Combining Texts

All the ideas for 'Individuals without Sortals', 'Science and Method' and 'Philosophy of Mathematics'

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24 ideas

4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / d. Naïve logical sets
23445 Naïve set theory says any formula defines a set, and coextensive sets are identical [Linnebo]
5. Theory of Logic / I. Semantics of Logic / 1. Semantics of Logic
23447 In classical semantics singular terms refer, and quantifiers range over domains [Linnebo]
5. Theory of Logic / K. Features of Logics / 1. Axiomatisation
23443 The axioms of group theory are not assertions, but a definition of a structure [Linnebo]
23444 To investigate axiomatic theories, mathematics needs its own foundational axioms [Linnebo]
6. Mathematics / A. Nature of Mathematics / 2. Geometry
10245 One geometry cannot be more true than another [Poincaré]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / d. Counting via concepts
17518 Counting 'coin in this box' may have coin as the unit, with 'in this box' merely as the scope [Ayers]
17516 If counting needs a sortal, what of things which fall under two sortals? [Ayers]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / g. Incompleteness of Arithmetic
23446 You can't prove consistency using a weaker theory, but you can use a consistent theory [Linnebo]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / a. Structuralism
23448 Mathematics is the study of all possible patterns, and is thus bound to describe the world [Linnebo]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique
23441 Logical truth is true in all models, so mathematical objects can't be purely logical [Linnebo]
6. Mathematics / C. Sources of Mathematics / 7. Formalism
23442 Game Formalism has no semantics, and Term Formalism reduces the semantics [Linnebo]
7. Existence / B. Change in Existence / 4. Events / a. Nature of events
17520 Events do not have natural boundaries, and we have to set them [Ayers]
9. Objects / A. Existence of Objects / 5. Individuation / a. Individuation
17519 To express borderline cases of objects, you need the concept of an 'object' [Ayers]
9. Objects / A. Existence of Objects / 5. Individuation / e. Individuation by kind
17510 Speakers need the very general category of a thing, if they are to think about it [Ayers]
17522 We use sortals to classify physical objects by the nature and origin of their unity [Ayers]
17515 Seeing caterpillar and moth as the same needs continuity, not identity of sortal concepts [Ayers]
17511 Recognising continuity is separate from sortals, and must precede their use [Ayers]
9. Objects / B. Unity of Objects / 1. Unifying an Object / a. Intrinsic unification
17517 Could the same matter have more than one form or principle of unity? [Ayers]
9. Objects / B. Unity of Objects / 3. Unity Problems / c. Statue and clay
17513 If there are two objects, then 'that marble, man-shaped object' is ambiguous [Ayers]
9. Objects / D. Essence of Objects / 5. Essence as Kind
17523 Sortals basically apply to individuals [Ayers]
9. Objects / E. Objects over Time / 5. Temporal Parts
17521 You can't have the concept of a 'stage' if you lack the concept of an object [Ayers]
17514 Temporal 'parts' cannot be separated or rearranged [Ayers]
9. Objects / F. Identity among Objects / 1. Concept of Identity
17509 Some say a 'covering concept' completes identity; others place the concept in the reference [Ayers]
9. Objects / F. Identity among Objects / 3. Relative Identity
17512 If diachronic identities need covering concepts, why not synchronic identities too? [Ayers]