Scotus Academicus, Tomus primus: De Deo in se subsistente

Note 1. With our Bassoli in 1. d. 2. q. 2. a. 1., the infinite is said to be that which lacks a term: which happens in two ways, namely privatively and negatively. In the former way, that is called infinite which from itself does not have a term, but can have one. Thus prime matter is said by the Platonists to be infinite, because from itself it has no form by which it is terminated and actualized; but it is in potency to receiving absolutely any forms whatsoever by which it is informed and determined. In the latter way, that is called infinite which is neither finite from itself, nor finitizable through another; but which contains in itself formally, or eminently, every perfection that can at all be thought of. The former infinite is said to be most imperfect, because it is near to nothing, and is pure physical potency; the latter, however, is most perfect, because it is purest act, excluding all imperfection and potency. The former is called by Philolaus the Pythagorean malignity, darkness, etc.; the latter, however, is called by him benignity and the splendor of God. Orpheus, moreover, calls the former infinite confusion and chaos; the latter, however, distinction and ornament.

Note 2. The infinite taken negatively is again twofold: one, namely, in a certain respect, the other, however, simply and absolutely. The former is that which can be called infinite in a certain genus of beings. Thus, e.g., a continuum can be called infinite in quantity, because not so many parts of it can be assigned but that more remain to be numbered and assigned: so likewise, if the sun had infinite light, and fire infinite heat, the former would be called infinite in light, the latter, however, in heat: the latter, however, is that which is infinite in every genus of perfection, because it contains in itself the whole amplitude of being formally or eminently; so that no species, no perfection can be conceived in the universe of beings which does not shine forth in it.

Note 3. A twofold definition of the infinite is found in Aristotle, lib. 3. of the Physics cap. 6.: the first indeed handed down by the Ancients, who held that the infinite is that outside of which there is nothing, that is, which so comprehends all things in itself that there is no perfection, nor entity of things, which it does not contain in itself in a noble manner: the latter, however, is handed down by Aristotle himself, as it were opposed to the former, saying that the infinite is that of which something is always outside; which namely can never be exhausted by dividing. Both of these definitions fit the infinity of God. For He is so infinite that He cannot be comprehended, and consequently there always remains something of Him which is not yet grasped and known: so likewise He contains all things in Himself, so that He leaves nothing outside Himself; for, as Justin Martyr speaks, in the Question to the Orthodox, That is supremely perfect which can in nothing receive addition or increase. But whether this infinity can be shown to belong to God by efficacious reason and be urged by authority, is what must be resolved here.

First conclusion. — By natural reason it can be demonstrated that God is infinite.

The Doctor proves this conclusion together with his followers in 1. d. 2. q. 2. n. 2, by four reasons taken 1. from His effective power, 2. from His intellective power, 3. from His appetibility, 4. from His eminent dignity.

I form the first thus: That being which from itself could produce infinite distinct species if they were possible, has necessarily infinite power, and consequently an infinite essence: but God can produce infinite species, if they were possible: therefore He has infinite power, and thereby an infinite essence. The major is evident, first indeed as regards the inference of an infinite essence from the infinity of power; for since operative power is founded in the essence, and emanates from it, whence the common axiom: Operating follows being, it is evident that the greater the power is, the more perfect the essence is, and consequently that infinite power argues infinite perfection and essence. The same major is evident also as regards the inference of infinite power from infinite effects distinct in species, which it could produce, if such effects were possible; for since each producible species has a perfection distinct from another species, it is evident that if the producible species were infinite, the producible perfections would likewise be infinite; and consequently, since a cause is the more perfect the more perfections it can produce, it rightly follows that the cause which can produce infinite perfections is infinitely perfect. The minor is also evident, because since God is the first cause, and consequently having in Himself the causality of all inferior causes, and able to produce whatever is producible, it follows that if infinite species of things were possible, He could also produce them; for His power would not be more determined to one number than to another, and consequently could extend itself to infinity. For if it were limited, that would be either from itself or from another; not from another, otherwise it would not be first and supreme: not from itself either, because just as it would be entirely independent in being, so likewise its power would be entirely unlimited, and consequently infinite.

You will reply 1. The multiplication of species to infinity seems impossible, since in any genus there is given something so perfect that a more perfect than it cannot be assigned: therefore from those infinite impossible species infinite power in God is not rightly inferred. — I answer 1. that the antecedent can be denied, although the Doctor seems to affirm it probably; for no reason appears for limiting the species of creatures to some determined number and certain perfection, beyond which a greater and greater one could not be produced. For who will deny that many other and always more perfect species of flowers, plants, or other creatures could be newly produced? Who will deny that another heaven can be added above the Empyrean, just as the Empyrean was added above the Firmament, and so on in turn to infinity? I answer 2. by denying the consequence, because the object of divine Power is not only an effect possible absolutely, but also one possible under any condition whatsoever. Hence it becomes true to say that if a chimera were a true being, God could produce it; and so of other conditioned things, which cannot be produced, not indeed from defect of power in the productive cause, but from the repugnance and defect of possibility in the effect to be produced. And so whether species diverse to infinity are possible absolutely, or only hypothetically, it is always rightly inferred from their presupposed hypothetical or absolute possibility that the power which could produce them would truly be infinite.

You will reply 2. From infinite effects distinct only in number it is not lawful to infer the infinity of the cause: therefore neither from infinite species. The consequence is evident by parity of reason. The Doctor proves the antecedent ibidem n. 26: No greater power is required to produce two effects successively than to produce one in a single instant: but to produce one fire, e.g., in a single instant, infinite power is not required: therefore neither would such power be required to produce two fires successively. The consequence is evident, for the infernal fire, which will be conserved in eternity, would produce infinite heats successively in infinite bodies, if infinite successions were applied to it, and yet that fire will not be of infinite power; similarly the Sun and the heaven, if they endure in eternity, will cause infinite effects of illumination and influence, and yet it will not follow from this that they have infinite power. — I deny the consequence, and the reason for the disparity is that to produce effects diverse only in number, no other power and perfection is required in the agent, but only the application of the same power in those successive productions: it is otherwise, however, with the production of infinite species, because since each species has a perfection diverse from another, it also presupposes a diverse perfection in the cause from which it is produced; since the whole perfection of the effect depends on the perfection of the cause, because no one gives what he does not have, and consequently the cause could not give some power to the effect unless it first had it: therefore it rightly follows that if the producible effects have infinite perfections, the productive cause must also contain diverse and infinite perfections.

2. The Doctor's reason is taken from the infinite knowledge of God, which can be formed thus: He who necessarily understands infinite intelligibles at once, has infinite perfection and intellective power: but God understands them at once: therefore, etc. The major is certain, for the power of understanding and knowing is the more excellent the more things it can perceive and know at once, and consequently a power which can know infinite things at once must necessarily be infinite. The minor is proved: for those things are reckoned infinite where not so many can be known by creatures but that many more still remain to be known, nor can the created intellect ever arrive at the end of all by knowing one after another: but such are all possible creatures, which God Himself distinctly knows at once from eternity; nor can anyone deny that the thoughts and volitions of the Angels and of rational souls, e.g., will be more and more to infinity through eternity a parte post, and that no term and number can be assigned which they do not exceed: therefore God's intellect, which from eternity knows all of them at once, must be infinite. The same must be said of God's will and love, by which He distinctly wills and loves at once all and each of the good acts to be exercised without end, more and more through eternity, by the Angels and blessed men.

3. The Doctor's reason is taken from the notion of final cause and appetibility: Our appetite, or our will, has a natural inclination to love the infinite good, and aspires to it as to the ultimate end: therefore such a good exists; for if its existence were repugnant, the will would not incline by natural desire to attain it; for a natural appetite ought not to be in vain: therefore since such infinite good is not repugnant, it must necessarily exist; otherwise it would not be the infinite good, because it would not be more excellent than every good; for an existing good is more excellent than a non-existing good: but that notion of the highest good can be found in none but the first cause: therefore the first cause, or God, must be of infinite goodness and perfection. It is confirmed: the end is more excellent than those things which are for the end: but all things which are in the universe, both existing and possible, are ordered to God as to the ultimate end: therefore since all these ordainable things are infinite in number, the ultimate end itself must also be infinite.

4. The Doctor's reason is taken from the dignity and highest perfection of God: God is the being than which a more excellent cannot be thought or imagined: therefore He is infinite. The consequence is proved: Of anything finite a more perfect can be thought: therefore no finite thing can be that than which a better cannot be thought. Next, God is a being of highest and most excellent perfection: therefore He is infinite. The antecedent is proved: That being alone is of highest perfection which has every perfection not repugnant to being: but infinite perfection is not repugnant to being: therefore, etc. The minor is proved: both because if infinity were repugnant to being, that repugnance would appear from the terms; which is manifestly false, since no weighty reason can be brought which would persuade that repugnance: and because if infinity were repugnant to being; most of all either because finiteness intrinsically belonged to being as such, or because it would be its property convertible with it: for it does not appear by what other reason infinity would be repugnant to it: but neither of these can be said. Not the first, because we can conceive being as such without finiteness, which could not happen if finiteness were of its formal notion. Not the second either, because it cannot be concluded from the notion of being, nor from any other head, that finiteness is a property convertible with being. — It is confirmed: God is a being from itself, because He is the first of all beings and the most excellent: therefore He is unlimited and infinite. The consequence is proved: A being from itself is most perfect as much as it can be and be conceived: but the most perfect being, than which a more perfect cannot be or be conceived, must be simply infinite in perfection; for it is more perfect to be simply infinite in perfection than to be finite: therefore since God is the most excellent of all beings, and contains formally or eminently all the perfections of finite things, it follows that He is infinite. — Add that if He were limited and finitized, it would be most of all either from Himself or from another: not from another, since He has no cause; not from Himself either, because whatever is finitized from itself is finitized either by reason of the matter or of the form of which it consists: but since God has neither matter nor form, He cannot be limited and finitized even by Himself.

You will say. That is infinite which surpasses and transcends the maximum finite; for if it does not exceed it, it will remain within the multitude of those things which are finite: but it is impossible that a maximum finite be given: therefore it is also impossible that the infinite be given. The minor is proved: If a maximum finite were given, it would follow that it would become infinite by the addition of one grade or finite part, and consequently that the infinite would arise from two finites; thus, e.g., an infinite quantity would arise from a maximum finite quantity by the addition of only one palm or finger: but it is contradictory that the infinite can be made from two finites: therefore a maximum finite cannot be given. — I deny the major, and to its proof I say that for something to be infinite, nothing else is required than that it exceed in perfection absolutely every finite thing, however perfect it may be; nor is it required that a maximum finite be given which is exceeded and surpassed by the infinite. Thus, e.g., the Mathematicians with Euclid lib. 5. of the Elements say that the circle is more perfect than all rectilinear figures, although among them none is most perfect, for they can be multiplied to infinity: and man is said to be the most perfect of all animals, although in fact no brute is given so perfect that a more perfect cannot be given. The other objections customarily made against this conclusion we have already solved in proving the existence of God.

You will say 2. If God's infinity could be proved naturally, His omnipotence could also be proved: but according to the Doctor in 1. dist. 2. q. 2. n. 27. and dist. 12. and Quodlib. 7., divine omnipotence cannot be demonstrated: therefore neither can His infinity. The major is certain: since omnipotence is nothing other than infinite power: the Doctor proves the minor at the assigned places, where he shows that God's omnipotence is believed by faith alone, and cannot be proved by any natural reason. — I answer 1. that the major can be denied. For although omnipotence signifies the same thing in reality as infinite power; they nevertheless differ as regards their precise and formal concept: since omnipotence is conceived by order to everything factible simply; but infinite power is conceived by order to that which is factible without imperfection: for since it could be doubted whether doing all things imports perfection, for some Philosophers with Aristotle judged that the efficiency of certain effects argues imperfection; hence it was rightly doubted by them that God is omnipotent and the maker of all things, lest He be infected with some imperfection: but since the concept of infinite power argues no imperfection, but rather imports the highest perfection, hence no one doubts that it must be attributed to God, the most perfect of beings. — I answer 2. by distinguishing the minor: Divine omnipotence cannot be demonstrated insofar as it is productive of all naturally producible effects, I deny; nor did any Philosopher ever doubt this: insofar as it is productive of things from nothing, and conferring of supernatural gifts, namely grace, charity, beatitude, etc. I concede. For nature supplies no means for proving these effects.

Second conclusion. — God's infinity is also confirmed by sacred authority.

For from the Scriptures God is called, Job 30. Higher than the heavens, deeper than the abysses, etc. Jeremiah 32. Incomprehensible in thought. Psalm 146. Great is the Lord, and great is His power, and of His greatness there is no end: And Ps. 95. Declare His glory among the Gentiles, His wonders among all peoples, for great is the Lord, and exceedingly praiseworthy; which words St. Augustine thus weighs:

And if it said all day long Great, Great, what Great would it say? for great is the Lord, and exceedingly praiseworthy: For what is a small tongue going to say in praising the Great? By saying exceedingly, it sent out a voice, and gave the thought something to savor, as if saying, what I cannot sound out, do you think; and when you have thought, it will be little. What no one's thought explains, someone's tongue explains. For great is the Lord, and exceedingly praiseworthy.

— Some add that passage of Baruch 3. He is great, and has no end, high, and immense. But that is not said of God, but of the place of God's possession, that is, of the world, whose greatness the Prophet exaggerates, so as to open to the Jews how much they owe to God, because above the other nations, among which they are fewer (as he notes ibidem), they were chosen to be His people and the sheep of His pasture. Nor only there, but also elsewhere the name of the Infinite is very often used metaphorically. Thus Numbers 32: a great abundance of riches and a multitude of cattle is said to be infinite. And 3. Kings cap. 3. An infinite people: And cap. 10. Exceedingly infinite gold.

You will reply. If these latter words are used metaphorically and amplificatorily, so that infinite is the same as very great, why not also the former? I answer that there is no parity, because Sacred Scripture everywhere most constantly preaches the infinity of God, nor does it subject anything from which the metaphor may be detected; nor does any reason appear persuading that one must depart from the genuine sense of Scripture. Add that the Lateran Council under Innocent 3. cap. Firmiter, established that it must be believed with certain faith that God is immense and incomprehensible; and consequently that He is infinite. The Holy Fathers confirm the same: Great is God, says St. Dionysius lib. De Divin. Nominib. cap. 9., and above all greatness, and leaping over all infinity. And St. Augustine, Serm. 1. de verbis Apostoli: Inestimable, ineffable, incomprehensible, beyond all things, outside all things, besides all things: And lib. De speculo, cap. 33.: Above whom nothing, outside whom nothing, without whom nothing, beyond whom nothing, beneath whom nothing. God under whom all, with whom all, in whom all. God from whom all things, through whom all things, in whom all things. And St. Gregory Nazian. Orat. 38. calls God an immense and unlimited sea of essence. The rest of the Holy Fathers affirm the same everywhere, who preach that God is infinite and is confined by no limits.