Combining Philosophers

All the ideas for H.Putnam/P.Oppenheim, Anon (Tor) and Michael D. Resnik

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12 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]
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]
14. Science / D. Explanation / 2. Types of Explanation / j. Explanations by reduction
Six reduction levels: groups, lives, cells, molecules, atoms, particles [Putnam/Oppenheim, by Watson]
24. Political Theory / A. Basis of a State / 1. A People / a. Human distinctiveness
God made man in his own image [Anon (Tor)]
26. Natural Theory / B. Natural Kinds / 5. Reference to Natural Kinds
The names of all the types of creature were given forever by Adam [Anon (Tor)]
28. God / A. Divine Nature / 6. Divine Morality / b. Euthyphro question
And God saw the light, that it was good [Anon (Tor)]