Combining Texts

All the ideas for 'In Defense of Essentialism', 'Mathematical Thought from Ancient to Modern Times' and 'Structuralism and the Notion of Dependence'

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19 ideas

5. Theory of Logic / K. Features of Logics / 1. Axiomatisation
17606 Axioms reveal the underlying assumptions, and reveal relationships between different areas [Kline]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / b. Varieties of structuralism
14085 'Deductivist' structuralism is just theories, with no commitment to objects, or modality [Linnebo]
14084 Non-eliminative structuralism treats mathematical objects as positions in real abstract structures [Linnebo]
14086 'Modal' structuralism studies all possible concrete models for various mathematical theories [Linnebo]
14087 'Set-theoretic' structuralism treats mathematics as various structures realised among the sets [Linnebo]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / d. Platonist structuralism
14089 Structuralism differs from traditional Platonism, because the objects depend ontologically on their structure [Linnebo]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / e. Structuralism critique
14083 Structuralism is right about algebra, but wrong about sets [Linnebo]
14090 In mathematical structuralism the small depends on the large, which is the opposite of physical structures [Linnebo]
7. Existence / C. Structure of Existence / 4. Ontological Dependence
14091 There may be a one-way direction of dependence among sets, and among natural numbers [Linnebo]
8. Modes of Existence / B. Properties / 4. Intrinsic Properties
14088 An 'intrinsic' property is either found in every duplicate, or exists independent of all externals [Linnebo]
9. Objects / A. Existence of Objects / 5. Individuation / e. Individuation by kind
14193 'Substance theorists' take modal properties as primitive, without structure, just falling under a sortal [Paul,LA]
14195 If an object's sort determines its properties, we need to ask what determines its sort [Paul,LA]
14196 Substance essentialism says an object is multiple, as falling under various different sortals [Paul,LA]
9. Objects / C. Structure of Objects / 8. Parts of Objects / b. Sums of parts
14198 Absolutely unrestricted qualitative composition would allow things with incompatible properties [Paul,LA]
9. Objects / D. Essence of Objects / 2. Types of Essence
14190 Deep essentialist objects have intrinsic properties that fix their nature; the shallow version makes it contextual [Paul,LA]
9. Objects / D. Essence of Objects / 6. Essence as Unifier
14191 Deep essentialists say essences constrain how things could change; modal profiles fix natures [Paul,LA]
9. Objects / D. Essence of Objects / 15. Against Essentialism
14192 Essentialism must deal with charges of arbitrariness, and failure to reduce de re modality [Paul,LA]
14197 An object's modal properties don't determine its possibilities [Paul,LA]
10. Modality / E. Possible worlds / 2. Nature of Possible Worlds / a. Nature of possible worlds
14189 'Modal realists' believe in many concrete worlds, 'actualists' in just this world, 'ersatzists' in abstract other worlds [Paul,LA]