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 1997,0198250126]].
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3. Truth / H. Deflationary Truth / 2. Deflationary Truth
9921

'True' is only occasionally useful, as in 'everything Fermat believed was true'

4. Formal Logic / D. Modal Logic ML / 1. Modal Logic
9924

Modal logic gives an account of metalogical possibility, not metaphysical possibility

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

4. Formal Logic / G. Formal Mereology / 1. Mereology
9928

Mereology implies that acceptance of entities entails acceptance of conglomerates

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

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

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

6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / c. Nominalist structuralism
9925

Structuralism and nominalism are normally rivals, but might work together

6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / b. Against mathematical platonism
9934

Number words became nouns around the time of Plato

7. Existence / C. Structure of Existence / 7. Abstract/Concrete / a. Abstract/concrete
9918

Abstract/concrete is a distinction of kind, not degree

9929

Much of what science says about concrete entities is 'abstractionladen'

7. Existence / C. Structure of Existence / 7. Abstract/Concrete / b. Levels of abstraction
9927

Mathematics has ascended to higher and higher levels of abstraction

9930

Abstraction is on a scale, of sets, to attributes, to typeformulas, to tokenformulas

18. Thought / E. Abstraction / 2. Abstracta by Selection
9919

The old debate classified representations as abstract, not entities

27. Natural Reality / C. SpaceTime / 1. Space / b. Space
9922

If space is really just a forcefield, then it is a physical entity
