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All the ideas for 'Logicism Revisited', 'On Concept and Object' and 'Relations'

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24 ideas

5. Theory of Logic / C. Ontology of Logic / 3. If-Thenism
10061 The If-thenist view only seems to work for the axiomatised portions of mathematics [Musgrave]
10065 Perhaps If-thenism survives in mathematics if we stick to first-order logic [Musgrave]
5. Theory of Logic / E. Structures of Logic / 1. Logical Form
4975 A thought can be split in many ways, so that different parts appear as subject or predicate [Frege]
5. Theory of Logic / I. Semantics of Logic / 3. Logical Truth
10049 Logical truths may contain non-logical notions, as in 'all men are men' [Musgrave]
10050 A statement is logically true if it comes out true in all interpretations in all (non-empty) domains [Musgrave]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / d. Peano arithmetic
10058 No two numbers having the same successor relies on the Axiom of Infinity [Musgrave]
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / c. Fregean numbers
9949 There is the concept, the object falling under it, and the extension (a set, which is also an object) [Frege, by George/Velleman]
6. Mathematics / C. Sources of Mathematics / 7. Formalism
10062 Formalism seems to exclude all creative, growing mathematics [Musgrave]
10063 Formalism is a bulwark of logical positivism [Musgrave]
7. Existence / A. Nature of Existence / 6. Criterion for Existence
18995 Frege mistakenly takes existence to be a property of concepts, instead of being about things [Frege, by Yablo]
8. Modes of Existence / A. Relations / 1. Nature of Relations
21339 We want the ontology of relations, not just a formal way of specifying them [Heil]
21349 Two people are indirectly related by height; the direct relation is internal, between properties [Heil]
21340 Maybe all the other features of the world can be reduced to relations [Heil]
8. Modes of Existence / A. Relations / 2. Internal Relations
21348 In the case of 5 and 6, their relational truthmaker is just the numbers [Heil]
21351 Truthmaking is a clear example of an internal relation [Heil]
21344 If R internally relates a and b, and you have a and b, you thereby have R [Heil]
8. Modes of Existence / B. Properties / 10. Properties as Predicates
10317 It is unclear whether Frege included qualities among his abstract objects [Frege, by Hale]
8. Modes of Existence / C. Powers and Dispositions / 4. Powers as Essence
21350 If properties are powers, then causal relations are internal relations [Heil]
9. Objects / A. Existence of Objects / 3. Objects in Thought
10535 Frege's 'objects' are both the referents of proper names, and what predicates are true or false of [Frege, by Dummett]
18. Thought / D. Concepts / 3. Ontology of Concepts / c. Fregean concepts
9839 Frege equated the concepts under which an object falls with its properties [Frege, by Dummett]
18. Thought / D. Concepts / 5. Concepts and Language / b. Concepts are linguistic
4973 As I understand it, a concept is the meaning of a grammatical predicate [Frege]
19. Language / A. Nature of Meaning / 2. Meaning as Mental
9167 Frege felt that meanings must be public, so they are abstractions rather than mental entities [Frege, by Putnam]
19. Language / A. Nature of Meaning / 5. Meaning as Verification
10060 Logical positivists adopted an If-thenist version of logicism about numbers [Musgrave]
19. Language / D. Propositions / 2. Abstract Propositions / a. Propositions as sense
4974 For all the multiplicity of languages, mankind has a common stock of thoughts [Frege]