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Ideas for 'Parmenides', 'Thinking About Logic' and 'The Architecture of Mathematics'

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4 ideas

6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / e. Peano arithmetic 2nd-order

10979

Although second-order arithmetic is incomplete, it can fully model normal arithmetic [Read]

10980

Second-order arithmetic covers all properties, ensuring categoricity [Read]

6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / g. Von Neumann numbers

10997

Von Neumann numbers are helpful, but don't correctly describe numbers [Read]

6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / a. Structuralism

10190

From the axiomatic point of view, mathematics is a storehouse of abstract structures [Bourbaki]