INFINITY
INFINITY
The actually infinite, however, is now and at every
moment complete, absolute, entirely determined.
The immeasuralMe, omnipresent spirit does not
advance from point to point without end, but is con-
stantly ever\-where, fills every "beyond" of every
assignable point. Hegel calls potential infinity the
improper {xchlechte) , actual infinity the true infinity.
The Infinity of God. — The actual infinity of God in every respect is Catholic dogma. In accordance with Holy Writ (III Kings, viii, 27; Ps. cxliv, 3: cxlvi, 5; Ecclus., xliii, 29 sqq.; Luke, i, 37, etc.) and unanimous tradition, the Vatican Council at its Third Session (cap. i) declared God to be almighty, eternal, immense, incomprehensible, infinite in intellect antl will and every perfection, really and essentially dis- tinct from the world, infinitely blessetl in Himself and through Himself, and inexpressibly above all things that can exist and be thought of besides Him. The infinity of God may also be proved from philosophy. God is the self-existing, uncreated Be- ing, whose entire explanation must be in Himself, in Whom there can be no trace of chance; but it would be mere chance, if God possessed only a finite degree of perfection, for, however high that degree might be, everything in the uncreated Being — His perfections, His individuality, His personality — admit the possi- bility of His possessing a still higher degree of entirety. From outside of Himself God cannot be limited, because, being uncreated. He is absolutelj' independent of external causes and conditions. Limitation would be chance; the more so because we can maintain not only that any given finite degree of perfection may be surpassed, but also, in a positive way, that an infinite being is possible. Aloreover, if God were finite, the existence of other gods. His equals or even His superiors in perfection, would be possible, and it would be mere chance if they did not exist. Of such gods no trace can be found, while, on the other hand, God's infinity is suggested Ijy various data of experience, and in particular by our unbounded longing after knowledge and happiness. The more man a man is and the more he follows his l)est thoughts and impulses, the less is he satisfied with merely finite cognitions and pleasures. That the essential cravings of our nature are not deceptive, is demonstrated at once by experience and speculation.
From the infinity of God it is easy to deduce all His perfections: His unity, simplicity, immutability, etc., though these may be proved also by other means. Many of God's attributes are nothing else than His infinity in a particular respect, e. g. His omnipotence is but the infinity of His power; His omniscience, the infinity of His knowledge. Whatever is known to be a pure unalloyed perfection, must be an attribute of God on account of His infinity. We say a pure unal- loyed perfection; for God, just because He is infinite, does not possess all perfections in the same way. Only pure perfections — i. e. those which incluile in their concept no trace of imperfection whatsoever — are con- tained in Him formally. We must therefore ascribe to Him the attributes wise, powerful, amiable etc., without any restriction, because these are all pure per- fections. Of the so-called mixed perfections, which incluile besides the positive reality also some imperfec- tions, as, e.g., extension. contrition, courage, sound rea- soning, and clear judgment. He possesses only the perfection without the connected imperfection. His is, for example, the all-pervading presence without composition; love for the good without having com- mitted sin; power without having to overcome fear; knowledge without formal reasoning or formal judg- ment. He possesses therefore the mixed perfections in a higher form — eminently, i. e. in the only form which is worthy of the infinite. But even the pure perfec- tions are contained in Him in a higher form than in the creature, in which they are dependent, derived, finite. God's perfection and that of the creature are the same
analogically only, not univocally. The error of An-
thropomorphism consists just in this, that it ascribes to
God human perfections, without first refining them;
whereas Agnosticism errs in its contention that, of all
the pure and good qualities which are found in crea-
tures, none can be ascribed to God. Those modern
writers too are mistaken, who hold the best form of
religious sentiment to be that which comprises the
largest number of elements and, if needs be, of con-
tradictions. According to them we should call God
both finite and infinite: finite, to escape .\gnosticism,
infinite, \o avoid .Anthropomorphism. But it is evi-
dent that the highest and absolute truth carmot be a
compound of contradictions.
The dogma of tiod's infinity is not only of the great- est import for theology in the strictest sense of the term (i. e. the treatise on God), but it throws new light upon the malice of .sin, which, on account of the dignity of Him Who is offended, becomes objectively infinite; upon the Infinite majesty of the Incarnate Word and the boundless value of His merits and satisfaction; upon the necessity of the Incarnation, if God's justice required an adequate satisfaction for sin.
Infinity and Monism. — How imperatively thought demands that infinity be ascribed to the self-existent Being is best shown by t he fact , that all those who have at any time identified, and especially those who now- adays identify God and the world — in short, all Mon- ists — almost universally speak of the infinity of their God. But this is an error. One has but to open one's eyes to see that the world is imperfect, and therefore finite. It avails nothing for the Monists to assume that the world is infinite in extension; all that could be inferred from this supposition would be an infinitely extended imperfection and finiteness. Xor do they gain anything by staking their hopes on evolution, and predicting infinity in the future for the world; uncre- ated existence involves infinity at every moment, at this present instant as well as at any future time, and not only potential but real, actual infinity. Others therefore maintain that the world is not their God, but an emanation from God; they must consequently grant that God has parts — else nothing could emanate from Him — and that these parts are subject to imper- fection, decay, and evil — in short that their God is not infinite. Hence others assert that the things of this world are not parts of the Absolute, but its manifes- tations, representations, forms, qualities, activities, accidents, attriliutes, affections, phenomena, modifica- tions. But if these are not mere words, if the things of this world are really modifications etc. of the Ab- solute, it follows again that, as much as it is in finite things, the Absolute is subject to limitation, evil, and sin, and is therefore not infinite. This leads many to take the last step by asserting that the things of this world are nothing in themselves, but simply thoughts and conations of the Absolute. But why lias not the Absolute grander and purer conceptions and volitions? Why has it contcnteil itself for thousands of years with the.se realistic self-representations, and not even yet attained with certainty an idealistic conception of reality? Turn as one may, in spite of all efforts to evade the consequence, the god of Monism is not an infinite being.
The Monists oliject that God as conceived by The- ists is a finite thing, since He is not in Himself all reality, but has, outside Himself, the reality of the world. However, it has been stated above that infinity and totality are two entirely different ideas, and that infinity does not, in every supposition, ex- clude the existence of other things besides itself. We say, not "in every supposition", for it may be that the infinite could not be infinite if certain beings existed. .V being uncreated or independent of God, or a Manichaean principle of evil, cannot exist be- side the infinite God, because it would limit His abso- lute perfections. This is the time-honoured proof for
