Combining Texts

All the ideas for 'Causes and Counterfactuals', 'The Limits of Abstraction' and 'Knowledge and the Philosophy of Number'

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24 ideas

2. Reason / D. Definition / 3. Types of Definition
9143 Implicit definitions must be satisfiable, creative definitions introduce things, contextual definitions build on things [Fine,K, by Cook/Ebert]
10143 'Creative definitions' do not presuppose the existence of the objects defined [Fine,K]
4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / d. Naïve logical sets
23623 Predicativism says only predicated sets exist [Hossack]
4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / e. Iterative sets
23624 The iterative conception has to appropriate Replacement, to justify the ordinals [Hossack]
4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / f. Limitation of Size
23625 Limitation of Size justifies Replacement, but then has to appropriate Power Set [Hossack]
5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / d. and
23628 The connective 'and' can have an order-sensitive meaning, as 'and then' [Hossack]
5. Theory of Logic / E. Structures of Logic / 6. Relations in Logic
23627 'Before' and 'after' are not two relations, but one relation with two orders [Hossack]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / h. Ordinal infinity
23626 Transfinite ordinals are needed in proof theory, and for recursive functions and computability [Hossack]
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / b. Mathematics is not set theory
23621 Numbers are properties, not sets (because numbers are magnitudes) [Hossack]
6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / a. For mathematical platonism
23622 We can only mentally construct potential infinities, but maths needs actual infinities [Hossack]
7. Existence / A. Nature of Existence / 4. Abstract Existence
10145 Abstracts cannot be identified with sets [Fine,K]
10136 Points in Euclidean space are abstract objects, but not introduced by abstraction [Fine,K]
10144 Postulationism says avoid abstract objects by giving procedures that produce truth [Fine,K]
18. Thought / E. Abstraction / 1. Abstract Thought
9144 Fine's 'procedural postulationism' uses creative definitions, but avoids abstract ontology [Fine,K, by Cook/Ebert]
18. Thought / E. Abstraction / 2. Abstracta by Selection
10141 Many different kinds of mathematical objects can be regarded as forms of abstraction [Fine,K]
18. Thought / E. Abstraction / 7. Abstracta by Equivalence
10135 We can abstract from concepts (e.g. to number) and from objects (e.g. to direction) [Fine,K]
9142 Fine considers abstraction as reconceptualization, to produce new senses by analysing given senses [Fine,K, by Cook/Ebert]
10137 Abstractionism can be regarded as an alternative to set theory [Fine,K]
10138 An object is the abstract of a concept with respect to a relation on concepts [Fine,K]
26. Natural Theory / C. Causation / 1. Causation
8430 Causal statements are used to explain, to predict, to control, to attribute responsibility, and in theories [Kim]
26. Natural Theory / C. Causation / 9. General Causation / c. Counterfactual causation
8396 Many counterfactuals have nothing to do with causation [Kim, by Tooley]
8429 Counterfactuals can express four other relations between events, apart from causation [Kim]
8428 Causation is not the only dependency relation expressed by counterfactuals [Kim]
26. Natural Theory / D. Laws of Nature / 9. Counterfactual Claims
4781 Many counterfactual truths do not imply causation ('if yesterday wasn't Monday, it isn't Tuesday') [Kim, by Psillos]