Combining Texts

All the ideas for 'Defending the Axioms', 'Structure of Scientific Revolutions (2nd ed)' and 'Essential Attribution'

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22 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 / 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 / C. Structure of Objects / 2. Hylomorphism / a. Hylomorphism
11184 Aristotelian essentialism is about shared properties, individuating essentialism about distinctive properties [Marcus (Barcan)]
11181 Aristotelian essentialism involves a 'natural' or 'causal' interpretation of modal operators [Marcus (Barcan)]
9. Objects / D. Essence of Objects / 7. Essence and Necessity / b. Essence not necessities
11180 Essentialist sentences are not theorems of modal logic, and can even be false [Marcus (Barcan)]
11186 'Essentially' won't replace 'necessarily' for vacuous properties like snub-nosed or self-identical [Marcus (Barcan)]
11185 'Is essentially' has a different meaning from 'is necessarily', as they often cannot be substituted [Marcus (Barcan)]
9. Objects / D. Essence of Objects / 14. Knowledge of Essences
11182 If essences are objects with only essential properties, they are elusive in possible worlds [Marcus (Barcan)]
10. Modality / E. Possible worlds / 1. Possible Worlds / a. Possible worlds
11183 The use of possible worlds is to sort properties (not to individuate objects) [Marcus (Barcan)]
10. Modality / E. Possible worlds / 3. Transworld Objects / b. Rigid designation
11187 In possible worlds, names are just neutral unvarying pegs for truths and predicates [Marcus (Barcan)]
14. Science / A. Basis of Science / 6. Falsification
18076 Most theories are continually falsified [Kuhn, by Kitcher]
22191 Kuhn's scientists don't aim to falsifying their paradigm, because that is what they rely on [Kuhn, by Gorham]
14. Science / B. Scientific Theories / 4. Paradigm
22183 Switching scientific paradigms is a conversion experience [Kuhn]
14. Science / B. Scientific Theories / 5. Commensurability
6162 Kuhn has a description theory of reference, so the reference of 'electron' changes with the descriptions [Rowlands on Kuhn]
22184 Incommensurability assumes concepts get their meaning from within the theory [Kuhn, by Okasha]
7619 Galileo's notions can't be 'incommensurable' if we can fully describe them [Putnam on Kuhn]
26. Natural Theory / D. Laws of Nature / 8. Scientific Essentialism / a. Scientific essentialism
11189 Dispositional essences are special, as if an object loses them they cease to exist [Marcus (Barcan)]