Combining Texts

All the ideas for 'On Motion', 'A Structural Account of Mathematics' and 'works'

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24 ideas

3. Truth / A. Truth Problems / 2. Defining Truth
10153 In everyday language, truth seems indefinable, inconsistent, and illogical [Tarski]
3. Truth / G. Axiomatic Truth / 1. Axiomatic Truth
19141 Tarski thought axiomatic truth was too contingent, and in danger of inconsistencies [Tarski, by Davidson]
4. Formal Logic / F. Set Theory ST / 3. Types of Set / b. Empty (Null) Set
9572 Realists about sets say there exists a null set in the real world, with no members [Chihara]
9550 We only know relational facts about the empty set, but nothing intrinsic [Chihara]
9562 In simple type theory there is a hierarchy of null sets [Chihara]
9573 The null set is a structural position which has no other position in membership relation [Chihara]
4. Formal Logic / F. Set Theory ST / 3. Types of Set / c. Unit (Singleton) Sets
9551 What is special about Bill Clinton's unit set, in comparison with all the others? [Chihara]
4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / a. Sets as existing
9549 The set theorist cannot tell us what 'membership' is [Chihara]
4. Formal Logic / F. Set Theory ST / 7. Natural Sets
9571 ZFU refers to the physical world, when it talks of 'urelements' [Chihara]
4. Formal Logic / F. Set Theory ST / 8. Critique of Set Theory
9563 A pack of wolves doesn't cease when one member dies [Chihara]
5. Theory of Logic / A. Overview of Logic / 4. Pure Logic
10048 There is no clear boundary between the logical and the non-logical [Tarski]
5. Theory of Logic / B. Logical Consequence / 4. Semantic Consequence |=
10694 Logical consequence is when in any model in which the premises are true, the conclusion is true [Tarski, by Beall/Restall]
10479 Logical consequence: true premises give true conclusions under all interpretations [Tarski, by Hodges,W]
5. Theory of Logic / E. Structures of Logic / 6. Relations in Logic
9561 The mathematics of relations is entirely covered by ordered pairs [Chihara]
5. Theory of Logic / K. Features of Logics / 2. Consistency
9552 Sentences are consistent if they can all be true; for Frege it is that no contradiction can be deduced [Chihara]
6. Mathematics / B. Foundations for Mathematics / 3. Axioms for Geometry
10157 Tarski improved Hilbert's geometry axioms, and without set-theory [Tarski, by Feferman/Feferman]
9553 Analytic geometry gave space a mathematical structure, which could then have axioms [Chihara]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / c. Nominalist structuralism
10192 We can replace existence of sets with possibility of constructing token sentences [Chihara, by MacBride]
7. Existence / D. Theories of Reality / 11. Ontological Commitment / e. Ontological commitment problems
9559 If a successful theory confirms mathematics, presumably a failed theory disconfirms it? [Chihara]
9566 No scientific explanation would collapse if mathematical objects were shown not to exist [Chihara]
18. Thought / E. Abstraction / 7. Abstracta by Equivalence
9568 I prefer the open sentences of a Constructibility Theory, to Platonist ideas of 'equivalence classes' [Chihara]
19. Language / B. Reference / 3. Direct Reference / b. Causal reference
9547 Mathematical entities are causally inert, so the causal theory of reference won't work for them [Chihara]
27. Natural Reality / B. Modern Physics / 1. Relativity / a. Special relativity
12709 Motion is not absolute, but consists in relation [Leibniz]
27. Natural Reality / B. Modern Physics / 4. Standard Model / a. Concept of matter
9574 'Gunk' is an individual possessing no parts that are atoms [Chihara]