Combining Texts

All the ideas for 'Mathematical Logic (revised)', 'Reflections on my Critics' and 'Science without Numbers'

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26 ideas

3. Truth / H. Deflationary Truth / 2. Deflationary Truth
12129 'Truth' may only apply within a theory [Kuhn]
4. Formal Logic / F. Set Theory ST / 8. Critique of Set Theory
9570 In Field's Platonist view, set theory is false because it asserts existence for non-existent things [Field,H, by Chihara]
5. Theory of Logic / B. Logical Consequence / 1. Logical Consequence
10260 Logical consequence is defined by the impossibility of P and ¬q [Field,H, by Shapiro]
5. Theory of Logic / E. Structures of Logic / 4. Variables in Logic
12221 'Corner quotes' (quasi-quotation) designate 'whatever these terms designate' [Quine]
5. Theory of Logic / F. Referring in Logic / 1. Naming / f. Names eliminated
19321 We might do without names, by converting them into predicates [Quine, by Kirkham]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / a. Numbers
8958 In Field's version of science, space-time points replace real numbers [Field,H, by Szabó]
6. Mathematics / B. Foundations for Mathematics / 3. Axioms for Geometry
18221 'Metric' axioms uses functions, points and numbers; 'synthetic' axioms give facts about space [Field,H]
6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / a. For mathematical platonism
8757 The Indispensability Argument is the only serious ground for the existence of mathematical entities [Field,H]
6. Mathematics / C. Sources of Mathematics / 3. Mathematical Nominalism
18212 Nominalists try to only refer to physical objects, or language, or mental constructions [Field,H]
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / b. Indispensability of mathematics
10261 The application of mathematics only needs its possibility, not its truth [Field,H, by Shapiro]
18218 Hilbert explains geometry, by non-numerical facts about space [Field,H]
9623 Field needs a semantical notion of second-order consequence, and that needs sets [Brown,JR on Field,H]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique
18215 It seems impossible to explain the idea that the conclusion is contained in the premises [Field,H]
6. Mathematics / C. Sources of Mathematics / 9. Fictional Mathematics
18214 Mathematics is only empirical as regards which theory is useful [Field,H]
18216 Abstractions can form useful counterparts to concrete statements [Field,H]
18210 Why regard standard mathematics as truths, rather than as interesting fictions? [Field,H]
7. Existence / D. Theories of Reality / 11. Ontological Commitment / a. Ontological commitment
18211 You can reduce ontological commitment by expanding the logic [Field,H]
8. Modes of Existence / B. Properties / 12. Denial of Properties
8959 Field presumes properties can be eliminated from science [Field,H, by Szabó]
9. Objects / A. Existence of Objects / 2. Abstract Objects / d. Problems with abstracta
18213 Abstract objects are only applicable to the world if they are impure, and connect to the physical [Field,H]
14. Science / B. Scientific Theories / 1. Scientific Theory
6809 Kuhn came to accept that all scientists agree on a particular set of values [Kuhn, by Bird]
14. Science / B. Scientific Theories / 5. Commensurability
12128 In theory change, words shift their natural reference, so the theories are incommensurable [Kuhn]
14. Science / D. Explanation / 2. Types of Explanation / a. Types of explanation
18222 Beneath every extrinsic explanation there is an intrinsic explanation [Field,H]
18. Thought / E. Abstraction / 4. Abstracta by Example
9917 'Abstract' is unclear, but numbers, functions and sets are clearly abstract [Field,H]
27. Natural Reality / B. Modern Physics / 2. Electrodynamics / b. Fields
18223 In theories of fields, space-time points or regions are causal agents [Field,H]
27. Natural Reality / C. Space / 4. Substantival Space
18220 Both philosophy and physics now make substantivalism more attractive [Field,H]
27. Natural Reality / C. Space / 5. Relational Space
18219 Relational space is problematic if you take the idea of a field seriously [Field,H]