Combining Texts

All the ideas for 'On the Question of Absolute Undecidability', 'A Puzzle Concerning Matter and Form' and 'Can there be Vague Objects?'

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13 ideas

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 / 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]
7. Existence / D. Theories of Reality / 10. Vagueness / b. Vagueness of reality
16129 Evans argues (falsely!) that a contradiction follows from treating objects as vague [Evans, by Lowe]
16459 Is it coherent that reality is vague, identities can be vague, and objects can have fuzzy boundaries? [Evans]
16460 Evans assumes there can be vague identity statements, and that his proof cannot be right [Evans, by Lewis]
16457 There clearly are vague identity statements, and Evans's argument has a false conclusion [Evans, by Lewis]
8. Modes of Existence / C. Powers and Dispositions / 4. Powers as Essence
16755 The possible Aristotelian view that forms are real and active principles is clearly wrong [Fine,K, by Pasnau]
9. Objects / B. Unity of Objects / 3. Unity Problems / e. Vague objects
14484 If a=b is indeterminate, then a=/=b, and so there cannot be indeterminate identity [Evans, by Thomasson]
9. Objects / F. Identity among Objects / 6. Identity between Objects
16224 There can't be vague identity; a and b must differ, since a, unlike b, is only vaguely the same as b [Evans, by PG]