display all the ideas for this combination of texts
5 ideas
12335 | Numbers are for measuring and for calculating (and the two must be consistent) [Badiou] |
Full Idea: Number is an instance of measuring (distinguishing the more from the less, and calibrating data), ..and a figure for calculating (one counts with numbers), ..and it ought to be a figure of consistency (the compatibility of order and calculation). | |
From: Alain Badiou (Briefings on Existence [1998], 11) |
12334 | There is no single unified definition of number [Badiou] |
Full Idea: Apparently - and this is quite unlike old Greek times - there is no single unified definition of number. | |
From: Alain Badiou (Briefings on Existence [1998], 11) |
12333 | Each type of number has its own characteristic procedure of introduction [Badiou] |
Full Idea: There is a heterogeneity of introductory procedures of different classical number types: axiomatic for natural numbers, structural for ordinals, algebraic for negative and rational numbers, topological for reals, mainly geometric for complex numbers. | |
From: Alain Badiou (Briefings on Existence [1998], 11) |
12322 | Must we accept numbers as existing when they no longer consist of units? [Badiou] |
Full Idea: Do we have to confer existence on numbers whose principle is to no longer consist of units? | |
From: Alain Badiou (Briefings on Existence [1998], 2) | |
A reaction: This very nicely expresses what seems to me perhaps the most important question in the philosophy of mathematics. I am reluctant to accept such 'unitless' numbers, but I then feel hopelessly old-fashioned and naïve. What to do? |
12327 | The undecidability of the Continuum Hypothesis may have ruined or fragmented set theory [Badiou] |
Full Idea: As we have known since Paul Cohen's theorem, the Continuum Hypothesis is intrinsically undecidable. Many believe Cohen's discovery has driven the set-theoretic project into ruin, or 'pluralized' what was once presented as a unified construct. | |
From: Alain Badiou (Briefings on Existence [1998], 6) | |
A reaction: Badiou thinks the theorem completes set theory, by (roughly) finalising its map. |