Combining Texts

All the ideas for 'fragments/reports', 'Remarks on the definition and nature of mathematics' and 'Constructibility and Mathematical Existence'

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9 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]
5. Theory of Logic / E. Structures of Logic / 8. Theories in Logic
17807 To study formal systems, look at the whole thing, and not just how it is constructed in steps [Curry]
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / c. Against mathematical empiricism
17806 It is untenable that mathematics is general physical truths, because it needs infinity [Curry]
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 / 6. Logicism / d. Logicism critique
17808 Saying mathematics is logic is merely replacing one undefined term by another [Curry]
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]
26. Natural Theory / A. Speculations on Nature / 5. Infinite in Nature
1748 Archelaus was the first person to say that the universe is boundless [Archelaus, by Diog. Laertius]
27. Natural Reality / G. Biology / 3. Evolution
5989 Archelaus said life began in a primeval slime [Archelaus, by Schofield]