Combining Texts

All the ideas for 'fragments/reports', 'Cantorian Abstraction: Recon. and Defence' and 'Maths as a Science of Patterns'

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14 ideas

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]
5. Theory of Logic / E. Structures of Logic / 4. Variables in Logic
9148 I think of variables as objects rather than as signs [Fine,K]
6. Mathematics / A. Nature of Mathematics / 1. Mathematics
6304 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
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]
15. Nature of Minds / C. Capacities of Minds / 5. Generalisation by mind
9152 If green is abstracted from a thing, it is only seen as a type if it is common to many things [Fine,K]
18. Thought / E. Abstraction / 2. Abstracta by Selection
9149 To obtain the number 2 by abstraction, we only want to abstract the distinctness of a pair of objects [Fine,K]
9150 We should define abstraction in general, with number abstraction taken as a special case [Fine,K]
18. Thought / E. Abstraction / 8. Abstractionism Critique
9146 After abstraction all numbers seem identical, so only 0 and 1 will exist! [Fine,K]
28. God / A. Divine Nature / 1. God
6011 There is a remote first god (the Good), and a second god who organises the material world [Numenius, by O'Meara]