Combining Texts

All the ideas for 'Realism in Mathematics', 'A Subject with No Object' and 'Vagueness: a global approach'

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29 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 / 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 / 7. Natural Sets
8755 Maddy replaces pure sets with just objects and perceived sets of objects [Maddy, by Shapiro]
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 / A. Overview of Logic / 6. Classical Logic
23548 Indeterminacy is in conflict with classical logic [Fine,K]
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 / I. Semantics of Logic / 1. Semantics of Logic
23539 Classical semantics has referents for names, extensions for predicates, and T or F for sentences [Fine,K]
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 / 6. Mathematics as Set Theory / a. Mathematics is set theory
10718 A natural number is a property of sets [Maddy, by Oliver]
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
9934 Number words became nouns around the time of Plato [Burgess/Rosen]
6. Mathematics / C. Sources of Mathematics / 2. Intuition of Mathematics
8756 Intuition doesn't support much mathematics, and we should question its reliability [Maddy, by Shapiro]
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / a. Mathematical empiricism
17733 We know mind-independent mathematical truths through sets, which rest on experience [Maddy, by Jenkins]
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]
7. Existence / D. Theories of Reality / 10. Vagueness / a. Problem of vagueness
23544 Local indeterminacy concerns a single object, and global indeterminacy covers a range [Fine,K]
23540 Conjoining two indefinites by related sentences seems to produce a contradiction [Fine,K]
23546 Standardly vagueness involves borderline cases, and a higher standpoint from which they can be seen [Fine,K]
7. Existence / D. Theories of Reality / 10. Vagueness / c. Vagueness as ignorance
23542 Identifying vagueness with ignorance is the common mistake of confusing symptoms with cause [Fine,K]
7. Existence / D. Theories of Reality / 10. Vagueness / f. Supervaluation for vagueness
23541 Supervaluation can give no answer to 'who is the last bald man' [Fine,K]
9. Objects / B. Unity of Objects / 3. Unity Problems / e. Vague objects
23545 We do not have an intelligible concept of a borderline case [Fine,K]
16. Persons / D. Continuity of the Self / 2. Mental Continuity / b. Self as mental continuity
23547 It seems absurd that there is no identity of any kind between two objects which involve survival [Fine,K]
18. Thought / E. Abstraction / 2. Abstracta by Selection
9919 The old debate classified representations as abstract, not entities [Burgess/Rosen]
26. Natural Theory / D. Laws of Nature / 4. Regularities / a. Regularity theory
23543 We identify laws with regularities because we mistakenly identify causes with their symptoms [Fine,K]
27. Natural Reality / C. Space / 2. Space
9922 If space is really just a force-field, then it is a physical entity [Burgess/Rosen]