Combining Texts

All the ideas for 'Necessary Existents', 'Essentials of Pragmatism' and 'Grundgesetze der Arithmetik 2 (Basic Laws)'

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16 ideas

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]
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]
12. Knowledge Sources / D. Empiricism / 3. Pragmatism
Instead of seeking Truth, we should seek belief that is beyond doubt [Peirce]
18. Thought / D. Concepts / 3. Ontology of Concepts / b. Concepts as abilities
A 'conception', the rational implication of a word, lies in its bearing upon the conduct of life [Peirce]
18. Thought / D. Concepts / 4. Structure of Concepts / b. Analysis of concepts
The definition of a concept is just its experimental implications [Peirce]
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]
19. Language / D. Propositions / 3. Concrete Propositions
Propositions (such as 'that dog is barking') only exist if their items exist [Williamson]