Combining Texts

All the ideas for 'Defending the Axioms', 'Truly Understood' and 'Ambitious, yet modest, Metaphysics'

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16 ideas

1. Philosophy / E. Nature of Metaphysics / 5. Metaphysics beyond Science
16415 Esoteric metaphysics aims to be top science, investigating ultimate reality [Hofweber]
1. Philosophy / E. Nature of Metaphysics / 7. Against Metaphysics
16413 Science has discovered properties of things, so there are properties - so who needs metaphysics? [Hofweber]
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 / G. Quantification / 1. Quantification
16416 The quantifier in logic is not like the ordinary English one (which has empty names, non-denoting terms etc) [Hofweber]
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]
18. Thought / A. Modes of Thought / 6. Judgement / a. Nature of Judgement
12608 Concepts are distinguished by roles in judgement, and are thus tied to rationality [Peacocke]
18. Thought / D. Concepts / 3. Ontology of Concepts / c. Fregean concepts
12605 A sense is individuated by the conditions for reference [Peacocke]
12607 Fregean concepts have their essence fixed by reference-conditions [Peacocke]
18. Thought / D. Concepts / 4. Structure of Concepts / a. Conceptual structure
12609 Concepts have distinctive reasons and norms [Peacocke]
18. Thought / D. Concepts / 4. Structure of Concepts / b. Analysis of concepts
12604 Any explanation of a concept must involve reference and truth [Peacocke]
19. Language / C. Assigning Meanings / 4. Compositionality
12610 Encountering novel sentences shows conclusively that meaning must be compositional [Peacocke]