Combining Texts

All the ideas for 'Mind and Its Place in Nature', 'Maths as a Science of Patterns' and 'Mathematics and Philosophy: grand and little'

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15 ideas

1. Philosophy / D. Nature of Philosophy / 5. Aims of Philosophy / e. Philosophy as reason
9808 Philosophy aims to reveal the grandeur of mathematics [Badiou]
4. Formal Logic / B. Propositional Logic PL / 2. Tools of Propositional Logic / e. Axioms of PL
6299 Axioms are often affirmed simply because they produce results which have been accepted [Resnik]
6. Mathematics / A. Nature of Mathematics / 1. Mathematics
9812 In mathematics, if a problem can be formulated, it will eventually be solved [Badiou]
6304 Mathematical realism says that maths exists, is largely true, and is independent of proofs [Resnik]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / a. The Infinite
9813 Mathematics shows that thinking is not confined to the finite [Badiou]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / a. Structuralism
6300 Mathematical constants and quantifiers only exist as locations within structures or patterns [Resnik]
6303 Sets are positions in patterns [Resnik]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / d. Platonist structuralism
6295 There are too many mathematical objects for them all to be mental or physical [Resnik]
6296 Maths is pattern recognition and representation, and its truth and proofs are based on these [Resnik]
6301 Congruence is the strongest relationship of patterns, equivalence comes next, and mutual occurrence is the weakest [Resnik]
6302 Structuralism must explain why a triangle is a whole, and not a random set of points [Resnik]
7. Existence / A. Nature of Existence / 3. Being / a. Nature of Being
9809 Mathematics inscribes being as such [Badiou]
7. Existence / A. Nature of Existence / 6. Criterion for Existence
9811 It is of the essence of being to appear [Badiou]
12. Knowledge Sources / B. Perception / 6. Inference in Perception
7628 Broad rejects the inferential component of the representative theory [Broad, by Maund]
21. Aesthetics / B. Nature of Art / 8. The Arts / b. Literature
9814 All great poetry is engaged in rivalry with mathematics [Badiou]