Combining Texts
Ideas for
'Axiomatic Theories of Truth', 'Briefings on Existence' and 'What is 'naturalized epistemology'?'
expand these ideas
|
start again
|
choose
another area for these texts
display all the ideas for this combination of texts
12 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]
|
12334
|
There is no single unified definition of number [Badiou]
|
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]
|
12322
|
Must we accept numbers as existing when they no longer consist of units? [Badiou]
|
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]
|
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / d. Peano arithmetic
16321
|
The compactness theorem can prove nonstandard models of PA [Halbach]
|
16343
|
The global reflection principle seems to express the soundness of Peano Arithmetic [Halbach]
|
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
16312
|
To reduce PA to ZF, we represent the non-negative integers with von Neumann ordinals [Halbach]
|
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / c. Nominalist structuralism
12329
|
If mathematics is a logic of the possible, then questions of existence are not intrinsic to it [Badiou]
|
6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / a. For mathematical platonism
12328
|
Platonists like axioms and decisions, Aristotelians like definitions, possibilities and logic [Badiou]
|
6. Mathematics / C. Sources of Mathematics / 6. Logicism / b. Type theory
16308
|
Set theory was liberated early from types, and recent truth-theories are exploring type-free [Halbach]
|
6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique
12331
|
Logic is definitional, but real mathematics is axiomatic [Badiou]
|