Combining Texts

All the ideas for 'fragments/reports', 'Truth by Convention' and 'Grundgesetze der Arithmetik 2 (Basic Laws)'

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23 ideas

1. Philosophy / F. Analytic Philosophy / 6. Logical Analysis
If if time is money then if time is not money then time is money then if if if time is not money... [Quine]
2. Reason / D. Definition / 2. Aims of Definition
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
We can't define a word by defining an expression containing it, as the remaining parts are a problem [Frege]
Definition by words is determinate but relative; fixing contexts could make it absolute [Quine]
2. Reason / D. Definition / 11. Ostensive Definition
Only what is logically complex can be defined; what is simple must be pointed to [Frege]
5. Theory of Logic / C. Ontology of Logic / 3. If-Thenism
Quine quickly dismisses If-thenism [Quine, by Musgrave]
5. Theory of Logic / C. Ontology of Logic / 4. Logic by Convention
Logic needs general conventions, but that needs logic to apply them to individual cases [Quine, by Rey]
Claims that logic and mathematics are conventional are either empty, uninteresting, or false [Quine]
Logic isn't conventional, because logic is needed to infer logic from conventions [Quine]
If a convention cannot be communicated until after its adoption, what is its role? [Quine]
6. Mathematics / A. Nature of Mathematics / 2. Geometry
If analytic geometry identifies figures with arithmetical relations, logicism can include geometry [Quine]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / b. Types of number
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
Real numbers are ratios of quantities [Frege, by Dummett]
6. Mathematics / B. Foundations for Mathematics / 3. Axioms for Geometry
There are four different possible conventional accounts of geometry [Quine]
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / c. Fregean numbers
Frege's biggest error is in not accounting for the senses of number terms [Hodes on Frege]
A number is a class of classes of the same cardinality [Frege, by Dummett]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / a. Early logicism
If mathematics follows from definitions, then it is conventional, and part of logic [Quine]
6. Mathematics / C. Sources of Mathematics / 7. Formalism
Formalism misunderstands applications, metatheory, and infinity [Frege, by Dummett]
Only applicability raises arithmetic from a game to a science [Frege]
9. Objects / B. Unity of Objects / 3. Unity Problems / e. Vague objects
The first demand of logic is of a sharp boundary [Frege]
18. Thought / E. Abstraction / 3. Abstracta by Ignoring
The modern account of real numbers detaches a ratio from its geometrical origins [Frege]
18. Thought / E. Abstraction / 8. Abstractionism Critique
If we abstract the difference between two houses, they don't become the same house [Frege]
21. Aesthetics / C. Artistic Issues / 7. Art and Morality
Musical performance can reveal a range of virtues [Damon of Ath.]