“Every quantity is intellectually conceivable as infinitely divisible.”

— Leonardo Da Vinci

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

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Leonardo Da Vinci 363

Italian Renaissance polymath 1452–1519

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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.
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“The division of labour is a consequence of the previous accumulation of capital… As the accumulation of capital must have preceded the division of labour, so its subsequent division can only be extended as capital is more and more accumulated. Accumulation and division act and react on each other. The quantity of raw materials which the same number of people can work up increases in a great proportion, as labour comes to be more and more subdivided; and acccording as the operations of each workman are reduced to a greater degree of identity and simplicity, he has, as already explained, a greater chance of discovering machines and processes for facilitating and abridging his labour. The quantity of industry, therefore, not only increases in every country with the increase of the stock or capital which sets it in motion; but, in consequence of this increase, the division of labour becomes extended, new and more powerful implements and machines are invented, and the same quantity of labour is thus made to produce an infinitely greater quantity of commodities”

John Ramsay McCulloch (1789–1864) Scottish economist, author and editor

Source: The principles of political economy, 1825, p. 95-96

“The hypothesis of God is a peculiar one, in that it supposes an infinitely incomprehensible object, although every hypothesis, as such, supposes its object to be truly conceived in the hypothesis.”

Charles Sanders Peirce (1839–1914) American philosopher, logician, mathematician, and scientist

Source: A Neglected Argument for the Reality of God (1908), II
Context: The hypothesis of God is a peculiar one, in that it supposes an infinitely incomprehensible object, although every hypothesis, as such, supposes its object to be truly conceived in the hypothesis. This leaves the hypothesis but one way of understanding itself; namely, as vague yet as true so far as it is definite, and as continually tending to define itself more and more, and without limit. The hypothesis, being thus itself inevitably subject to the law of growth, appears in its vagueness to represent God as so, albeit this is directly contradicted in the hypothesis from its very first phase. But this apparent attribution of growth to God, since it is ineradicable from the hypothesis, cannot, according to the hypothesis, be flatly false. Its implications concerning the Universes will be maintained in the hypothesis, while its implications concerning God will be partly disavowed, and yet held to be less false than their denial would be. Thus the hypothesis will lead to our thinking of features of each Universe as purposed; and this will stand or fall with the hypothesis. Yet a purpose essentially involves growth, and so cannot be attributed to God. Still it will, according to the hypothesis, be less false to speak so than to represent God as purposeless.

“We are a little piece of continual change, looking at an infinite quantity of continual change.”

B.K.S. Iyengar (1918–2014) Indian yoga teacher and scholar

Source: Light on Life: The Yoga Journey to Wholeness, Inner Peace, and Ultimate Freedom, p. 7

“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.
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“The prejudices of the second species, since they impose upon the intellect by the sensual conditions restricting the mind if it wishes in certain cases to attain to what is intellectual, lurk more deeply. One of them is that which affects knowledge of quantity, the other that affecting knowledge of qualities generally. The former is: every actual multiplicity can be given numerically, and hence, every infinite quantity; the latter, whatever is impossible contradicts itself. In either of them the concept of time, it is true, does not enter into the very notion of the predicate, nor is it attributed as a qualification to the subject. But yet it serves as a means for forming an idea of the predicate, and thus, being a condition, affects the intellectual concept of the subject to the extent that the latter is only attained by its aid.”

Immanuel Kant (1724–1804) German philosopher

Kant's Inaugural Dissertation (1770), Section V On The Method Respecting The Sensuous And The Intellectual In Metaphysics

“There is no doubt that we cannot do without variable quantities in the sense of the potential infinite. But from this very fact the necessity of the actual infinite can be demonstrated.”

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

"Über die verschiedenen Ansichten in Bezug auf die actualunendlichen Zahlen" ["Over the different views with regard to the actual infinite numbers"] - Bihand Till Koniglen Svenska Vetenskaps Akademiens Handigar (1886)

“Education alone can conduct us to that enjoyment which is, at once, best in quality and infinite in quantity.”

Horace Mann (1796–1859) American politician

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“The post-Freudians … have fallen victim to the ravages of the intellectual division of labor.”

Russell Jacoby (1945) American historian

Source: Social Amnesia: A Critique of Conformist Psychology from Adler to Laing (1975), p. 58

“Number is limited multitude or a combination of units or a flow of quantity made up of units; and the first division of number is even and odd.”

Nicomachus (60–120) Ancient Greek mathematician

Context: Nicomachus of Gerasa: Introduction to Arithmetic (1926), Book I, Chapter VII

“Every quantity is intellectually conceivable as infinitely divisible.”

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Leonardo Da Vinci 363

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