Combining Texts

All the ideas for 'Mahaprajnaparamitashastra', 'Grundgesetze der Arithmetik 2 (Basic Laws)' and 'Human Knowledge: its scope and limits'

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18 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]
5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / c. not
Is it possible to state every possible truth about the whole course of nature without using 'not'? [Russell]
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]
10. Modality / A. Necessity / 6. Logical Necessity
Some facts about experience feel like logical necessities [Russell]
12. Knowledge Sources / D. Empiricism / 5. Empiricism Critique
It is hard to explain how a sentence like 'it is not raining' can be found true by observation [Russell]
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 / F. Communication / 3. Denial
If we define 'this is not blue' as disbelief in 'this is blue', we eliminate 'not' as an ingredient of facts [Russell]
23. Ethics / C. Virtue Theory / 3. Virtues / a. Virtues
The six perfections are giving, morality, patience, vigour, meditation, and wisdom [Nagarjuna]
27. Natural Reality / A. Classical Physics / 1. Mechanics / a. Explaining movement
Russell's 'at-at' theory says motion is to be at the intervening points at the intervening instants [Russell, by Psillos]