Combining Philosophers

All the ideas for H.Putnam/P.Oppenheim, Thoralf Skolem and JP Burgess / G Rosen

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21 ideas

3. Truth / H. Deflationary Truth / 2. Deflationary Truth
9921 'True' is only occasionally useful, as in 'everything Fermat believed was true' [Burgess/Rosen]
4. Formal Logic / D. Modal Logic ML / 1. Modal Logic
9924 Modal logic gives an account of metalogical possibility, not metaphysical possibility [Burgess/Rosen]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets
17879 Axiomatising set theory makes it all relative [Skolem]
4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / d. Naïve logical sets
9933 The paradoxes are only a problem for Frege; Cantor didn't assume every condition determines a set [Burgess/Rosen]
4. Formal Logic / F. Set Theory ST / 8. Critique of Set Theory
13536 Skolem did not believe in the existence of uncountable sets [Skolem]
4. Formal Logic / G. Formal Mereology / 1. Mereology
9928 Mereology implies that acceptance of entities entails acceptance of conglomerates [Burgess/Rosen]
5. Theory of Logic / E. Structures of Logic / 6. Relations in Logic
9926 A relation is either a set of sets of sets, or a set of sets [Burgess/Rosen]
5. Theory of Logic / J. Model Theory in Logic / 3. Löwenheim-Skolem Theorems
17878 If a 1st-order proposition is satisfied, it is satisfied in a denumerably infinite domain [Skolem]
5. Theory of Logic / L. Paradox / 5. Paradoxes in Set Theory / a. Set theory paradoxes
9932 The paradoxes no longer seem crucial in critiques of set theory [Burgess/Rosen]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / a. Numbers
9923 We should talk about possible existence, rather than actual existence, of numbers [Burgess/Rosen]
6. Mathematics / B. Foundations for Mathematics / 1. Foundations for Mathematics
17880 Integers and induction are clear as foundations, but set-theory axioms certainly aren't [Skolem]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / c. Nominalist structuralism
9925 Structuralism and nominalism are normally rivals, but might work together [Burgess/Rosen]
6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / b. Against mathematical platonism
17881 Mathematician want performable operations, not propositions about objects [Skolem]
9934 Number words became nouns around the time of Plato [Burgess/Rosen]
7. Existence / C. Structure of Existence / 7. Abstract/Concrete / a. Abstract/concrete
9918 Abstract/concrete is a distinction of kind, not degree [Burgess/Rosen]
9929 Much of what science says about concrete entities is 'abstraction-laden' [Burgess/Rosen]
7. Existence / C. Structure of Existence / 7. Abstract/Concrete / b. Levels of abstraction
9927 Mathematics has ascended to higher and higher levels of abstraction [Burgess/Rosen]
9930 Abstraction is on a scale, of sets, to attributes, to type-formulas, to token-formulas [Burgess/Rosen]
14. Science / D. Explanation / 2. Types of Explanation / j. Explanations by reduction
20653 Six reduction levels: groups, lives, cells, molecules, atoms, particles [Putnam/Oppenheim, by Watson]
18. Thought / E. Abstraction / 2. Abstracta by Selection
9919 The old debate classified representations as abstract, not entities [Burgess/Rosen]
27. Natural Reality / C. Space / 2. Space
9922 If space is really just a force-field, then it is a physical entity [Burgess/Rosen]