Ideas from 'Replies on 'Limits of Abstraction'' by Kit Fine [2005], by Theme Structure

[found in 'Philosophical Studies' (ed/tr -) [- ,]].

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