Combining Texts

All the ideas for 'Introduction to 'Properties'', 'Essential Attribution' and 'Defending the Axioms'

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20 ideas

2. Reason / B. Laws of Thought / 6. Ockham's Razor
4037 Ockham's Razor is the principle that we need reasons to believe in entities [Mellor/Oliver]
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]
8. Modes of Existence / B. Properties / 6. Categorical Properties
4027 Properties are respects in which particular objects may be alike or differ [Mellor/Oliver]
8. Modes of Existence / B. Properties / 12. Denial of Properties
4029 Nominalists ask why we should postulate properties at all [Mellor/Oliver]
9. Objects / C. Structure of Objects / 2. Hylomorphism / a. Hylomorphism
11181 Aristotelian essentialism involves a 'natural' or 'causal' interpretation of modal operators [Marcus (Barcan)]
11184 Aristotelian essentialism is about shared properties, individuating essentialism about distinctive properties [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)]
18. Thought / E. Abstraction / 5. Abstracta by Negation
4039 Abstractions lack causes, effects and spatio-temporal locations [Mellor/Oliver]
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)]