Articulus 10 Article 10 Utrum Deus possit facere infinita Whether God can make infinite things Decimo autem incidenter quaesitum fuit utrum Deus possit facere infinita. In the tenth article we ask a question which arose incidentally: can God make infinites? Et videtur quod sic. Rationes enim in mente divina existentes, sunt factivae rerum, nec una impedit aliam a sua actione. Cum ergo sint infinitae rationes in mente divina, possunt ex eis consequi infiniti effectus, divina potentia exequente. Obj. 1: It seems that he can, for natures existing in the divine mind are productive of things, and one does not impede another by its action. Since there are infinite natures in the divine mind, infinite effects could follow from them~ were the divine power to carry them into execution. Praeterea, potentia creatoris in infinitum excedit potentiam creaturae. Sed de potentia creaturae est ut producantur infinita successive. Ergo Deus potest simul producere infinita. Obj. 2: The power of the Creator infinitely surpasses that of a creature. But a creature can produce infinites successively. Therefore, God can produce infinites simultaneously. Praeterea, frustra est potentia quae non reducitur ad actum, et maxime si ad actum reduci non possit. Sed potentia Dei infinitorum est. Ergo frustra esset talis potentia, nisi posset actu facere infinita. Obj. 3: A power is useless if it is not put into act; it is especially useless if it cannot be put into act. But God’s power extends to infinites. Hence, such a power would be useless if he could not actually make infinites. Sed contra. Est quod Seneca dicit: idea est exemplar rerum quae naturaliter fiunt. Sed non possunt naturaliter esse infinita, et ita nec fieri, ut videtur; quia quod non potest esse, non potest fieri. Ergo in Deo infinitorum non erit idea. Sed Deus nihil potest operari nisi per ideam; ergo Deus non potest operari infinita. On the contrary (1): Seneca’s opinion is on the contrary: an idea is an exemplar off things coming into being naturally. But, since there cannot be infinite things naturally, it would seem that they cannot come to be; for what cannot be cannot come to be. Therefore, there will be no idea of infinites in God. But God cannot make anything except through an idea. Therefore, he cannot make infinites. Praeterea, cum dicitur Deus creare res, nihil novum ex parte creantis ponitur, sed ex parte creaturae tantum; unde hoc videtur esse (idem) dictu Deum creare res, quod res exire in esse a Deo. Ergo, eadem ratione, Deum posse creare res, idem est quod res posse exire in esse a Deo. Sed res infinitae non possunt fieri, quia non est in creatura potentia ad actum infinitum. Ergo nec Deus potest infinita actu facere. Furthermore (2): When God is said to create a thing, nothing new on the part of the Creator is affirmed but only on the part of the creature. Hence, it seems the same to say that God creates things as to say that things come forth into being from God. For the same reason, therefore, to say that God can create things is to say that things are able to come forth from God into being. But infinite things cannot come to be, for no creature has the capacity for infinite act. Hence, even God cannot make actual infinites. Responsio. Dicendum, quod duplex invenitur infiniti distinctio. Uno modo distinguitur per potentiam et actum; et dicitur infinitum potentia quod semper in successione consistit, ut in generatione et tempore et divisione continui, in quibus omnibus est potentia ad infinitum, semper uno post aliud accepto; actu autem infinitum, sicut si poneremus lineam terminis carentem. Alio modo distinguitur infinitum per se, et per accidens; cuius distinctionis intellectus hoc modo patet. Infiniti enim ratio, ut dictum est, quantitati congruit; quantitas autem per prius dicitur de discreta quantitate quam de continua; et ideo ad videndum qualiter sit per se et per accidens infinitum, considerandum est quod multitudo quandoque requiritur per se, quandoque vero est per accidens tantum. Per se quidem multitudo requiritur, ut patet in causis ordinatis et effectibus, quorum unum habet dependentiam essentialem ad aliud; sicut anima movet calorem naturalem, quo moventur nervi et musculi, quibus moventur manus, quae movent baculum, quo movetur lapis; in his enim quodlibet posteriorum per se dependet a quolibet praecedentium. Sed per accidens multitudo invenitur, quando omnia quae in multitudine continentur, quasi loco unius ponuntur, et indifferenter se habent sive sint unum, sive multa, vel pauciora vel plura; sicut si aedificator facit domum, in cuius factione plures serras consumit successive, multitudo serrarum non requiritur ad factionem domus nisi per accidens ex hoc quod una non potest semper durare; nec differt aliquid ad domum, quotcumque ponantur; unde nec una earum habet dependentiam ad aliam, sicut erat quando multitudo requirebatur per se. Secundum ergo hoc de infinito variae opiniones processerunt. I answer that: the infinite can be distinguished in two ways. In one way, it is distinguished by means of potency and act. A potential infinite is that which consists in an endless succession. For example, we find potential infinity in generation, in time, and in the division of a continuum; for, when one member is given, another always follows. An example of an actual infinite, however, would be a line which we would assume to have no termini. In the second way, an essential infinite is distinguished from an accidental infinite. This distinction is explained as follows: the character of the infinite, as mentioned above, belongs to quantity. Now, quantity is predicated first of all of discrete quantity rather than of continuous quantity. Hence, in order to see what is infinite essentially and what is infinite accidentally, we must consider that a multitude is sometimes required essentially and sometimes merely accidentally. Essentially a multitude is required in ordered causes and effects where one has an essential dependence upon another. For example, the soul sets in motion the natural heat by which nerves and muscles are moved, which, in turn, move the hands, which move a stick by which a stone is moved. In this series, each of the later members essentially depends upon every one that precedes. But an accidental multitude is found when all the members of the multitude are posited, as it were, in place of one; and their mutual relation is such that it is a matter of indifference whether they be one or many, or more or fewer. For example, if a builder makes a house in whose construction he wears out many saws successively, a multitude of saws is required for the erection of the house only accidentally, that is, because one saw cannot last forever. It does not matter to the house how many saws are used; hence, one saw does not have that dependence upon another which we find when a multitude is required essentially. There are many different opinions about the infinite. Quidam enim antiqui philosophi posuerunt infinitum in actu non solum per accidens, sed per se; volentes quod infinitum esset de necessitate eius quod ponebant principium; unde etiam processum causarum in infinitum ponebant. Sed hanc opinionem philosophus reprobat in II Metaphys., et in III Phys. Alii vero Aristotelem sequentes concesserunt, quod infinitum per se inveniri non potest neque in actu neque in potentia, quia non est possibile quod aliquid essentialiter dependeat ab infinitis; sic enim eius esse nunquam compleretur. Sed infinitum per accidens posuerunt non solum esse in potentia, sed in actu; unde Algazel in sua Metaphysica ponit animas humanas a corporibus separatas esse infinitas, quia hoc sequitur ex hoc quod mundus, secundum ipsum, est aeternus: nec hoc inconveniens reputat, quia animarum ad invicem non est aliqua dependentia; unde in multitudine illarum animarum non invenitur infinitum nisi per accidens. Quidam vero posuerunt, quod infinitum actu nec per se nec per accidens esse potest; sed solum infinitum in potentia, quod in successione consistit, ut docetur in III Physic.; et haec est positio Commentatoris in II Metaphys. Sed hoc quod infinitum esse actu non possit, potest contingere ex duobus: vel quia esse actu repugnet infinito ex hoc ipso quod infinitum est, vel propter aliquid aliud; sicut moveri sursum repugnat triangulo plumbeo, non quia triangulus, sed quia plumbeus. Si ergo infinitum actu esse possit secundum rei naturam, secundum mediam opinionem; vel si etiam esse non possit impediente aliquo alio quam ipsa ratione infiniti; dico, quod Deus potest facere infinitum actu esse. Si autem esse actu repugnet infinito secundum suam rationem, tunc Deus hoc facere non potest; sicut non potest facere hominem esse animal irrationale, quia hoc esset contradictoria esse simul. Utrum autem esse actu repugnet infinito secundum rationem suam, vel non, quia incidenter hoc motum est, discutiendum alias relinquatur ad praesens. Ad argumenta autem utriusque partis respondendum. Some ancient philosophers posited actual infinites, both essential and accidental, thinking that an infinite would necessarily be a result of what they posited as a beginning. For this reason, they also posited an infinite process of causes. The Philosopher refutes this position, however. Others, following Aristotle, conceded that an essential infinite cannot be found either in act or in potency, because it is impossible for a thing to depend essentially upon an infinite number of things; for, if this were true, then its own act of existence would never be formally constituted. But they posited an accidental infinite, both in potency and in act. Algazel holds: there are an infinite number of human souls separated from bodies—something which he thought followed from his view that the world is eternal. He saw no difficulty since they have no mutual dependence, and so in their multiplicity they constituted merely an accidental infinity. Others asserted that there cannot be an actual infinite, either essential or accidental. They admitted a potential infinite, which, as is taught in the Physics, consists in succession; and this is the position of the Commentator. But for either of two reasons it can happen that an actual infinite cannot exist: either because to be in act is contradictory to the infinite by the very fact that it is infinite; or because of some extrinsic reason—as being lifted up is repugnant to a lead triangle, not because it is a triangle, but because it is lead. But if an actual infinite is not contradictory to the infinite as such and can exist, as I hold, or if it cannot exist merely because of some impediment extrinsic to the notion of an infinite, then I say that God can make an actual infinite. If, however, actual existence is repugnant to the very notion of an infinite, then God cannot make one, just as, for example, he cannot make a man be an irrational animal. This would mean that two contradictories would coincide in one act of existence. However, whether or not it is intrinsically repugnant for an actual infinite to exist must be discussed elsewhere, since this question arose only incidentally. Answers, however, must be given to the difficulties on both sides. Ad primum igitur dicendum, quod rationes quae sunt in mente divina, non producunt se in creatura secundum modum quo sunt in Deo, sed secundum modum quem patitur ratio creaturae; unde, quamvis sunt immateriales, tamen ex eis res in esse materiali producuntur. Si ergo de ratione infiniti sit quod non sit simul in actu sed in successione, sicut philosophus dicit in III Physicorum; tunc rationes infinitae quae sunt in mente divina, non possunt se in creaturis conficere omnes simul, sed secundum successionem; et sic non sequitur esse infinita actu. Reply Obj. 1: Natures in the divine mind are not reproduced in a creature the way in which they are in God, but in the way which the nature of a creature allows. Hence, although they themselves are immaterial, from them are brought forth things with a material act of existence. If, therefore, as the Philosopher says, it is of the essence of an infinite to exist, not actually and simultaneously, but merely successively, then the infinite natures in the divine mind cannot all be produced in creatures simultaneously but only successively. So, it does not follow that there are actual infinites. Ad secundum dicendum, quod virtus creaturae dicitur aliquid non posse dupliciter. Uno modo ex defectu virtutis; et tunc de illo quod creatura non potest, recte arguitur quod Deus possit. Alio modo ex eo quod illud quod creaturae impossibile dicitur, in seipso quamdam repugnantiam continet; et hoc, sicut nec creaturae, ita nec Deo est possibile, ut contradictoria esse simul; et de talibus erit infinitum esse actu, si esse in actu rationi infiniti repugnet. Reply Obj. 2: The power of a creature is said to be wanting in two ways. First, it can be wanting because of a lack of strength. In this respect, it is correct to argue that what a creature cannot do God can do. Second, it can be wanting because that which is said to be impossible for a creature to do contains in itself some intrinsic repugnance. In this respect, it is possible neither for a creature nor for God - as, for instance, that contradictories should exist simultaneously, and that an infinite actually exist falls into this class, if to exist actually is repugnant to the nature of an infinite. Ad tertium dicendum, quod frustra est quod non pertingit finem ad quem est, ut dicitur II Physic.; unde ex hoc quod potentia non reducitur ad actum, non dicitur esse frustra, nisi in quantum effectus eius, vel ipse actus diversus ab ea existens, est potentiae finis. Nullus autem divinae potentiae effectus est finis ipsius, nec actus eius est diversus ab eo; et ideo ratio non sequitur. Reply Obj. 3: As is said in the Physics, a being is useless if it does not attain the end for which it exists. Hence, a power is not said to be had in vain simply because it is not put into act, but only because its effect or the very act, being distinct from the power itself, is the end for which the power exists. However, no effect of the divine power is its end, nor is its act distinct from it. Hence, the argument does not follow. Ad primum vero quod in contrarium obiicitur, dicendum, quod quamvis secundum naturam non possint esse infinita simul, possunt tamen fieri; quia esse infiniti non consistit in simul essendo, sed est sicut ea quae sunt in fieri, ut dies, et agon, ut in III Physicorum dicitur. Nec tamen sequitur quod Deus sola illa facere possit quae naturaliter fiunt. Idea enim secundum praedictam assignationem accipitur secundum practicam cognitionem, quia est ex hoc quod determinatur a divina voluntate ad actum; potest autem Deus voluntate sua multa alia facere quam quae ab ipso determinata sunt ut sint, vel fuerint, vel futura sint. Reply Sed Contra 1: Although the members of infinites may not naturally be able to exist simultaneously, they may, however, come into being. For the essence of an infinite does not consist in simultaneous existence; but it is like things which are in a state of becoming, such as a day or a contest, as is said in the Physics. Nor does it follow that God is able to make only things which come into being naturally. It is true that according to the meaning given previously an idea was taken as applying to practical knowledge, which is an idea for this reason that it is determined by the divine will to an act. However, by his will God is able to make many things other than those which he has determined to exist now, in the past, or in the future. Ad secundum dicendum, quod quamvis in creatione nihil sit novum nisi quod est ex parte creaturae, tamen creationis nomen non solum hoc importat, sed etiam quod est ex parte Dei; significat enim divinam actionem, quae est sua essentia, et connotat effectum in creatura, qui est accipere esse a Deo; unde non sequitur quod Deum posse creare aliquid, idem sit quod aliquid posse creari ab eo: alias, antequam creatura esset, nihil creare potuisset, nisi creaturae potentia praeexisteret; quod est ponere materiam aeternam. Unde, quamvis potentia creaturae non sit ad hoc quod sint infinita actu, non ex hoc removetur quin Deus possit infinita actu facere. Reply Sed Contra 2: Although in creation there is nothing new except in reference to the creature, the word creation implies not only this newness but also something on the part of God; for it signifies a divine action, which is his essence, and connotes an effect in a creature, which is the reception of being from God. So, it does not follow that it is the same to say that God can create something as to say that something can be created by him. Otherwise, before there was a creature, nothing could be created unless the potency of a creature first existed. This would be positing eternal matter. Therefore, although the potency of a creature does not extend to the existence of actual infinites, this does not exclude ability on the part of God to make actual infinites. Articulus 11 Article 11 Utrum scientia aequivoce pure dicatur de Deo et nobis Whether knowledge predicated of God and man is purely equivocal Undecimo quaeritur utrum scientia aequivoce pure dicatur de Deo et nobis. In the eleventh article we ask: is knowledge predicated of God and men purely equivocally? Et videtur quod sic. Ubicumque enim est communitas univocationis vel analogiae, ibi est aliqua similitudo. Sed inter creaturam et Deum nulla potest esse similitudo. Ergo non potest aliquid esse utrique commune secundum univocationem vel secundum analogiam. Si ergo nomen scientiae de Deo et nobis dicitur, hoc erit aequivoce tantum. Probatio mediae. Isa. XL, 18, dicitur: cui similem fecistis Deum? etc., quasi dicat: nulli similis esse potest. Obj. 1: It seems that it is, for wherever there exists a common ground for univocal or analogical statement, there exists a certain likeness. But there can be no likeness between a creature and God. Therefore, there cannot be anything common to both either univocally or analogically. Consequently,’ if knowledge is predicated of God and of us, it will be merely an equivocal predication. Proof of the minor: In Isaiah 40:18 we read: to whom then have you likened God? —as if to say: he can resemble no one. Praeterea, ubicumque est aliqua similitudo, ibi est aliqua comparatio. Sed Dei ad creaturam nulla potest esse comparatio, cum creatura sit finita, et Deus infinitus. Ergo nulla potest esse eorum similitudo; et sic idem quod prius. Obj. 2: Wherever a likeness exists, some comparison is possible. But no comparison between God and creature is possible, since a creature is finite and God is infinite. Therefore, no likeness can exist between them, and the original difficulty stands. Praeterea, ubicumque est aliqua comparatio, ibi oportet esse aliquam formam quae secundum magis vel minus vel aequaliter a pluribus habeatur. Sed hoc non potest dici de Deo, et creatura quia sic esset aliquid Deo simplicius. Ergo inter ipsum et creaturam non est aliqua comparatio; et ita nec similitudo nec communitas, nisi aequivocationis tantum. Obj. 3: Whenever a comparison is possible, there must be some form possessed to a greater and a lesser degree or equally by several things. But this cannot be said of God and a creature, for then something would be-more simple than God. Therefore, no comparison between God and a creature is possible, nor is any likeness or community possible apart from that of equivocation. Praeterea, maior est distantia eorum quorum nulla est similitudo, quam quorum est similitudo aliqua. Sed inter Deum et creaturam est infinita distantia, qua nulla maior esse potest; ergo non est inter ea aliqua similitudo, et sic idem quod prius. Obj. 4: There is a greater distance between things which bear no resemblance than between those which do resemble each other. But there is an infinite distance between God and a creature; indeed, no greater distance is possible. Therefore, there is no likeness between them; thus, the original difficulty returns. Praeterea, maior est distantia creaturae ad Deum quam entis creati ad non ens, cum ens creatum non excedat non ens nisi secundum quantitatem suae entitatis, quae non est infinita. Sed enti et non enti nihil potest esse commune nisi secundum aequivocationem tantum, ut dicitur in VI Metaph.: ut, puta, si id quod vocamus hominem, alii vocent non hominem. Ergo nec Deo et creaturae potest esse aliquid commune nisi secundum aequivocationem puram. Obj. 5: A greater distance lies between a creature and God than lies between a created being and non-being; for a created being surpasses non-being only by reason of the amount of its entity, which is not infinite. But, as is said in the Metaphysics: there is nothing common to being and non-being except by equivocation, which happens, for example, when that which we call man is called non-man by others. Hence, there cannot be anything common to God and a creature except by a pure equivocation. Praeterea, in omnibus analogiis ita est, quod vel unum ponitur in definitione alterius, sicut ponitur substantia in definitione accidentis, et actus in definitione potentiae; vel aliquid idem ponitur in definitione utriusque, sicut sanitas animalis ponitur in definitione sani, quod dicitur de urina et cibo, quorum alterum est conservativum, alterum significativum sanitatis. Sed creatura et Deus non hoc modo se habent, neque quod unum in definitione ponatur alterius, neque quod aliquid idem in definitione utriusque ponatur, etiam dato quod Deus definitionem haberet. Ergo videtur quod nihil secundum analogiam dici possit de Deo, et creaturis; et ita restat quod aequivoce pure dicatur quidquid de eis communiter dicitur. Obj. 6: All analogates are such that either one is placed in the definition of another—as substance is placed in the definition of accident, and act, in the definition of potency—or the same thing is placed in the definition of both—as the health of an animal is placed in the definition of healthy, which is predicated of urine and food since one is the sign of this health and the other conserves it. But God and creatures are not related in this manner: one is not placed in the definition of the other, nor is something identical placed in the definition of each, even on the supposition that God could be defined. Therefore, it seems that nothing can be predicated analogously of God and creatures. As a consequence, any term predicated of both of them is used only equivocally. Praeterea, magis differt substantia et accidens quam duae species substantiae. Sed idem nomen impositum ad significandum duas species substantiae secundum propriam utriusque rationem, aequivoce pure de his dicitur, sicut hoc nomen canis impositum caelesti, latrabili, et marino. Ergo multo fortius, si unum nomen imponatur substantiae et accidenti. Sed nostra scientia est accidens, divina autem, est substantia. Ergo nomen scientiae de utraque pure aequivoce dicitur. Obj. 7: Substance and accident differ more than do two species of substances. But when the same word is used to signify two species of substances according to formal character proper to each, the predication is merely equivocal. This happens, for example, when the word dog is applied to the dog-star, a barking dog, and the dog-fish. It would be a far more equivocal predication if one word were applied to a substance and an accident. Now, our knowledge is an accident and that of God, a substance. Therefore, the word knowledge is predicated equivocally of God’s and of ours. Praeterea, scientia nostra non est nisi quaedam imago divinae scientiae. Sed nomen rei non convenit imagini nisi aequivoce, unde animal aequivoce dicitur de vero animali et picto secundum philosophum in praedicamentis; ergo et nomen scientiae pure aequivoce dicitur de scientia Dei et nostra. Obj. 8: Our knowledge is merely an image of the divine knowledge. But the name of a thing cannot be applied to its image except by equivocation. Hence, animal, according to the Philosopher, is predicated equivocally of a real animal and of one in a picture. Therefore, the word knowledge is likewise predicated only equivocally of God’s knowledge and ours. Sed contra. Est quod philosophus dicit in V Metaph., quod illud est perfectum simpliciter in quo omnium generum perfectiones inveniuntur; et hoc est Deus, ut Commentator ibidem dicit. Sed perfectiones aliorum generum non dicerentur inveniri in ipso, nisi aliqua similitudo esset perfectionis ipsius ad aliorum generum perfectiones. Ergo creaturae ad eum est aliqua similitudo; non ergo pure aequivoce dicitur scientia, vel quidquid aliud dicitur, de creatura et Deo. On the contrary (1): The Philosopher says that that is perfect, absolutely speaking, in which the perfections of all genera are found. As the Commentator remarks on this passage, such a being is God. But the perfections of other genera could not be said to be found in him unless there were some resemblance between his perfection and the perfections of other genera. Hence, a creature resembles God in some way. Knowledge, therefore, and whatever else is predicated of God and creatures is not a pure equivocation. Praeterea, Genes. I, 26 dicitur: faciamus hominem ad imaginem et similitudinem nostram. Ergo est aliqua similitudo creaturae ad Deum, et sic idem quod prius. Furthermore (2): Genesis 1:26 says: let us make man to our image and likeness. Therefore, some likeness exists between God and creature. We conclude as before. Responsio. Dicendum, quod impossibile est dicere aliquid univoce praedicari de creatura et Deo. In omnibus enim univocis communis est ratio nominis utrique eorum de quibus nomen univoce praedicatur; et sic quantum ad illius nominis rationem univoca in aliquo aequalia sunt, quamvis secundum esse unum altero possit esse prius vel posterius, sicut in ratione numeri omnes numeri sunt aequales, quamvis secundum naturam rei unus altero naturaliter prior sit. Creatura autem quantumcumque imitetur Deum, non tamen potest pertingere ad hoc ut eadem ratione aliquid sibi conveniat qua convenit Deo: illa enim quae secundum eamdem rationem sunt in diversis, sunt eis communia secundum rationem substantiae sive quidditatis, sed sunt discreta secundum esse. Quidquid autem est in Deo, hoc est suum proprium esse; sicut enim essentia in eo est idem quod esse, ita scientia est idem quod esse scientem in eo; unde, cum esse quod est proprium unius rei non possit alteri communicari, impossibile est ut creatura pertingat ad eamdem rationem habendi aliquid quod habet Deus, sicut impossibile est quod ad idem esse perveniat. Similiter etiam esset in nobis: si enim in Socrate non differret homo et hominem esse, impossibile esset quod homo univoce diceretur de eo et Platone, quibus est esse diversum; nec tamen potest dici quod omnino aequivoce praedicetur quidquid de Deo et creaturis dicitur, quia nisi esset aliqua convenientia creaturae ad Deum secundum rem, sua essentia non esset creaturarum similitudo; et ita cognoscendo suam essentiam non cognosceret creaturas. Similiter etiam nec nos ex rebus creatis in cognitionem Dei pervenire possemus; nec nominum quae creaturis aptantur, unum magis de eo dicendum esset quam aliud; quia in aequivocis non differt quodcumque nomen imponatur, ex quo nulla rei convenientia attenditur. I answer that: it is impossible to say that something is predicated univocally of a creature and God because in all univocal predication the nature signified by the name is common to those of whom the univocal predication is made. Hence, from the point of view of the nature signified by the predicate, the subjects of the univocal. predication are equal, even though from the point of view of its real existence one may take precedence over another. For example, all numbers are equal from the point of view of the nature of number, even though, by the nature of things, one number is naturally prior to another. No matter how much a creature imitates God, however, a point cannot be reached where something would belong to it for the same reason it belongs to God. For things which have the same formal characters but are in separate subjects are common to the same subjects in regard to substance or quiddity but distinct in regard to the act of being. But whatever is in God is his own act of being; and just as his essence is the same as his act of being, so is his knowledge the same as his act of being a knower. Hence, since the act of existence proper to one thing cannot be communicated to another, it is impossible that a creature ever attain to the possession of something in the same manner in which God has it, just as it is impossible for it to attain the same act of being as that which God has. The same is true of us. If man and to exist as man did not differ in Socrates, man could not be predicated univocally of him and Plato, whose acts of existing are distinct. Nevertheless, it cannot be said that whatever is predicated of God and creatures is an equivocal predication; for, unless there were at least some real agreement between creatures and God, his essence would not be the likeness of creatures, and so he could not know them by knowing his essence. Similarly, we would not be able to attain any knowledge of God from creatures, nor from among the names devised for creatures could we apply one to him more than another; for in equivocal predication it makes no difference what name is used, since the word does not signify any real agreement. Unde dicendum est, quod nec omnino univoce, nec pure aequivoce, nomen scientiae de scientia Dei et nostra praedicatur; sed secundum analogiam, quod nihil est dictu quam secundum proportionem. Convenientia autem secundum proportionem potest esse dupliciter: et secundum haec duo attenditur analogiae communitas. Est enim quaedam convenientia inter ipsa quorum est ad invicem proportio, eo quod habent determinatam distantiam vel aliam habitudinem ad invicem, sicut binarius cum unitate, eo quod est eius duplum; convenientia etiam quandoque attenditur non duorum ad invicem inter quae sit proportio sed magis duarum ad invicem proportionum, sicut senarius convenit cum quaternario ex hoc quod sicut senarius est duplum ternarii, ita quaternarius binarii. Prima ergo convenientia est proportionis, secunda autem proportionalitatis; unde et secundum modum primae convenientiae invenimus aliquid analogice dictum de duobus quorum unum ad alterum habitudinem habet; sicut ens dicitur de substantia et accidente ex habitudine quam accidens ad substantiam habet; et sanum dicitur de urina et animali, ex eo quod urina habet aliquam habitudinem ad sanitatem animalis. Quandoque vero dicitur aliquid analogice secundo modo convenientiae; sicut nomen visus dicitur de visu corporali et intellectu, eo quod sicut visus est in oculo, ita intellectus in mente. Quia ergo in his quae primo modo analogice dicuntur, oportet esse aliquam determinatam habitudinem inter ea quibus est aliquid per analogiam commune, impossibile est aliquid per hunc modum analogiae dici de Deo et creatura; quia nulla creatura habet talem habitudinem ad Deum per quam possit divina perfectio determinari. Sed in alio modo analogiae nulla determinata habitudo attenditur inter ea quibus est aliquid per analogiam commune; et ideo secundum illum modum nihil prohibet aliquod nomen analogice dici de Deo et creatura. Consequently, it must be said that knowledge is predicated neither entirely univocally nor yet purely equivocally of God’s knowledge and ours. Instead, it is predicated analogously, or, in other words, according to a proportion. Since an agreement according to proportion can happen in two ways, two kinds of community can be noted in analogy. There is a certain agreement between things having a proportion to each other from the fact that they have a determinate distance between each other or some other relation to each other, like the proportion which the number two has to unity in as far as it is the double of unity. Again, the agreement is occasionally noted not between two things which have a proportion between them, but rather between two related proportions—for example, six has something in common with four because six is two times three, just as four is two times two. The first type of agreement is one of proportion; the second, of proportionality. We find something predicated analogously of two realities according to the first type of agreement when one of them has a relation to the other, as when being is predicated of substance and accident because of the relation which accident has to substance, or as when healthy is predicated of urine and animal because urine has some relation to the health of an animal. Sometimes, however, a thing is predicated analogously according to the second type of agreement, as when sight is predicated of bodily sight and of the intellect because understanding is in the mind as sight is in the eye. In those terms predicated according to the first type of analogy, there must be some definite relation between the things having something in common analogously. Consequently, nothing can be predicated analogously of God and creature according to this type of analogy; for no creature has such a relation to God that it could determine the divine perfection. But in the other type of analogy, no definite relation is involved between the things which have something in common analogously, so there is no reason why some name cannot be predicated analogously of God and creature in this manner. Sed tamen hoc dupliciter contingit: quandoque enim illud nomen importat aliquid ex principali significato, in quo non potest attendi convenientia inter Deum et creaturam, etiam modo praedicto; sicut est in omnibus quae symbolice de Deo dicuntur, ut cum dicitur Deus leo, vel sol, vel aliquid huiusmodi, quia in horum definitione cadit materia, quae Deo attribui non potest. Quandoque vero nomen quod de Deo et creatura dicitur, nihil importat ex principali significato secundum quod non possit attendi praedictus convenientiae modus inter creaturam et Deum; sicut sunt omnia in quorum definitione non clauditur defectus, nec dependent a materia secundum esse, ut ens, bonum, et alia huiusmodi. But this can happen in two ways. Sometimes the name implies something belonging to the thing primarily designated which cannot be common to God and creature even in the manner described above. This would be true, for example, of anything predicated of God metaphorically, as when God is called lion, sun, and the like, because their definition includes matter which cannot be attributed to God. At other times, however, a term predicated of God and creature implies nothing in its principal meaning which would prevent our finding between a creature and God an agreement of the type described above. To this kind belong all attributes which include no defect nor depend on matter for their act of existence, for example, being, the good, and similar things. Ad primum igitur dicendum, quod sicut Dionysius dicit in IX cap. De divinis nominibus, Deus nullo modo creaturis similis dicendus est, sed creaturae possunt similes Deo dici aliquo modo. Quod enim ad imitationem alicuius fit, si perfecte illud imitetur, simpliciter potest ei simile dici; sed non e converso, quia homo non dicitur similis suae imagini, sed e converso: si autem imperfecte imitetur, tunc potest dici et simile et dissimile illud quod imitatur ei ad cuius imitationem fit: simile quidem, secundum hoc quod repraesentat; sed non simile, inquantum a perfecta repraesentatione deficit. Et ideo sacra Scriptura Deum creaturis esse similem omnibus modis negat, sed creaturam esse similem Deo quandoque quidem concedit, quandoque autem negat: concedit, cum dicit hominem ad similitudinem Dei factum; sed negat, cum dicit in Psal.: Deus, quis similis erit tibi? Reply Obj. 1: As Dionysius says, God can in no way be said to be similar to creatures, but creatures can be said to be similar to him in some sense. For what is made in imitation of something, if it imitates it perfectly, can be said to be like it absolutely. The opposite, however, is not true; for a man is not said to be similar to his image but vice versa. However, if the imitation is imperfect, then it is said to be both like and unlike that which it imitates: like, in so far as it resembles it; unlike, in so far as it falls short of a perfect representation. It is for this reason that Holy Scripture denies that creatures are similar to God in every respect. It does, however, sometimes grant that creatures are similar to God, and sometimes deny this. It grants the similarity when it says that man is made in the likeness of God, but denies it when it says: O God, who is like to thee? (Ps 71:19). Ad secundum dicendum, quod philosophus, in I Topic., ponit duplicem modum similitudinis. Unum qui invenitur in diversis generibus; et hic attenditur secundum proportionem vel proportionalitatem, ut quando alterum se habet ad alterum sicut aliud ad aliud, ut ipse ibidem dicit. Alium modum in his quae sunt eiusdem generis, ut quando idem diversis inest. Similitudo autem non requirit comparationem secundum determinatam habitudinem quae primo modo dicitur, sed solum quae secundo; unde non oportet ut primus modus similitudinis a Deo removeatur respectu creaturae. Reply Obj. 2: The Philosopher distinguishes two kinds of likenesses. One is found between things in different genera, and is taken according to proportion or proportionality; that is, one thing is related to another as a third thing is related to a fourth, as Aristotle himself says in the same place. The second kind of likeness is found existing between things in the same genus, as when the same thing is found in distinct subjects. Now, likeness of the first kind does not demand a comparison based on a definite relationship as does that of the second kind. Consequently, the possibility of the first type of likeness existing between God and creature should not be excluded. Ad tertium dicendum, quod obiectio illa manifeste procedit de similitudine secundi modi, quam concedimus creaturae ad Deum non esse. Reply Obj. 3: That difficulty arises from the second type of likeness; and we grant that this type does not exist between creature and God. Ad quartum dicendum, quod similitudo quae attenditur ex eo quod aliqua duo participant unum, vel ex eo quod unum habet habitudinem determinatam ad aliud, ex qua scilicet ex uno alterum comprehendi possit per intellectum, diminuit distantiam; non autem similitudo quae est secundum convenientiam proportionum. Talis enim similitudo similiter invenitur in multum vel parum distantibus; non enim est maior similitudo proportionalitatis inter duo et unum et sex et tria, quam inter duo et unum, et centum et quinquaginta. Et ideo infinita distantia creaturae ad Deum similitudinem praedictam non tollit. Reply Obj. 4: A likeness that is found because two things share something in common or because one has such a determinate relation to the other that from one the other can be grasped by the intellect—such a likeness diminishes distance. A likeness according to an agreement of proportion does not; for such a likeness is also found between things far or little distant. Indeed, there is no greater likeness of proportionality between two to one and six to three than there is between two to one and one hundred to fifty. Consequently, the infinite distance between a creature and God does not take away the likeness mentioned above. Ad quintum dicendum, quod etiam enti et non enti aliquid secundum analogiam convenit, quia ipsum non ens, ens dicitur analogice, ut patet in IV Metaphysic.; unde nec distantia quae est inter creaturam et Deum, communitatem analogiae impedire potest. Reply Obj. 5: There is some agreement between being and non-being according to analogy, for non-being itself is called being analogously, as is made clear in the Metaphysics. Consequently, the distance lying between a creature and God cannot prevent a common ground for analogical statement.