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Single Idea 18090

[filed under theme 6. Mathematics / A. Nature of Mathematics / 5. The Infinite / a. The Infinite ]

Full Idea

If there is, unqualifiedly, no infinite, it is clear that many impossible things result. For there will be a beginning and an end of time, and magnitudes will not be divisible into magnitudes, and number will not be infinite.

Gist of Idea

Without infinity time has limits, magnitudes are indivisible, and numbers come to an end

Source

Aristotle (Physics [c.337 BCE], 206b09), quoted by David Bostock - Philosophy of Mathematics 1.8

Book Ref

Bostock,David: 'Philosophy of Mathematics: An Introduction' [Wiley-Blackwell 2009], p.24

A Reaction

This is a commitment to infinite time, and uncountable real numbers, and infinite ordinals. Dedekind cuts are implied. Nice.

The 26 ideas with the same theme [the status and nature of infinity as a number]:

18090 Without infinity time has limits, magnitudes are indivisible, and numbers come to an end [Aristotle]
7555 Zeno achieved the statement of the problems of infinitesimals, infinity and continuity [Russell on Zeno of Citium]
8738 Postulate 2 says a line can be extended continuously [Euclid, by Shapiro]
13151 Not all infinites are equal [Newton]
10856 A truly infinite quantity does not need to be a variable [Bolzano]
15902 Irrationals and the Dedekind Cut implied infinite classes, but they seemed to have logical difficulties [Cantor, by Lavine]
15908 It was Cantor's diagonal argument which revealed infinities greater than that of the real numbers [Cantor, by Lavine]
9633 No one shall drive us out of the paradise the Cantor has created for us [Hilbert]
12460 We extend finite statements with ideal ones, in order to preserve our logic [Hilbert]
12462 Only the finite can bring certainty to the infinite [Hilbert]
14420 Infinity and continuity used to be philosophy, but are now mathematics [Russell]
14119 We do not currently know whether, of two infinite numbers, one must be greater than the other [Russell]
14133 There are cardinal and ordinal theories of infinity (while continuity is entirely ordinal) [Russell]
18708 Infinity is not a number, so doesn't say how many; it is the property of a law [Wittgenstein]
17809 Gödel showed that the syntactic approach to the infinite is of limited value [Kreisel]
10491 Infinite natural numbers is as obvious as infinite sentences in English [Boolos]
9813 Mathematics shows that thinking is not confined to the finite [Badiou]
13509 We can establish truths about infinite numbers by means of induction [Hart,WD]
17799 Cantor's infinite is an absolute, of all the sets or all the ordinal numbers [Mayberry]
17797 Cantor extended the finite (rather than 'taming the infinite') [Mayberry]
18518 Infinite numbers are qualitatively different - they are not just very large numbers [Heil]
10866 Cantor's account of infinities has the shaky foundation of irrational numbers [Clegg]
15949 The theory of infinity must rest on our inability to distinguish between very large sizes [Lavine]
15947 The infinite is extrapolation from the experience of indefinitely large size [Lavine]
17730 Combining the concepts of negation and finiteness gives the concept of infinity [Jenkins]
17923 Intuitionists only accept a few safe infinities [Colyvan]