Combining Texts

Ideas for 'Philosophy of Mathematics', 'Meditations' and 'works'

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6 ideas

6. Mathematics / A. Nature of Mathematics / 1. Mathematics

2252	Surely maths is true even if I am dreaming? [Descartes]

2430	I can learn the concepts of duration and number just from observing my own thoughts [Descartes]

6. Mathematics / B. Foundations for Mathematics / 2. Proof in Mathematics

10885

Computer proofs don't provide explanations [Horsten]

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

17885

Gödel eventually hoped for a generalised completeness theorem leaving nothing undecidable [Gödel, by Koellner]

10614

The real reason for Incompleteness in arithmetic is inability to define truth in a language [Gödel]

6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory

10881

The concept of 'ordinal number' is set-theoretic, not arithmetical [Horsten]