Combining Texts

All the ideas for 'Logicism and Ontological Commits. of Arithmetic', 'Abstract Objects' and 'The Rationalists'

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21 ideas

3. Truth / F. Semantic Truth / 2. Semantic Truth
10017 Truth in a model is more tractable than the general notion of truth [Hodes]
10018 Truth is quite different in interpreted set theory and in the skeleton of its language [Hodes]
5. Theory of Logic / A. Overview of Logic / 7. Second-Order Logic
10015 Higher-order logic may be unintelligible, but it isn't set theory [Hodes]
5. Theory of Logic / D. Assumptions for Logic / 4. Identity in Logic
10011 Identity is a level one relation with a second-order definition [Hodes]
5. Theory of Logic / I. Semantics of Logic / 1. Semantics of Logic
10016 When an 'interpretation' creates a model based on truth, this doesn't include Fregean 'sense' [Hodes]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / a. Numbers
10027 Mathematics is higher-order modal logic [Hodes]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / f. Arithmetic
10026 Arithmetic must allow for the possibility of only a finite total of objects [Hodes]
6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / a. For mathematical platonism
10021 It is claimed that numbers are objects which essentially represent cardinality quantifiers [Hodes]
10022 Numerical terms can't really stand for quantifiers, because that would make them first-level [Hodes]
7. Existence / D. Theories of Reality / 7. Fictionalism
10023 Talk of mirror images is 'encoded fictions' about real facts [Hodes]
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]
9. Objects / B. Unity of Objects / 2. Substance / c. Types of substance
4304 Descartes says there are two substance, Spinoza one, and Leibniz infinitely many [Cottingham]
12. Knowledge Sources / C. Rationalism / 1. Rationalism
4303 The notion of substance lies at the heart of rationalist metaphysics [Cottingham]
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]
26. Natural Theory / C. Causation / 9. General Causation / d. Causal necessity
4306 For rationalists, it is necessary that effects be deducible from their causes [Cottingham]