Combining Texts

Ideas for 'On the Question of Absolute Undecidability', 'Minds, Brains and Science' and 'Sets, Aggregates and Numbers'

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5 ideas

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]

6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / c. Fregean numbers

17817

Defining 'three' as the principle of collection or property of threes explains set theory definitions [Yourgrau]

6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / b. Mathematics is not set theory

17815

We can't use sets as foundations for mathematics if we must await results from the upper reaches [Yourgrau]

17821

You can ask all sorts of numerical questions about any one given set [Yourgrau]