Combining Texts

All the ideas for 'Metaphysics', 'A Structural Account of Mathematics' and 'The Foundations of Mathematics'

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

26 ideas

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 / 4. Axioms for Sets / f. Axiom of Infinity V
13430 Infinity: there is an infinity of distinguishable individuals [Ramsey]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / p. Axiom of Reducibility
13428 Reducibility: to every non-elementary function there is an equivalent elementary function [Ramsey]
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 / D. Assumptions for Logic / 4. Identity in Logic
13427 Either 'a = b' vacuously names the same thing, or absurdly names different things [Ramsey]
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]
5. Theory of Logic / L. Paradox / 1. Paradox
13334 Contradictions are either purely logical or mathematical, or they involved thought and language [Ramsey]
6. Mathematics / B. Foundations for Mathematics / 3. Axioms for Geometry
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]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique
13426 Formalists neglect content, but the logicists have focused on generalizations, and neglected form [Ramsey]
6. Mathematics / C. Sources of Mathematics / 7. Formalism
13425 Formalism is hopeless, because it focuses on propositions and ignores concepts [Ramsey]
7. Existence / C. Structure of Existence / 8. Stuff / a. Pure stuff
16771 A composite is a true unity if all of its parts fall under one essence [Scheibler]
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]
11. Knowledge Aims / A. Knowledge / 4. Belief / d. Cause of beliefs
22328 I just confront the evidence, and let it act on me [Ramsey]
13. Knowledge Criteria / C. External Justification / 3. Reliabilism / a. Reliable knowledge
22325 A belief is knowledge if it is true, certain and obtained by a reliable process [Ramsey]
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 / 4. Standard Model / a. Concept of matter
9574 'Gunk' is an individual possessing no parts that are atoms [Chihara]