Ideas from 'Philosophy of Mathematics' by Leon Horsten [2007], by Theme Structure

[found in 'Stanford Online Encyclopaedia of Philosophy' (ed/tr Stanford University) [plato.stanford.edu ,-]].

Click on the Idea Number for the full details    |     back to texts     |     expand these ideas


2. Reason / D. Definition / 8. Impredicative Definition
Predicative definitions only refer to entities outside the defined collection
5. Theory of Logic / J. Model Theory in Logic / 2. Isomorphisms
A theory is 'categorical' if it has just one model up to isomorphism
6. Mathematics / A. Nature of Mathematics / 4. The Infinite / g. Continuum Hypothesis
Cantor's Continuum Hypothesis says there is a gap between the natural and the real numbers
6. Mathematics / A. Nature of Mathematics / 6. Proof in Mathematics
Computer proofs don't provide explanations
6. Mathematics / B. Foundations for Mathematics / 5. Mathematics as Set Theory / a. Mathematics is set theory
The concept of 'ordinal number' is set-theoretic, not arithmetical