18090 | Without infinity time has limits, magnitudes are indivisible, and numbers come to an end [Aristotle] |
8738 | Postulate 2 says a line can be extended continuously [Shapiro on Euclid] |
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 [Lavine on Cantor] |
15908 | It was Cantor's diagonal argument which revealed infinities greater than that of the real numbers [Lavine on Cantor] |
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] |
7555 | Zeno achieved the statement of the problems of infinitesimals, infinity and continuity [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] |
17797 | Cantor extended the finite (rather than 'taming the infinite') [Mayberry] |
17799 | Cantor's infinite is an absolute, of all the sets or all the ordinal numbers [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] |
15947 | The infinite is extrapolation from the experience of indefinitely large size [Lavine] |
15949 | The theory of infinity must rest on our inability to distinguish between very large sizes [Lavine] |
17730 | Combining the concepts of negation and finiteness gives the concept of infinity [Jenkins] |
17923 | Intuitionists only accept a few safe infinities [Colyvan] |