“I have never proceeded from any Genus supremum of the actual infinite. Quite the contrary, I have rigorously proved that there is absolutely no Genus supremum of the actual infinite. What surpasses all that is finite and transfinite is no Genus; it is the single, completely individual unity in which everything is included, which includes the Absolute, incomprehensible to the human understanding. This is the Actus Purissimus, which by many is called God.”

— Georg Cantor

As quoted in Out of the Mouths of Mathematicians : A Quotation Book for Philomaths (1993) by Rosemary Schmalz.
Context: I have never proceeded from any Genus supremum of the actual infinite. Quite the contrary, I have rigorously proved that there is absolutely no Genus supremum of the actual infinite. What surpasses all that is finite and transfinite is no Genus; it is the single, completely individual unity in which everything is included, which includes the Absolute, incomprehensible to the human understanding. This is the Actus Purissimus, which by many is called God.
I am so in favor of the actual infinite that instead of admitting that Nature abhors it, as is commonly said, I hold that Nature makes frequent use of it everywhere, in order to show more effectively the perfections of its Author. Thus I believe that there is no part of matter which is not — I do not say divisible — but actually divisible; and consequently the least particle ought to be considered as a world full of an infinity of different creatures.

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Georg Cantor 27

mathematician, inventor of set theory 1845–1918

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“What I assert and believe to have demonstrated in this and earlier works is that following the finite there is a transfinite (which one could also call the supra-finite), that is an unbounded ascending ladder of definite modes, which by their nature are not finite but infinite, but which just like the finite can be determined by well-defined and distinguishable numbers.”

Georg Cantor (1845–1918) mathematician, inventor of set theory

As quoted in Understanding the Infinite (1994) by Shaughan Lavine ~ ISBN 0674921178

“What I declare and believe to have demonstrated in this work as well as in earlier papers is that following the finite there is a transfinite (transfinitum)--which might also be called supra-finite (suprafinitum), that is, there is an unlimited ascending ladder of modes, which in its nature is not finite but infinite, but which can be determined as can the finite by determinate, well-defined and distinguishable numbers.”

Georg Cantor (1845–1918) mathematician, inventor of set theory

From Kant to Hilbert (1996)

“God in His infinite grandeur without any quantity and absolutely indivisible, which we call immensity, is necessarily all in every extension or space or place which exists or can be imagined.”

Nicole Oresme (1323–1382) French philosopher

Book II, Ch. 2, p. 279.
Le livre du ciel et du monde (1377)

“Only to the extent that a man has emancipated himself…from all that is generic, does he count as a free spirit within a human community. No man is all genus, none is all individuality.”

Rudolf Steiner book Philosophy of Freedom

Philosophy of Freedom. Chapter 14

“The actual infinite arises in three contexts: first when it is realized in the most complete form, in a fully independent otherworldly being, in Deo, where I call it the Absolute Infinite or simply Absolute; second when it occurs in the contingent, created world; third when the mind grasps it in abstracto as a mathematical magnitude, number or order type.”

Georg Cantor (1845–1918) mathematician, inventor of set theory

As quoted in Mind Tools: The Five Levels of Mathematical Reality (1988) by Rudy Rucker. ~ ISBN 0395468108

“It is true that impatience, the mother of stupidity, praises brevity, as if such persons had not life long enough to serve them to acquire a complete knowledge of one single subject, such as the human body; and then they want to comprehend the mind of God in which the universe is included, weighing it minutely and mincing it into infinite parts, as if they had to dissect it!”

Leonardo Da Vinci (1452–1519) Italian Renaissance polymath

The Notebooks of Leonardo da Vinci (1883), XIX Philosophical Maxims. Morals. Polemics and Speculations.

“Man's unhappiness, as I construe, comes of his greatness; it is because there is an Infinite in him, which with all his cunning he cannot quite bury under the Finite.”

Thomas Carlyle (1795–1881) Scottish philosopher, satirical writer, essayist, historian and teacher

Bk. I, ch. 9.
1830s, Sartor Resartus (1833–1834)

“Infinity, in its first form (the improper-infinite) presents itself as a variable finite [veranderliches Endliches]; in the other form (which I call the proper infinite [Eigentlich-unendliche]) it appears as a thoroughly determinate [bestimmtes] infinite.”

Georg Cantor (1845–1918) mathematician, inventor of set theory

From Kant to Hilbert (1996)

“So far from holding God to be finite, I hold, and in the book clearly teach, that all minds are infinite (in the true qualitative sense of the word), and God preeminently so. (See my pp. 330 seq., 363, and 373). Eternity, self-existence, self-activity, freedom, and infinity are to me all interchangeable terms, and are so treated wherever they turn up in the course of the book. My reviewer falls into a non sequitur when he concludes that I make God finite because I make him one of a community of spirits, each absolutely real; not God's finitude, but his definiteness, is what follows from that. This confusion of the definite with the finite is very common, and is the explanation of two tendencies in sceptical thinking — the tendency to deny the personality of God, whose infinity is supposed to mean his utter indefiniteness, and the tendency, in recoil from the former, to assert God's finitude in order to save his personality, which of course must be definite. But the true infinite, as distinguished from the pseudo-infinite, the infinite of quality in contrast to the infinite of quantity, is entirely definite; more definite, indeed, than any finite can be.”

George Holmes Howison (1834–1916) American philosopher

Source: The Limits of Evolution, and Other Essays, Illustrating the Metaphysical Theory of Personal Ideaalism (1905), Appendix E: Reply to Criticisms of Mr. J.M.E. McTaggert, p.421-2

“The infinite… happens to subsist in a way contrary to what is asserted by others: for the infinite is not that beyond which there is nothing, but it is that of which there is always something beyond. …But that pertaining to which there is nothing beyond is perfect and whole. …that of which nothing is absent pertaining to the parts …the whole is that pertaining to which there is nothing beyond. But that pertaining to which something external is absent, that is not all …But nothing is perfect which has not an end; and the end is a bound. On this account… Parmenides spoke better than Melissus: for the latter says that the infinite is a whole; but the former, that the whole is finite, and equally balanced from the middle: for to conjoin the infinite with the universe and the whole, is not to connect line with line.”

Aristotle book Physics

Book III, Ch. IX, pp. 168-169.
Physics

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Georg Cantor 27

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