“I. Thesis. Finite elements of Space and Time. Antithesis.”

Continuity.
Antimonies
Gesammelte Mathematische Werke (1876)

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German mathematician 1826–1866

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“Thesis. Finite, Representable. Antithesis. Infinite, System of Notions lying at the limit of the representable.”

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“III. Thesis. A God working in Time. (Government of the world). Antithesis. A timeless, personal, omniscient, al-mighty, all-benevolent God”

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“II. Thesis. Freedom, i. e., not the power absolutely to originate, but to pass judgement between two or more possibilities. Antithesis.”

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“This justification, though open upon the entire universe through time and space, will always be finite.”

Conclusion
The Ethics of Ambiguity (1947)
Context: In Plato, art is mystification because there is the heaven of Ideas; but in the earthly domain all glorification of the earth is true as soon as it is realized. Let men attach value to words, forms, colors, mathematical theorems, physical laws, and athletic prowess; let them accord value to one another in love and friendship, and the objects, the events, and the men immediately have this value; they have it absolutely. It is possible that a man may refuse to love anything on earth; he will prove this refusal and he will carry it out by suicide. If he lives, the reason is that, whatever he may say, there still remains in him some attachment to existence; his life will be commensurate with this attachment; it will justify itself to the extent that it genuinely justifies the world.
This justification, though open upon the entire universe through time and space, will always be finite. Whatever one may do, one never realizes anything but a limited work, like existence itself which tries to establish itself through that work and which death also limits. It is the assertion of our finiteness which doubtless gives the doctrine which we have just evoked its austerity and, in some eyes, its sadness. As soon as one considers a system abstractly and theoretically, one puts himself, in effect, on the plane of the universal, thus, of the infinite. … existentialism does not offer to the reader the consolations of an abstract evasion: existentialism proposes no evasion. On the contrary, its ethics is experienced in the truth of life, and it then appears as the only proposition of salvation which one can address to men. Taking on its own account Descartes’ revolt against the evil genius, the pride of the thinking reed in the face of the universe which crushes him, it asserts that, despite his limits, through them, it is up to each one to fulfill his existence as an absolute. Regardless of the staggering dimensions of the world about us, the density of our ignorance, the risks of catastrophes to come, and our individual weakness within the immense collectivity, the fact remains that we are absolutely free today if we choose to will our existence in its finiteness, a finiteness which is open on the infinite. And in fact, any man who has known real loves, real revolts, real desires, and real will knows quite well that he has no need of any outside guarantee to be sure of his goals; their certitude comes from his own drive. There is a very old saying which goes: “Do what you must, come what may.” That amounts to saying in a different way that the result is not external to the good will which fulfills itself in aiming at it. If it came to be that each man did what he must, existence would be saved in each one without there being any need of dreaming of a paradise where all would be reconciled in death.

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“Language has time as its element; all other media have space as their element.”

Sören Kierkegaard (1813–1855) Danish philosopher and theologian, founder of Existentialism

Source: Either/Or: A Fragment of Life

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“The world's nature is a harmonious compound of infinite and finite elements”

Philolaus (-470–-390 BC) ancient greek philosopher

The Life of Pythagoras (1919)
Context: Fragment 1. (Stob.21.7; Diog.#.8.85) The world's nature is a harmonious compound of infinite and finite elements; similar is the totality of the world in itself, and of all it contains.
b. All beings are necessarily finite or infinite, or simultaneously finite and infinite; but they could not all be infinite only.

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“Time and space are finite in extent, but they don't have any boundary or edge. They would be like the surface of the earth, but with two more dimensions.”

Stephen Hawking (1942–2018) British theoretical physicist, cosmologist, and author

Source: Black Holes and Baby Universes

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“A ring of polynomials in any number of variables over a ring of coeffcients that has an identity element and a finite basis, itself has a finite basis.”

Emmy Noether (1882–1935) German mathematician

As quoted in Morris Kline, Mathematical Thought From Ancient to Modern Times (1972) p. 1153.

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