Combining Texts

All the ideas for 'Replies on 'Limits of Abstraction'', 'On Second-Order Logic' and 'On Metaphysics (frags)'

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22 ideas

1. Philosophy / F. Analytic Philosophy / 7. Limitations of Analysis
10571 Concern for rigour can get in the way of understanding phenomena [Fine,K]
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 / A. Overview of Logic / 7. Second-Order Logic
14249 Boolos reinterprets second-order logic as plural logic [Boolos, by Oliver/Smiley]
10830 Second-order logic metatheory is set-theoretic, and second-order validity has set-theoretic problems [Boolos]
5. Theory of Logic / C. Ontology of Logic / 1. Ontology of Logic
10829 A sentence can't be a truth of logic if it asserts the existence of certain sets [Boolos]
5. Theory of Logic / G. Quantification / 2. Domain of Quantification
10832 '∀x x=x' only means 'everything is identical to itself' if the range of 'everything' is fixed [Boolos]
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]
5. Theory of Logic / K. Features of Logics / 4. Completeness
10834 Weak completeness: if it is valid, it is provable. Strong: it is provable from a set of sentences [Boolos]
5. Theory of Logic / K. Features of Logics / 6. Compactness
13841 Why should compactness be definitive of logic? [Boolos, by Hacking]
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 / e. Peano arithmetic 2nd-order
10833 Many concepts can only be expressed by second-order logic [Boolos]
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 / 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]
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]
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]
26. Natural Theory / A. Speculations on Nature / 2. Natural Purpose / c. Purpose denied
5990 Theophrastus doubted whether nature could be explained teleologically [Theophrastus, by Gottschalk]