Combining Texts

All the ideas for 'On the Question of Absolute Undecidability', 'Lecture on Nominalism' and 'works'

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11 ideas

2. Reason / F. Fallacies / 1. Fallacy

21697

The Struthionic Fallacy is that of burying one's head in the sand [Quine]

4. Formal Logic / D. Modal Logic ML / 3. Modal Logic Systems / h. System S5

7791	The simplest of the logics based on possible worlds is Lewis's S5 [Lewis,CI, by Girle]

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 / 6. Relations in Logic

21698

All relations, apart from ancestrals, can be reduced to simpler logic [Quine]

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 / 3. Mathematical Nominalism

21696

Nominalism rejects both attributes and classes (where extensionalism accepts the classes) [Quine]

10. Modality / A. Necessity / 2. Nature of Necessity

11002

Equating necessity with informal provability is the S4 conception of necessity [Lewis,CI, by Read]