Combining Texts

All the ideas for 'Abstract Objects', 'Paradoxes of the Infinite' and 'Against 'Ostrich Nominalism''

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13 ideas

4. Formal Logic / F. Set Theory ST / 1. Set Theory
9987 An aggregate in which order does not matter I call a 'set' [Bolzano]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / a. The Infinite
10856 A truly infinite quantity does not need to be a variable [Bolzano]
7. Existence / D. Theories of Reality / 3. Reality
8507 Some think of reality as made of things; I prefer facts or states of affairs [Armstrong]
8. Modes of Existence / D. Universals / 1. Universals
8506 Particulars and properties are distinguishable, but too close to speak of a relation [Armstrong]
8. Modes of Existence / E. Nominalism / 1. Nominalism / a. Nominalism
8505 Refusal to explain why different tokens are of the same type is to be an ostrich [Armstrong]
9. Objects / A. Existence of Objects / 2. Abstract Objects / d. Problems with abstracta
8915 How we refer to abstractions is much less clear than how we refer to other things [Rosen]
18. Thought / E. Abstraction / 2. Abstracta by Selection
8917 The Way of Abstraction used to say an abstraction is an idea that was formed by abstracting [Rosen]
18. Thought / E. Abstraction / 5. Abstracta by Negation
8912 Nowadays abstractions are defined as non-spatial, causally inert things [Rosen]
8913 Chess may be abstract, but it has existed in specific space and time [Rosen]
8914 Sets are said to be abstract and non-spatial, but a set of books can be on a shelf [Rosen]
18. Thought / E. Abstraction / 6. Abstracta by Conflation
8916 Conflating abstractions with either sets or universals is a big claim, needing a big defence [Rosen]
18. Thought / E. Abstraction / 7. Abstracta by Equivalence
8918 Functional terms can pick out abstractions by asserting an equivalence relation [Rosen]
8919 Abstraction by equivalence relationships might prove that a train is an abstract entity [Rosen]