Combining Philosophers

Ideas for Jerrold J. Katz, S.Mumford/R.Lill Anjum and Stephen Read

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5 ideas

6. Mathematics / A. Nature of Mathematics / 5. The Infinite / d. Actual infinite

11025

Infinite cuts and successors seems to suggest an actual infinity there waiting for us [Read]

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 / C. Sources of Mathematics / 1. Mathematical Platonism / b. Against mathematical platonism

2521	'Real' maths objects have no causal role, no determinate reference, and no abstract/concrete distinction [Katz]