Combining Texts

All the ideas for 'Types and Ontology', 'Positions' and 'Maths as a Science of Patterns'

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11 ideas

1. Philosophy / H. Continental Philosophy / 6. Deconstruction
Deconstruction is not neutral; it intervenes [Derrida]
2. Reason / C. Styles of Reason / 1. Dialectic
I try to analyse certain verbal concepts which block and confuse the dialectical process [Derrida]
4. Formal Logic / B. Propositional Logic PL / 2. Tools of Propositional Logic / e. Axioms of PL
Axioms are often affirmed simply because they produce results which have been accepted [Resnik]
6. Mathematics / A. Nature of Mathematics / 1. Mathematics
Mathematical realism says that maths exists, is largely true, and is independent of proofs [Resnik]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / a. Structuralism
Mathematical constants and quantifiers only exist as locations within structures or patterns [Resnik]
Sets are positions in patterns [Resnik]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / d. Platonist structuralism
Structuralism must explain why a triangle is a whole, and not a random set of points [Resnik]
There are too many mathematical objects for them all to be mental or physical [Resnik]
Maths is pattern recognition and representation, and its truth and proofs are based on these [Resnik]
Congruence is the strongest relationship of patterns, equivalence comes next, and mutual occurrence is the weakest [Resnik]
7. Existence / E. Categories / 1. Categories
Categories can't overlap; they are either disjoint, or inclusive [Sommers, by Westerhoff]