Ideas from 'Replies on 'Limits of Abstraction'' by Kit Fine [2005], by Theme Structure
[found in 'Philosophical Studies' (ed/tr -) [- ,]].
green numbers give full details |
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expand these ideas
1. Philosophy / F. Analytic Philosophy / 7. Limitations of Analysis
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10571
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Concern for rigour can get in the way of understanding phenomena
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4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / e. Iterative sets
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10565
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There is no stage at which we can take all the sets to have been generated
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4. Formal Logic / G. Formal Mereology / 3. Axioms of Mereology
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10564
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We might combine the axioms of set theory with the axioms of mereology
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5. Theory of Logic / G. Quantification / 5. Second-Order Quantification
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10569
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If you ask what F the second-order quantifier quantifies over, you treat it as first-order
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5. Theory of Logic / I. Semantics of Logic / 1. Semantics of Logic
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10570
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Assigning an entity to each predicate in semantics is largely a technical convenience
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6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / b. Types of number
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10573
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Dedekind cuts lead to the bizarre idea that there are many different number 1's
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6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / i. Reals from cuts
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10575
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Why should a Dedekind cut correspond to a number?
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6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / l. Zero
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10574
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Unless we know whether 0 is identical with the null set, we create confusions
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6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / b. Mathematics is not set theory
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10560
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Set-theoretic imperialists think sets can represent every mathematical object
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6. Mathematics / C. Sources of Mathematics / 6. Logicism / a. Early logicism
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10568
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Logicists say mathematics can be derived from definitions, and can be known that way
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7. Existence / C. Structure of Existence / 7. Abstract/Concrete / b. Levels of abstraction
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10563
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A generative conception of abstracts proposes stages, based on concepts of previous objects
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18. Thought / E. Abstraction / 7. Abstracta by Equivalence
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10561
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Abstraction-theoretic imperialists think Fregean abstracts can represent every mathematical object
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10562
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We can combine ZF sets with abstracts as urelements
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10567
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We can create objects from conditions, rather than from concepts
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