Combining Texts

Ideas for 'Unconscious Cerebral Initiative', 'Naturalism in Mathematics' and 'Introduction to the Philosophy of Mathematics'

expand these ideas     |    start again     |     choose another area for these texts

display all the ideas for this combination of texts

14 ideas

6. Mathematics / B. Foundations for Mathematics / 1. Foundations for Mathematics
17922 Reducing real numbers to rationals suggested arithmetic as the foundation of maths [Colyvan]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / f. Mathematical induction
17936 Transfinite induction moves from all cases, up to the limit ordinal [Colyvan]
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / c. Fregean numbers
18182 The extension of concepts is not important to me [Maddy]
18177 In the ZFC hierarchy it is impossible to form Frege's set of all three-element sets [Maddy]
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / e. Caesar problem
18164 Frege solves the Caesar problem by explicitly defining each number [Maddy]
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
18184 Making set theory foundational to mathematics leads to very fruitful axioms [Maddy]
18185 Unified set theory gives a final court of appeal for mathematics [Maddy]
18183 Set theory brings mathematics into one arena, where interrelations become clearer [Maddy]
17940 Most mathematical proofs are using set theory, but without saying so [Colyvan]
18186 Identifying geometric points with real numbers revealed the power of set theory [Maddy]
18188 The line of rationals has gaps, but set theory provided an ordered continuum [Maddy]
18163 Mathematics rests on the logic of proofs, and on the set theoretic axioms [Maddy]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / a. Structuralism
17931 Structuralism say only 'up to isomorphism' matters because that is all there is to it [Colyvan]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / e. Structuralism critique
17932 If 'in re' structures relies on the world, does the world contain rich enough structures? [Colyvan]