Combining Texts

All the ideas for 'fragments/reports', 'Anselm and Actuality' and 'Maths as a Science of Patterns'

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10 ideas

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]
4. Formal Logic / D. Modal Logic ML / 4. Alethic Modal Logic
For modality Lewis rejected boxes and diamonds, preferring worlds, and an index for the actual one [Lewis, by Stalnaker]
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
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]
Structuralism must explain why a triangle is a whole, and not a random set of points [Resnik]
13. Knowledge Criteria / E. Relativism / 2. Knowledge as Convention
By nature people are close to one another, but culture drives them apart [Hippias]