“Plato… introduces two infinities, because both in increase and diminution there appears to be transcendency, and a progression to infinity. Though… he did not use them: for neither is there infinity in numbers by diminution or division; since unity is a minimum: nor by increase; for he extends number as far as to the decad.”

Book III, Ch. VIII, p. 167.
Physics

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

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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.”

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