Combining Texts

Ideas for 'On the Question of Absolute Undecidability', 'The Relation of Sense-Data to Physics' and 'Philosophy of Arithmetic'

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6 ideas

6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / l. Zero

9837	0 is not a number, as it answers 'how many?' negatively [Husserl, by Dummett]

6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / a. Units

9576	Multiplicity in general is just one and one and one, etc. [Husserl]

6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / e. Counting by correlation

17444

Husserl said counting is more basic than Frege's one-one correspondence [Husserl, by Heck]

6. Mathematics / A. Nature of Mathematics / 5. The Infinite / i. Cardinal infinity

17890

There are at least eleven types of large cardinal, of increasing logical strength [Koellner]

6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / d. Peano arithmetic

17887

PA is consistent as far as we can accept, and we expand axioms to overcome limitations [Koellner]

6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / g. Incompleteness of Arithmetic

17891

Arithmetical undecidability is always settled at the next stage up [Koellner]