Combining Texts

All the ideas for 'Logicism and Ontological Commits. of Arithmetic', 'Grundgesetze der Arithmetik 2 (Basic Laws)' and 'Human Flourishing, Ethics and Liberty'

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24 ideas

2. Reason / D. Definition / 2. Aims of Definition
13886 Later Frege held that definitions must fix a function's value for every possible argument [Frege, by Wright,C]
2. Reason / D. Definition / 7. Contextual Definition
9845 We can't define a word by defining an expression containing it, as the remaining parts are a problem [Frege]
2. Reason / D. Definition / 11. Ostensive Definition
10019 Only what is logically complex can be defined; what is simple must be pointed to [Frege]
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 / 3. Nature of Numbers / b. Types of number
9886 Cardinals say how many, and reals give measurements compared to a unit quantity [Frege]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / g. Real numbers
9889 Real numbers are ratios of quantities [Frege, by Dummett]
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 / B. Foundations for Mathematics / 5. Definitions of Number / c. Fregean numbers
10553 A number is a class of classes of the same cardinality [Frege, by Dummett]
10020 Frege's biggest error is in not accounting for the senses of number terms [Hodes on Frege]
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]
6. Mathematics / C. Sources of Mathematics / 7. Formalism
9887 Formalism misunderstands applications, metatheory, and infinity [Frege, by Dummett]
8751 Only applicability raises arithmetic from a game to a science [Frege]
7. Existence / D. Theories of Reality / 7. Fictionalism
10023 Talk of mirror images is 'encoded fictions' about real facts [Hodes]
9. Objects / B. Unity of Objects / 3. Unity Problems / e. Vague objects
9891 The first demand of logic is of a sharp boundary [Frege]
18. Thought / E. Abstraction / 3. Abstracta by Ignoring
9890 The modern account of real numbers detaches a ratio from its geometrical origins [Frege]
18. Thought / E. Abstraction / 8. Abstractionism Critique
11846 If we abstract the difference between two houses, they don't become the same house [Frege]
22. Metaethics / C. The Good / 1. Goodness / d. Good as virtue
5121 Basing ethics on flourishing makes it consequentialist, as actions are judged by contributing to it [Harman]
22. Metaethics / C. The Good / 2. Happiness / b. Eudaimonia
5120 What counts as 'flourishing' must be relative to various sets of values [Harman]