Combining Texts

All the ideas for 'De Natura Corporis', 'The Question of Ontology' and 'Must We Believe in Set Theory?'

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20 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]
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 / 5. Definitions of Number / c. Fregean numbers
12215 The existence of numbers is not a matter of identities, but of constituents of the world [Fine,K]
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]
6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / b. Against mathematical platonism
12211 It is plausible that x^2 = -1 had no solutions before complex numbers were 'introduced' [Fine,K]
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / a. Mathematical empiricism
12209 The indispensability argument shows that nature is non-numerical, not the denial of numbers [Fine,K]
7. Existence / A. Nature of Existence / 1. Nature of Existence
12214 'Exists' is a predicate, not a quantifier; 'electrons exist' is like 'electrons spin' [Fine,K]
7. Existence / A. Nature of Existence / 4. Abstract Existence
12212 Just as we introduced complex numbers, so we introduced sums and temporal parts [Fine,K]
7. Existence / A. Nature of Existence / 6. Criterion for Existence
12216 Real objects are those which figure in the facts that constitute reality [Fine,K]
12218 Being real and being fundamental are separate; Thales's water might be real and divisible [Fine,K]
7. Existence / D. Theories of Reality / 1. Ontologies
12217 For ontology we need, not internal or external views, but a view from outside reality [Fine,K]
7. Existence / D. Theories of Reality / 11. Ontological Commitment / b. Commitment of quantifiers
12213 Ontological claims are often universal, and not a matter of existential quantification [Fine,K]
8. Modes of Existence / C. Powers and Dispositions / 2. Powers as Basic
12710 As well as extension, bodies contain powers [Leibniz]
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]