Combining Texts

All the ideas for 'Defending the Axioms', 'Letters to Russell' and 'Moral Relativism'

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13 ideas

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 / 3. Nature of Numbers / g. Real numbers
18253 I wish to go straight from cardinals to reals (as ratios), leaving out the rationals [Frege]
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]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / a. Early logicism
18166 The loss of my Rule V seems to make foundations for arithmetic impossible [Frege]
9. Objects / A. Existence of Objects / 2. Abstract Objects / c. Modern abstracta
18269 Logical objects are extensions of concepts, or ranges of values of functions [Frege]
12. Knowledge Sources / B. Perception / 5. Interpretation
22449 When we say 'is red' we don't mean 'seems red to most people' [Foot]
22. Metaethics / A. Ethics Foundations / 1. Nature of Ethics / e. Ethical cognitivism
22451 All people need affection, cooperation, community and help in trouble [Foot]
22. Metaethics / B. Value / 1. Nature of Value / f. Ultimate value
22452 Do we have a concept of value, other than wanting something, or making an effort to get it? [Foot]