Combining Texts

All the ideas for 'Truth and Probability', 'Principles of Arithmetic, by a new method' and 'Naming and Necessity notes and addenda'

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21 ideas

6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / d. Peano arithmetic
13949 All models of Peano axioms are isomorphic, so the models all seem equally good for natural numbers [Cartwright,R on Peano]
18113 PA concerns any entities which satisfy the axioms [Peano, by Bostock]
17634 Peano axioms not only support arithmetic, but are also fairly obvious [Peano, by Russell]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / g. Incompleteness of Arithmetic
15653 We can add Reflexion Principles to Peano Arithmetic, which assert its consistency or soundness [Halbach on Peano]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / a. Early logicism
17635 Arithmetic can have even simpler logical premises than the Peano Axioms [Russell on Peano]
9. Objects / A. Existence of Objects / 5. Simples
17000 We might fix identities for small particulars, but it is utopian to hope for such things [Kripke]
9. Objects / C. Structure of Objects / 6. Constitution of an Object
11868 A different piece of wood could have been used for that table; constitution isn't identity [Wiggins on Kripke]
9. Objects / F. Identity among Objects / 5. Self-Identity
17044 A relation can clearly be reflexive, and identity is the smallest reflexive relation [Kripke]
9. Objects / F. Identity among Objects / 9. Sameness
16999 A vague identity may seem intransitive, and we might want to talk of 'counterparts' [Kripke]
10. Modality / A. Necessity / 7. Natural Necessity
17058 What many people consider merely physically necessary I consider completely necessary [Kripke]
4970 What is often held to be mere physical necessity is actually metaphysical necessity [Kripke]
10. Modality / B. Possibility / 1. Possibility
17059 Unicorns are vague, so no actual or possible creature could count as a unicorn [Kripke]
10. Modality / B. Possibility / 8. Conditionals / d. Non-truthfunction conditionals
13766 'If' is the same as 'given that', so the degrees of belief should conform to probability theory [Ramsey, by Ramsey]
10. Modality / E. Possible worlds / 1. Possible Worlds / e. Against possible worlds
4950 Possible worlds are useful in set theory, but can be very misleading elsewhere [Kripke]
10. Modality / E. Possible worlds / 3. Transworld Objects / b. Rigid designation
17003 Kaplan's 'Dthat' is a useful operator for transforming a description into a rigid designation [Kripke]
10. Modality / E. Possible worlds / 3. Transworld Objects / c. Counterparts
9221 The best known objection to counterparts is Kripke's, that Humphrey doesn't care if his counterpart wins [Kripke, by Sider]
12. Knowledge Sources / A. A Priori Knowledge / 8. A Priori as Analytic
17052 The a priori analytic truths involving fixing of reference are contingent [Kripke]
14. Science / C. Induction / 6. Bayes's Theorem
19143 Ramsey gave axioms for an uncertain agent to decide their preferences [Ramsey, by Davidson]
15. Nature of Minds / A. Nature of Mind / 1. Mind / a. Mind
4969 I regard the mind-body problem as wide open, and extremely confusing [Kripke]
19. Language / B. Reference / 3. Direct Reference / c. Social reference
4956 A description may fix a reference even when it is not true of its object [Kripke]
19. Language / B. Reference / 4. Descriptive Reference / b. Reference by description
17032 Even if Gödel didn't produce his theorems, he's still called 'Gödel' [Kripke]