Combining Texts

All the ideas for 'Defending the Axioms', 'Physiologia' and 'A Subject with No Object'

expand these ideas     |    start again     |     specify just one area for these texts

23 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 / j. Axiom of Choice IX
17610 The Axiom of Choice paradoxically allows decomposing a sphere into two identical spheres [Maddy]
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 / G. Formal Mereology / 1. Mereology
9928 Mereology implies that acceptance of entities entails acceptance of conglomerates [Burgess/Rosen]
5. Theory of Logic / C. Ontology of Logic / 3. If-Thenism
17620 Critics of if-thenism say that not all starting points, even consistent ones, are worth studying [Maddy]
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 / K. Features of Logics / 1. Axiomatisation
17605 Hilbert's geometry and Dedekind's real numbers were role models for axiomatization [Maddy]
17625 If two mathematical themes coincide, that suggest a single deep truth [Maddy]
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 / A. Nature of Mathematics / 5. The Infinite / g. Continuum Hypothesis
17615 Every infinite set of reals is either countable or of the same size as the full set of reals [Maddy]
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
17618 Set-theory tracks the contours of mathematical depth and fruitfulness [Maddy]
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 / 4. Mathematical Empiricism / c. Against mathematical empiricism
17614 The connection of arithmetic to perception has been idealised away in modern infinitary mathematics [Maddy]
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]
9. Objects / C. Structure of Objects / 4. Quantity of an Object
16674 The quantity is just the matter, in that it has extended parts and is diffuse [Charleton]
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]