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
'True' is only occasionally useful, as in 'everything Fermat believed was true'
4. Formal Logic / D. Modal Logic ML / 1. Modal Logic
Modal logic gives an account of metalogical possibility, not metaphysical possibility
4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / d. Na´ve logical sets
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
Mereology implies that acceptance of entities entails acceptance of conglomerates
5. Theory of Logic / E. Structures of Logic / 6. Relations in Logic
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
The paradoxes no longer seem crucial in critiques of set theory
6. Mathematics / A. Nature of Mathematics / 3. Numbers / a. Numbers
We should talk about possible existence, rather than actual existence, of numbers
6. Mathematics / B. Foundations for Mathematics / 6. Mathematical Structuralism / c. Nominalist structuralism
Structuralism and nominalism are normally rivals, but might work together
6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / b. Against mathematical platonism
Number words became nouns around the time of Plato
7. Existence / C. Structure of Existence / 7. Abstract/Concrete / a. Abstract/concrete
Abstract/concrete is a distinction of kind, not degree
Much of what science says about concrete entities is 'abstraction-laden'
7. Existence / C. Structure of Existence / 7. Abstract/Concrete / b. Levels of abstraction
Mathematics has ascended to higher and higher levels of abstraction
Abstraction is on a scale, of sets, to attributes, to type-formulas, to token-formulas
18. Thought / D. Concepts / 6. Abstract Concepts / b. Abstracta from selection
The old debate classified representations as abstract, not entities
26. Natural Theory / B. Concepts of Nature / 3. Space / a. Space
If space is really just a force-field, then it is a physical entity