Combining Texts

All the ideas for 'fragments/reports', 'Grundgesetze der Arithmetik 2 (Basic Laws)' and 'Interview with Baggini and Stangroom'

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19 ideas

1. Philosophy / H. Continental Philosophy / 1. Continental Philosophy
Analytic philosophy has much higher standards of thinking than continental philosophy [Williamson]
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]
4. Formal Logic / E. Nonclassical Logics / 4. Fuzzy Logic
Fuzzy logic uses a continuum of truth, but it implies contradictions [Williamson]
5. Theory of Logic / A. Overview of Logic / 3. Value of Logic
Formal logic struck me as exactly the language I wanted to think in [Williamson]
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]
7. Existence / D. Theories of Reality / 10. Vagueness / c. Vagueness as ignorance
Close to conceptual boundaries judgement is too unreliable to give knowledge [Williamson]
9. Objects / B. Unity of Objects / 3. Unity Problems / e. Vague objects
The first demand of logic is of a sharp boundary [Frege]
What sort of logic is needed for vague concepts, and what sort of concept of truth? [Williamson]
12. Knowledge Sources / B. Perception / 1. Perception
How can one discriminate yellow from red, but not the colours in between? [Williamson]
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.]