Combining Texts

All the ideas for 'Realism in Mathematics', 'Presupposition' and 'Philosophy without Intuitions'

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8 ideas

2. Reason / E. Argument / 7. Thought Experiments

20183

So-called 'though experiments' are just philosophers observing features of the world [Cappelen]

4. Formal Logic / A. Syllogistic Logic / 3. Term Logic

19053

Logic would be more natural if negation only referred to predicates [Dummett]

4. Formal Logic / F. Set Theory ST / 7. Natural Sets

8755	Maddy replaces pure sets with just objects and perceived sets of objects [Maddy, by Shapiro]

5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / c. not

19052

Natural language 'not' doesn't apply to sentences [Dummett]

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

10718

A natural number is a property of sets [Maddy, by Oliver]

6. Mathematics / C. Sources of Mathematics / 2. Intuition of Mathematics

8756	Intuition doesn't support much mathematics, and we should question its reliability [Maddy, by Shapiro]

6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / a. Mathematical empiricism

17733

We know mind-independent mathematical truths through sets, which rest on experience [Maddy, by Jenkins]

12. Knowledge Sources / E. Direct Knowledge / 2. Intuition

20182

The word 'intuitive' often plays not role at all in arguments, and can be removed [Cappelen]