Combining Texts

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

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18 ideas

1. Philosophy / F. Analytic Philosophy / 4. Conceptual Analysis
To explain a concept, we need its purpose, not just its rules of usage [Dummett]
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]
2. Reason / D. Definition / 11. Ostensive Definition
Only what is logically complex can be defined; what is simple must be pointed to [Frege]
3. Truth / A. Truth Problems / 1. Truth
It is part of the concept of truth that we aim at making true statements [Dummett]
3. Truth / A. Truth Problems / 2. Defining Truth
We must be able to specify truths in a precise language, like winning moves in a game [Dummett]
3. Truth / F. Semantic Truth / 2. Semantic Truth
Tarski's truth is like rules for winning games, without saying what 'winning' means [Dummett, by Davidson]
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 / 5. Definitions of Number / c. Fregean numbers
A number is a class of classes of the same cardinality [Frege, by Dummett]
Frege's biggest error is in not accounting for the senses of number terms [Hodes on Frege]
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]
13. Knowledge Criteria / E. Relativism / 2. Knowledge as Convention
By nature people are close to one another, but culture drives them apart [Hippias]
18. Thought / E. Abstraction / 1. Abstract Thought
You can't infer a dog's abstract concepts from its behaviour [Dummett]
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]