“[B]ecause that which is finite is always bounded with reference to something… it is necessary that there should be no end… [N]umber also appears to be infinite, and mathematical magnitudes, and that which is beyond the heavens. And since that which is beyond is infinite, body also appears to be infinite, and it would seem that there are infinite worlds; for why is there rather void here than there? …If also there is a vacuum, and an infinite place, it is necessary that there should be an infinite body: for in things which have a perpetual subsistence, capacity differs nothing from being. The speculation of the infinite is, however, attended with doubt: for many impossibilities happen both to those who do not admit that it has a subsistence, and to those who do. …It is …especially the province of a natural philosopher to consider if there be a sensible infinite magnitude.”

— Aristotle , book Physics

Book III, Ch. V, p. 156.
Physics

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Aristotle 230

Classical Greek philosopher, student of Plato and founder o… -384–-321 BC

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“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.
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“Since the science of nature is conversant with magnitudes, motion, and time, each of which must necessarily be either infinite or finite…[we] should speculate the infinite, and consider whether it is or not; and if it is what it is. …[A]ll those who appear to have touched on a philosophy of this kind… consider it as a certain principle of beings. Some, indeed, as the Pythagoreans and Plato, consider it, per se, not as being an accident to any thing else, but as having an essential subsistence… the Pythagoreans… consider the infinite as subsisting in sensibles; for they do not make number to be separate; and they assert that what is beyond the heavens is infinite; but Plato says that beyond the heavens there is not any body, nor ideas, because these are no where: he affirms, however, that the infinite is both in sensibles, and in ideas. …Plato establishes two infinities, viz. the great and the small.”

Aristotle book Physics

Book III, Ch. IV, pp. 150-152.
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“A shadow may be infinitely dark, and also of infinite degrees of absence of darkness. The beginnings and ends of shadow lie between the light and darkness and may be infinitely diminished and infinitely increased. Shadow is the means by which bodies display their form. The forms of bodies could not be understood in detail but for shadow.”

Leonardo Da Vinci (1452–1519) Italian Renaissance polymath

The Notebooks of Leonardo da Vinci (1883), III Six books on Light and Shade

“[I]t is impossible that each of the elements should be infinite. For that is body which has interval on all sides; and that is infinite which has extension without bound.”

Aristotle book Physics

Book III, Ch. VII, p. 159.
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“[T]he infinite is in capacity. That, however, which is infinite in capacity is not to be assumed as that which is infinite in energy. …[I]t has its being in capacity, and in division and diminution. …[I]t is always possible to assume something beyond it. It does not, however, on this account surpass every definite magnitude; as in division it surpasses every definite magnitude, and will be less.”

Aristotle book Physics

Book III, Ch. VIII, pp. 164-166.
Physics

“[H]ow will one part of the infinite be above, and another below? Or how will it have extremes or a middle? Further still, every sensible body is in place; but the species and differences of place are upward and downward, before and behind, to the right hand and to the left: and these things not only thus subsist with relation to us, and by position, but have a definite subsistence in the universe itself. But it is impossible that these things should be in the infinite: and… that there should be an infinite place. But every body is in place; and therefore it is also impossible that there should be an infinite body. …[T]herefore …there is not an infinite body in energy.”

Aristotle book Physics

Book III, Ch. VII, pp. 163-164.
Physics

“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)

“Since… nature is a principle of motion and mutation… it is necessary that we should not be ignorant of what motion is… But motion appears to belong to things continuous; and the infinite first presents itself to the view in that which is continuous. …[F]requently …those who define the continuous, employ the nature or the infinite, as if that which is divisible to infinity is continuous.”

Aristotle book Physics

Book III, Ch. I, pp. 135-136.
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“God is Infinite and His Shadow is also infinite.”

Meher Baba (1894–1969) Indian mystic

18 : The Four Journeys, p. 22.
The Everything and the Nothing (1963)
Context: God is Infinite and His Shadow is also infinite. The Shadow of God is the Infinite Space that accommodates the infinite Gross Sphere which, with its occurrences of millions of universes, within and without the ranges of men's knowledge, is the Creation that issued from the Point of Finiteness in the infinite Existence that is God.

“All those… who discourse concerning nature, always subject a certain other nature of… elements, to the infinite… But no one of those who make the elements to be finite introduces infinity. Such, however, as make infinite elements, as Anaxagoras and Democritus, say that the infinite is continuous by contact. …Rationally, too, do all philosophers consider the infinite as a principle; for it cannot be in vain, nor can any other power be present with it than that of a principle: for all things are either the principle, or from the principle; but of the infinite there is no principle, since otherwise it would have an end. …it is also unbegotten and uncorruptible, as being a certain principle: for… end is the corruption of everything. …It likewise appears to comprehend and govern all things, as those assert who do not introduce other causes beside the infinite… It would seem also that this is divine: for it is immortal and indestructible, as Anaximander says, and most of the physiologists.”

Aristotle book Physics

Book III, Ch. IV, pp. 152-155.
Physics

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