Combining Texts

All the ideas for 'On the Question of Absolute Undecidability', 'Substances without Substrata' and 'On Multiplying Entities'

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11 ideas

2. Reason / B. Laws of Thought / 6. Ockham's Razor
8207 The quest for simplicity drove scientists to posit new entities, such as molecules in gases [Quine]
8208 In arithmetic, ratios, negatives, irrationals and imaginaries were created in order to generalise [Quine]
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 / B. Change in Existence / 4. Events / c. Reduction of events
8205 Explaining events just by bodies can't explain two events identical in space-time [Quine]
10. Modality / A. Necessity / 11. Denial of Necessity
8206 Necessity could be just generalisation over classes, or (maybe) quantifying over possibilia [Quine]
19. Language / F. Communication / 6. Interpreting Language / c. Principle of charity
6316 We translate in a way that makes the largest possible number of statements true [Wilson,NL]