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All the ideas for 'works (fragments)', 'Philosophy of Mathematics' and 'Replies on 'Limits of Abstraction''

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28 ideas

1. Philosophy / F. Analytic Philosophy / 7. Limitations of Analysis
10571 Concern for rigour can get in the way of understanding phenomena [Fine,K]
2. Reason / A. Nature of Reason / 9. Limits of Reason
1812 All discussion is full of uncertainty and contradiction (Mode 11) [Agrippa, by Diog. Laertius]
1813 All reasoning endlessly leads to further reasoning (Mode 12) [Agrippa, by Diog. Laertius]
1811 Proofs often presuppose the thing to be proved (Mode 15) [Agrippa, by Diog. Laertius]
1815 Reasoning needs arbitrary faith in preliminary hypotheses (Mode 14) [Agrippa, by Diog. Laertius]
4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / d. Naïve logical sets
23445 Naïve set theory says any formula defines a set, and coextensive sets are identical [Linnebo]
4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / e. Iterative sets
10565 There is no stage at which we can take all the sets to have been generated [Fine,K]
4. Formal Logic / G. Formal Mereology / 3. Axioms of Mereology
10564 We might combine the axioms of set theory with the axioms of mereology [Fine,K]
5. Theory of Logic / G. Quantification / 5. Second-Order Quantification
10569 If you ask what F the second-order quantifier quantifies over, you treat it as first-order [Fine,K]
5. Theory of Logic / I. Semantics of Logic / 1. Semantics of Logic
10570 Assigning an entity to each predicate in semantics is largely a technical convenience [Fine,K]
23447 In classical semantics singular terms refer, and quantifiers range over domains [Linnebo]
5. Theory of Logic / K. Features of Logics / 1. Axiomatisation
23443 The axioms of group theory are not assertions, but a definition of a structure [Linnebo]
23444 To investigate axiomatic theories, mathematics needs its own foundational axioms [Linnebo]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / b. Types of number
10573 Dedekind cuts lead to the bizarre idea that there are many different number 1's [Fine,K]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / i. Reals from cuts
10575 Why should a Dedekind cut correspond to a number? [Fine,K]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / l. Zero
10574 Unless we know whether 0 is identical with the null set, we create confusions [Fine,K]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / g. Incompleteness of Arithmetic
23446 You can't prove consistency using a weaker theory, but you can use a consistent theory [Linnebo]
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / b. Mathematics is not set theory
10560 Set-theoretic imperialists think sets can represent every mathematical object [Fine,K]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / a. Structuralism
23448 Mathematics is the study of all possible patterns, and is thus bound to describe the world [Linnebo]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / a. Early logicism
10568 Logicists say mathematics can be derived from definitions, and can be known that way [Fine,K]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique
23441 Logical truth is true in all models, so mathematical objects can't be purely logical [Linnebo]
6. Mathematics / C. Sources of Mathematics / 7. Formalism
23442 Game Formalism has no semantics, and Term Formalism reduces the semantics [Linnebo]
7. Existence / C. Structure of Existence / 7. Abstract/Concrete / b. Levels of abstraction
10563 A generative conception of abstracts proposes stages, based on concepts of previous objects [Fine,K]
13. Knowledge Criteria / A. Justification Problems / 2. Justification Challenges / a. Agrippa's trilemma
8850 Agrippa's Trilemma: justification is infinite, or ends arbitrarily, or is circular [Agrippa, by Williams,M]
13. Knowledge Criteria / E. Relativism / 1. Relativism
1814 Everything is perceived in relation to another thing (Mode 13) [Agrippa, by Diog. Laertius]
18. Thought / E. Abstraction / 7. Abstracta by Equivalence
10561 Abstraction-theoretic imperialists think Fregean abstracts can represent every mathematical object [Fine,K]
10562 We can combine ZF sets with abstracts as urelements [Fine,K]
10567 We can create objects from conditions, rather than from concepts [Fine,K]