Combining Texts

All the ideas for 'Identity and Spatio-Temporal Continuity', 'Constructibility and Mathematical Existence' and 'Letters to Russell'

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8 ideas

4. Formal Logic / F. Set Theory ST / 8. Critique of Set Theory

8758	We could talk of open sentences, instead of sets [Chihara, by Shapiro]

6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / g. Real numbers

18253

I wish to go straight from cardinals to reals (as ratios), leaving out the rationals [Frege]

6. Mathematics / C. Sources of Mathematics / 6. Logicism / a. Early logicism

18166

The loss of my Rule V seems to make foundations for arithmetic impossible [Frege]

6. Mathematics / C. Sources of Mathematics / 6. Logicism / b. Type theory

10265

Chihara's system is a variant of type theory, from which he can translate sentences [Chihara, by Shapiro]

8759	We can replace type theory with open sentences and a constructibility quantifier [Chihara, by Shapiro]

6. Mathematics / C. Sources of Mathematics / 10. Constructivism / a. Constructivism

10264

Introduce a constructibility quantifiers (Cx)Φ - 'it is possible to construct an x such that Φ' [Chihara, by Shapiro]

9. Objects / A. Existence of Objects / 2. Abstract Objects / c. Modern abstracta

18269

Logical objects are extensions of concepts, or ranges of values of functions [Frege]

9. Objects / A. Existence of Objects / 5. Individuation / e. Individuation by kind

13128

'Ultimate sortals' cannot explain ontological categories [Westerhoff on Wiggins]