Combining Texts

Ideas for 'fragments/reports', 'Briefings on Existence' and 'The Structure and Content of Truth'

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5 ideas

6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / a. Numbers

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)

6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / b. Types of number

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?

6. Mathematics / A. Nature of Mathematics / 5. The Infinite / g. Continuum Hypothesis

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.