Combining Texts

All the ideas for 'Defending the Axioms', 'Interview with Baggini and Stangroom' and 'Naming and Necessity notes and addenda'

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24 ideas

1. Philosophy / D. Nature of Philosophy / 5. Aims of Philosophy / e. Philosophy as reason
6855 Interesting philosophers hardly every give you explicitly valid arguments [Martin,M]
2. Reason / E. Argument / 1. Argument
6856 Valid arguments can be rejected by challenging the premises or presuppositions [Martin,M]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / j. Axiom of Choice IX
17610 The Axiom of Choice paradoxically allows decomposing a sphere into two identical spheres [Maddy]
5. Theory of Logic / C. Ontology of Logic / 3. If-Thenism
17620 Critics of if-thenism say that not all starting points, even consistent ones, are worth studying [Maddy]
5. Theory of Logic / K. Features of Logics / 1. Axiomatisation
17605 Hilbert's geometry and Dedekind's real numbers were role models for axiomatization [Maddy]
17625 If two mathematical themes coincide, that suggest a single deep truth [Maddy]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / g. Continuum Hypothesis
17615 Every infinite set of reals is either countable or of the same size as the full set of reals [Maddy]
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
17618 Set-theory tracks the contours of mathematical depth and fruitfulness [Maddy]
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / c. Against mathematical empiricism
17614 The connection of arithmetic to perception has been idealised away in modern infinitary mathematics [Maddy]
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 / 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]
12. Knowledge Sources / B. Perception / 1. Perception
6857 An error theory of perception says our experience is not as it seems to be [Martin,M]
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]