Combining Texts

All the ideas for 'On the Question of Absolute Undecidability', 'Identity and Necessity' and 'What is Cantor's Continuum Problem?'

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20 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]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets
8679 We perceive the objects of set theory, just as we perceive with our senses [Gödel]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / o. Axiom of Constructibility V = L
9942 Gödel proved the classical relative consistency of the axiom V = L [Gödel, by Putnam]
5. Theory of Logic / F. Referring in Logic / 1. Naming / b. Names as descriptive
9175 We may fix the reference of 'Cicero' by a description, but thereafter the name is rigid [Kripke]
5. Theory of Logic / F. Referring in Logic / 1. Naming / c. Names as referential
9171 The function of names is simply to refer [Kripke]
5. Theory of Logic / K. Features of Logics / 5. Incompleteness
17894 We have no argument to show a statement is absolutely undecidable [Koellner]
5. Theory of Logic / L. Paradox / 5. Paradoxes in Set Theory / a. Set theory paradoxes
18062 Set-theory paradoxes are no worse than sense deception in physics [Gödel]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / g. Continuum Hypothesis
10868 The Continuum Hypothesis is not inconsistent with the axioms of set theory [Gödel, by Clegg]
13517 If set theory is consistent, we cannot refute or prove the Continuum Hypothesis [Gödel, by Hart,WD]
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 / a. Mathematical empiricism
10271 Basic mathematics is related to abstract elements of our empirical ideas [Gödel]
10. Modality / D. Knowledge of Modality / 3. A Posteriori Necessary
9174 It is necessary that this table is not made of ice, but we don't know it a priori [Kripke]
10. Modality / E. Possible worlds / 3. Transworld Objects / b. Rigid designation
9172 A 'rigid designator' designates the same object in all possible worlds [Kripke]
9173 We cannot say that Nixon might have been a different man from the one he actually was [Kripke]
10. Modality / E. Possible worlds / 3. Transworld Objects / c. Counterparts
9176 Modal statements about this table never refer to counterparts; that confuses epistemology and metaphysics [Kripke]
17. Mind and Body / A. Mind-Body Dualism / 7. Zombies
9177 Identity theorists must deny that pains can be imagined without brain states [Kripke]
17. Mind and Body / E. Mind as Physical / 7. Anti-Physicalism / e. Modal argument
9178 Pain, unlike heat, is picked out by an essential property [Kripke]