suitably use this method, because both are universal sciences and in a sense treat of the same subject. Alio modo dicitur processus rationalis ex termino in quo sistitur procedendo: ultimus enim terminus ad quem rationis inquisitio perducere debet, est intellectus principiorum, in quae resolvendo iudicamus; quod quidem quando fit, non dicitur processus vel probatio rationabilis sed demonstrativa. Quandoque autem inquisitio rationis non potest usque ad praedictum terminum perduci, sed sistitur in ipsa inquisitione, quando scilicet inquirenti adhuc manet via ad utrumlibet, et hoc contingit quando per probabiles rationes proceditur, quae natae sunt facere opinionem vel fidem, non scientiam; et sic rationabilis processus dividitur contra demonstrativum. Et hoc modo rationabiliter procedi potest in qualibet scientia, ut ex probabilibus paretur via ad necessarias probationes; et hic est alius modus quo logica utimur in scientiis demonstrativis, non quidem ut est docens, sed ut est utens. Et his duobus modis denominatur processus rationalis a scientia rationali: his enim modis usitatur logica, quae rationalis scientia dicitur, in scientiis demonstrativis, ut dicit Commentator in I Physicorum. In a second way, a method is called rational because of the end that terminates the thinking process. For the ultimate end that rational inquiry ought to reach is the understanding of principles, in which we resolve our judgments. And when this takes place, it is not called a rational procedure or proof but a demonstration. Sometimes, however, rational inquiry, cannot arrive at the ultimate end, but stops in the course of the investigation itself; that is to say, when several possible solutions still remain open to the investigator. This happens when we proceed by means of probable arguments, which by their nature produce opinion or belief, but not science. In this sense, rational method is opposed to demonstrative method. We can proceed by this rational method in all the sciences, preparing the way for necessary, proofs by probable arguments. This is another use of logic in the demonstrative sciences; not indeed as having a teaching function, but as being an instrument. In these two ways, then, a method is called rational from rational science, for, as the Commentator says, in both of them logic (which is another name for rational science) is used in the demonstrative sciences. Tertio modo dicitur aliquis processus rationalis a potentia rationali, in quantum scilicet in procedendo sequimur proprium modum animae rationalis in cognoscendo; et sic rationabilis processus est proprius scientiae naturalis. Scientia enim naturalis in suis processibus servat proprium modum rationalis animae quantum ad duo. In a third way, a method is called rational from the rational power, that is, inasmuch as in our procedure we follow the manner proper to the rational soul in knowing, and in this sense the rational method is proper to natural science. For in its procedures natural science keeps the characteristic method of the rational soul in two ways. Primo quantum ad hoc quod sicut anima rationalis a sensibilibus, quae sunt nota magis quoad nos, accipit cognitionem intelligibilium, quae sunt magis nota secundum naturam, ita scientia naturalis procedit ex his quae sunt nota magis quoad nos et minus nota secundum naturam, ut patet in I Physicorum, et demonstratio quae est per signum vel effectum maxime usitatur in scientia naturali. First, in this respect, that just as the rational soul receives from sensible things (which are more knowable relatively to us) knowledge of intelligible things (which are more knowable in their nature), so natural science proceeds from what is better known to us and less knowable in its own nature. This is evident in the Physics. Moreover, demonstration by means of a sign or an effect is used especially in natural science. Secundo quia cum rationis sit de uno in aliud discurrere, hoc maxime in scientia naturali observatur, ubi ex cognitione unius rei in cognitionem alterius devenitur, sicut ex cognitione effectus in cognitionem causae. Second, natural science uses a rational method in this respect, that it is characteristic of reason to move from one thing to another; and this method is observed particularly in natural science, where we go from the knowledge of one thing to the knowledge of another; for example, from the knowledge of an effect to the knowledge of its cause. Et non solum proceditur ab uno in aliud secundum rationem quod non est aliud secundum rem, sicut si ab animali procedatur ad hominem: in scientiis enim mathematicis proceditur per ea tantum quae sunt de essentia rei, cum demonstrent solum per causam formalem, et ideo non demonstratur in eis aliquid de una re per aliam rem, sed per propriam diffinitionem illius rei: etsi enim aliquae demonstrationes dentur de circulo ex triangulo vel e converso, hoc non est nisi in quantum in circulo est potentia triangulus et e converso. And the procedure in natural science is not only a movement from one thing to another distinct from it in the mind and not in reality, as when we go from the concept animal to the concept man. In the mathematical sciences we proceed only by means of what is of the essence of a thing, since they demonstrate only through a formal cause. In these sciences, therefore, we do not demonstrate something about one thing through another thing, but through the proper definition of that thing. It is true that some demonstrations about the circle are made by means of the triangle or vice versa, but this is only because the triangle is potentially in the circle and vice versa. Sed in scientia naturali, in qua fit demonstratio per causas extrinsecas, probatur aliquid de una re per aliam rem omnino extrinsecam; et ita modus rationis maxime in scientia naturali observatur, et propter hoc scientia naturalis inter alias est maxime hominis intellectui conformis. But in natural science, where demonstration takes place through extrinsic causes, something is proved of one thing through another thing entirely external to it. So the method of reason is particularly observed in natural science; and on this account natural science among all the others is most in conformity with the human intellect. Attribuitur ergo rationabiliter procedere scientiae naturali, non quod ei soli conveniat, sed quia ei praecipue competit. Consequently, we say that natural science proceeds rationally, not because this is true of it alone, but because it is especially characteristic of it. Ad primum ergo dicendum, quod ratio illa procedit de processu qui dicitur rationabilis secundum primum modum: sic enim processus rationabilis est proprius rationali scientiae et divinae, non autem naturali. Reply Obj. 1: That argument is based on the method that is called rational in the first way. In this sense a rational method is proper to rational and divine science, but not to natural science. Ad secundum dicendum, quod ratio illa procedit de processu qui dicitur rationabilis secundo modo. Reply Obj. 2: That argument is based on the method that is called rational in the second way. Ad tertium dicendum, quod in omnibus scientiis servatur quantum ad hoc modus rationis, quod proceditur de uno in aliud secundum rationem, non autem quod procedatur de una re in aliam; sed hoc est proprium naturalis scientiae, ut dictum est. Reply Obj. 3: The method of reason is observed in all the sciences insofar as they proceed from one item to another that is mentally distinct from it, but not in the sense that they go from one thing to another thing. As has been said, that is proper to natural science. Ad quartum dicendum, quod Philosophus ibi pro eodem ponit ratiocinativum et opinativum; unde patet quod pertinet ad secundum modum assignatum; ratiocinativo autem vel opinativo attribuit Philosophus ibidem agibilia humana, de quibus est scientia moralis, ratione suae contingentiae. Unde potest ex dictis colligi quod primus modus rationabilitatis est maxime proprius scientiae rationali, secundus scientiae morali, tertius scientiae naturali. Reply Obj. 4: In that place the Philosopher considers the reasoning and deliberative parts of the soul to be identical: so it is clear that they are related to the second mode of rational procedure mentioned above. In the same place, moreover, because of their contingency he assigns human actions, which are the objects of moral science, to the reasoning or deliberative part of the soul. From what has been said, then, we can gather that the first mode of rationality is most characteristic of rational science, the second of moral science, and the third of natural science. II II Ad secundam quaestionem dicendum, quod disciplinaliter procedere attribuitur scientiae mathematicae non quia ipsa sola disciplinaliter procedat, sed quia hoc ei praecipue competit. Cum enim discere nihil sit aliud quam ab alio scientiam accipere, tunc dicimur disciplinabiliter procedere, quando processus noster ad certam cognitionem perducit, quae scientia dicitur; quod quidem maxime contingit in mathematicis scientiis: cum enim mathematica sit media inter naturalem et divinam, ipsa est utraque certior. Naturali quidem propter hoc quod eius consideratio est a motu et materia absoluta, cum naturalis consideratio in materia et motu versetur. Ex hoc autem quod consideratio naturalis est circa materiam, eius cognitio a pluribus dependet, scilicet ex consideratione materiae ipsius et formae et dispositionum materialium, et proprietatum quae consequuntur formam in materia; ubicumque autem ad aliquid cognoscendum oportet plura considerare, est difficilior cognitio, unde in I Posteriorum dicitur quod minus certa scientia est quae est ex additione, ut geometria arithmetica. Ex hoc vero quod eius consideratio est circa res mobiles et quae non uniformiter se habent, eius cognitio est minus firma; quia eius demonstrationes frequenter procedunt ut in maiori parte, ex hoc quod contingit aliquando aliter se habere. Et ideo etiam quanto aliqua scientia magis appropinquat ad singularia, sicut scientiae operativae, ut medicina, alchimia et moralis, minus possunt habere de certitudine; propter multitudinem eorum quae consideranda sunt in talibus scientiis, quorum quodlibet si omittatur sequetur error, et propter eorum variabilitatem. To the second question I answer that mathematical science is said to proceed according to the mode of learning, not because it alone does so, but because this is especially characteristic of it. For, since learning is nothing else than the taking of knowledge from another, we are said to proceed according to the mode of learning when our procedure leads to certain knowledge, which is called science. Now this occurs particularly in the mathematical sciences. Because mathematics is situated between natural and divine science, it is more certain than either. It is more certain than natural science because its investigation is not bound up with motion and matter, while the investigation of natural science centers upon matter and motion. Now from the very fact that natural science deals with matter, its knowledge depends upon many factors, upon the consideration of matter itself, of form, and of the material dispositions and properties accompanying form in matter. And whenever there are many factors to be considered in order to know something, knowledge is more difficult. Thus the Posterior Analytics says that a science is less certain that results from adding on some item, as geometry adds something to arithmetic. If the inquiry in a science is about things that are mobile and lack uniformity, its knowledge is less exact because its demonstrations are often valid only in the majority of cases, owing to the fact that things sometimes happen differently. So, too, the more a science draws close to particulars (as do practical sciences like medicine, alchemy, and ethics), the less certain they can be because of the many factors to be taken into account in these sciences, the omission of any one of which will lead to error, and also because of their variability. Est etiam processus mathematicae certior quam processus scientiae divinae; quia ea de quibus est scientia divina sunt magis a sensibilibus remota, a quibus nostra cognitio initium sumit, et quantum ad substantias separatas, in quarum cognitionem insufficienter inducunt ea quae a sensibilibus accipimus, et quantum ad ea quae sunt communia omnibus entibus, quae sunt maxime universalia, et sic maxime remota a particularibus cadentibus sub sensu. Mathematica autem ipsa in sensu cadunt et imaginationi subiacent, ut figura, linea et numerus, et huiusmodi; et ideo intellectus humanus a phantasmatibus accipiens facilius capit horum cognitionem, et certius, quam intelligentiae alicuius, vel etiam quam quiditatem substantiae, et actum et potentiam et alia huiusmodi. Et sic patet quod mathematica consideratio est facilior et certior quam naturalis et theologica, et multo plus quam scientiae aliae operativae; et ideo ipsa maxime dicitur disciplinaliter procedere. Et hoc est quod Ptolemaeus dicit in principio Almagesti: alia duo genera theorici potius quis opinionem quam conceptionem scientialem dicat, theologicum quidem propter inapparens ipsius et incomprehensibile, physicum vero propter materiae instabile et immanifestum; solum autem mathematicum inquisitionis firmam stabilemque fidem intendentibus dabit, velut utique demonstratione per indubitabiles vias facta. The method of mathematics is also more certain than the method of divine science, because the objects of divine science are further removed from sensible things, from which our knowledge takes its origin. This is true both in the case of the separate substances (to which our knowledge of the sense world gives us inadequate access), and also in the case of the principles common to all things (which are most universal and therefore furthest removed from the particular things falling under the senses). But mathematical entities do fall under the senses and they are objects of our imagination; for example, figures, lines, numbers, and the like. So the human intellect, which takes its knowledge from images, knows these things with greater ease and certainty than it does a separate Intelligence, or even the nature of substance, act, potency, and the like. It is clear, then, that mathematical inquiry, is easier and more certain than physical and theological, and much more so than that of the other sciences that are practical, and for this reason it is said especially to proceed according to the mode of learning. This is what Ptolemy asserts in the beginning of the Almagest: “Let us call the other two kinds of theoretical knowledge opinion rather than science: theology because of its obscurity and incomprehensibility, physics because of the instability and obscurity of matter. The mathematical type of investigation alone will give the inquirer firm and unshaken certainty through demonstrations carried out by unquestionable methods.” Ad primum ergo dicendum, quod quamvis in qualibet scientia disciplina accipiatur, tamen in mathematica facilius et certius, ut dictum est. Reply Obj. 1: Although we learn in all the sciences, nevertheless, as we have said, we do so with greater ease and certitude in mathematics.