Combining Texts

All the ideas for 'On the Question of Absolute Undecidability', 'Remarks on the definition and nature of mathematics' and 'Pragmatism in Retrospect'

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12 ideas

3. Truth / E. Pragmatic Truth / 1. Pragmatic Truth
15335 Peirce's theory offers anti-realist verificationism, but surely how things are is independent of us? [Horsten on Peirce]
14796 Independent truth (if there is any) is the ultimate result of sufficient enquiry [Peirce]
4. Formal Logic / F. Set Theory ST / 1. Set Theory
17884 Mathematical set theory has many plausible stopping points, such as finitism, and predicativism [Koellner]
17893 'Reflection principles' say the whole truth about sets can't be captured [Koellner]
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]
5. Theory of Logic / K. Features of Logics / 5. Incompleteness
17894 We have no argument to show a statement is absolutely undecidable [Koellner]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / i. Cardinal infinity
17890 There are at least eleven types of large cardinal, of increasing logical strength [Koellner]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / d. Peano arithmetic
17887 PA is consistent as far as we can accept, and we expand axioms to overcome limitations [Koellner]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / g. Incompleteness of Arithmetic
17891 Arithmetical undecidability is always settled at the next stage up [Koellner]
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 / d. Logicism critique
17808 Saying mathematics is logic is merely replacing one undefined term by another [Curry]
12. Knowledge Sources / D. Empiricism / 3. Pragmatism
14795 Pragmatism is a way of establishing meanings, not a theory of metaphysics or a set of truths [Peirce]