Ideas from 'A Subject with No Object' by JP Burgess / G Rosen [1997], by Theme Structure
[found in 'A Subject with No Object' by Burgess,J/Rosen,G [OUP 1997,0-19-825012-6]].
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3. Truth / H. Deflationary Truth / 2. Deflationary Truth
9921
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'True' is only occasionally useful, as in 'everything Fermat believed was true'
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4. Formal Logic / D. Modal Logic ML / 1. Modal Logic
9924
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Modal logic gives an account of metalogical possibility, not metaphysical possibility
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4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / d. Naïve logical sets
9933
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The paradoxes are only a problem for Frege; Cantor didn't assume every condition determines a set
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4. Formal Logic / G. Formal Mereology / 1. Mereology
9928
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Mereology implies that acceptance of entities entails acceptance of conglomerates
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5. Theory of Logic / E. Structures of Logic / 6. Relations in Logic
9926
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A relation is either a set of sets of sets, or a set of sets
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5. Theory of Logic / L. Paradox / 5. Paradoxes in Set Theory / a. Set theory paradoxes
9932
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The paradoxes no longer seem crucial in critiques of set theory
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6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / a. Numbers
9923
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We should talk about possible existence, rather than actual existence, of numbers
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6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / c. Nominalist structuralism
9925
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Structuralism and nominalism are normally rivals, but might work together
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6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / b. Against mathematical platonism
9934
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Number words became nouns around the time of Plato
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7. Existence / C. Structure of Existence / 7. Abstract/Concrete / a. Abstract/concrete
9918
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Abstract/concrete is a distinction of kind, not degree
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9929
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Much of what science says about concrete entities is 'abstraction-laden'
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7. Existence / C. Structure of Existence / 7. Abstract/Concrete / b. Levels of abstraction
9927
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Mathematics has ascended to higher and higher levels of abstraction
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9930
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Abstraction is on a scale, of sets, to attributes, to type-formulas, to token-formulas
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18. Thought / E. Abstraction / 2. Abstracta by Selection
9919
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The old debate classified representations as abstract, not entities
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27. Natural Reality / C. Space / 2. Space
9922
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If space is really just a force-field, then it is a physical entity
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