Combining Texts

All the ideas for 'Syntagma', 'Can there be Vague Objects?' and 'Structuralism and the Notion of Dependence'

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19 ideas

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]
7. Existence / D. Theories of Reality / 10. Vagueness / b. Vagueness of reality
16129 Evans argues (falsely!) that a contradiction follows from treating objects as vague [Evans, by Lowe]
16459 Is it coherent that reality is vague, identities can be vague, and objects can have fuzzy boundaries? [Evans]
16460 Evans assumes there can be vague identity statements, and that his proof cannot be right [Evans, by Lewis]
16457 There clearly are vague identity statements, and Evans's argument has a false conclusion [Evans, by Lewis]
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]
8. Modes of Existence / B. Properties / 8. Properties as Modes
16730 If matter is entirely atoms, anything else we notice in it can only be modes [Gassendi]
9. Objects / B. Unity of Objects / 3. Unity Problems / e. Vague objects
14484 If a=b is indeterminate, then a=/=b, and so there cannot be indeterminate identity [Evans, by Thomasson]
9. Objects / F. Identity among Objects / 6. Identity between Objects
16224 There can't be vague identity; a and b must differ, since a, unlike b, is only vaguely the same as b [Evans, by PG]
14. Science / D. Explanation / 2. Types of Explanation / j. Explanations by reduction
16619 We observe qualities, and use 'induction' to refer to the substances lying under them [Gassendi]
26. Natural Theory / A. Speculations on Nature / 6. Early Matter Theories / g. Atomism
16593 Atoms are not points, but hard indivisible things, which no force in nature can divide [Gassendi]
16729 How do mere atoms produce qualities like colour, flavour and odour? [Gassendi]