### All the ideas for 'Matter and Memory', 'Science without Numbers' and 'Must We Believe in Set Theory?st3=George Boolos'

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33 ideas

###### 4. Formal Logic / F. Set Theory ST / 1. Set Theory
 10482 The logic of ZF is classical first-order predicate logic with identity [Boolos]
###### 4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets
 10492 A few axioms of set theory 'force themselves on us', but most of them don't [Boolos]
###### 4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / d. Naïve logical sets
 10485 Naïve sets are inconsistent: there is no set for things that do not belong to themselves [Boolos]
###### 4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / e. Iterative sets
 10484 The iterative conception says sets are formed at stages; some are 'earlier', and must be formed first [Boolos]
###### 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]
###### 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 / A. Nature of Mathematics / 5. The Infinite / a. The Infinite
 10491 Infinite natural numbers is as obvious as infinite sentences in English [Boolos]
###### 6. Mathematics / A. Nature of Mathematics / 5. The Infinite / f. Uncountable infinities
 10483 Mathematics and science do not require very high orders of infinity [Boolos]
###### 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
 10490 Mathematics isn't surprising, given that we experience many objects as abstract [Boolos]
 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]
 9623 Field needs a semantical notion of second-order consequence, and that needs sets [Brown,JR on Field,H]
 18218 Hilbert explains geometry, by non-numerical facts about space [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 / A. Nature of Existence / 3. Being / c. Becoming
 21846 Bergson was a rallying point, because he emphasised becomings and multiplicities [Bergson, by Deleuze]
###### 7. Existence / D. Theories of Reality / 10. 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]
###### 8. Modes of Existence / D. Universals / 1. Universals
 10488 It is lunacy to think we only see ink-marks, and not word-types [Boolos]
###### 9. Objects / A. Existence of Objects / 2. Abstract Objects / a. Nature of abstracta
 10487 I am a fan of abstract objects, and confident of their existence [Boolos]
###### 9. Objects / A. Existence of Objects / 2. Abstract Objects / c. Modern abstracta
 10489 We deal with abstract objects all the time: software, poems, mistakes, triangles.. [Boolos]
###### 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]
###### 12. Knowledge Sources / E. Direct Knowledge / 4. Memory
 21854 Bergson showed that memory is not after the event, but coexists with it [Bergson, by Deleuze]
###### 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-Time / 1. Space / d. Substantival space
 18220 Both philosophy and physics now make substantivalism more attractive [Field,H]
###### 27. Natural Reality / C. Space-Time / 1. Space / e. Relational space
 18219 Relational space is problematic if you take the idea of a field seriously [Field,H]