Combining Texts

All the ideas for 'Defending the Axioms', 'The Ages of the World' and 'Naming and Necessity preface'

expand these ideas     |    start again     |     specify just one area for these texts

16 ideas

4. Formal Logic / D. Modal Logic ML / 1. Modal Logic
16985 Possible worlds allowed the application of set-theoretic models to modal logic [Kripke]
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 / F. Referring in Logic / 1. Naming / c. Names as referential
16982 A man has two names if the historical chains are different - even if they are the same! [Kripke]
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 / F. Identity among Objects / 1. Concept of Identity
16981 With the necessity of self-identity plus Leibniz's Law, identity has to be an 'internal' relation [Kripke]
9. Objects / F. Identity among Objects / 8. Leibniz's Law
4942 The indiscernibility of identicals is as self-evident as the law of contradiction [Kripke]
10. Modality / C. Sources of Modality / 1. Sources of Necessity
16984 I don't think possible worlds reductively reveal the natures of modal operators etc. [Kripke]
10. Modality / D. Knowledge of Modality / 2. A Priori Contingent
9385 The very act of designating of an object with properties gives knowledge of a contingent truth [Kripke]
10. Modality / E. Possible worlds / 1. Possible Worlds / a. Possible worlds
4943 Instead of talking about possible worlds, we can always say "It is possible that.." [Kripke]
10. Modality / E. Possible worlds / 2. Nature of Possible Worlds / a. Nature of possible worlds
16983 Probability with dice uses possible worlds, abstractions which fictionally simplify things [Kripke]
23. Ethics / C. Virtue Theory / 2. Elements of Virtue Theory / e. Character
20957 We don't choose our characters, yet we still claim credit for the actions our characters perform [Schelling]