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 / 5. Against Analysis
10571

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
10565

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
10564

We might combine the axioms of set theory with the axioms of mereology

5. Theory of Logic / G. Quantification / 5. SecondOrder Quantification
10569

If you ask what F the secondorder quantifier quantifies over, you treat it as firstorder

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

6. Mathematics / A. Nature of Mathematics / 3. Numbers / b. Types of number
10573

Dedekind cuts lead to the bizarre idea that there are many different number 1's

6. Mathematics / A. Nature of Mathematics / 3. Numbers / i. Reals from cuts
10575

Why should a Dedekind cut correspond to a number?

6. Mathematics / A. Nature of Mathematics / 3. Numbers / l. Zero
10574

Unless we know whether 0 is identical with the null set, we create confusions

6. Mathematics / B. Foundations for Mathematics / 5. Mathematics as Set Theory / b. Mathematics is not set theory
10560

Settheoretic imperialists think sets can represent every mathematical object

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

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

18. Thought / E. Abstraction / 7. Abstracta by Equivalence
10567

We can create objects from conditions, rather than from concepts

10561

Abstractiontheoretic imperialists think Fregean abstracts can represent every mathematical object

10562

We can combine ZF sets with abstracts as urelements
