Ideas from 'Grundgesetze der Arithmetik 2 (Basic Laws)' by Gottlob Frege [1903], by Theme Structure
[found in 'Translations from the Writings of Gottlob Frege' by Frege,Gottlob (ed/tr Geach,P/Black,M) [Blackwell 1980,0-631-12911-1]].
green numbers give full details |
back to texts
|
expand these ideas
2. Reason / D. Definition / 2. Aims of Definition
13886
|
Later Frege held that definitions must fix a function's value for every possible argument [Wright,C]
|
2. Reason / D. Definition / 7. Contextual Definition
9845
|
We can't define a word by defining an expression containing it, as the remaining parts are a problem
|
2. Reason / D. Definition / 11. Ostensive Definition
10019
|
Only what is logically complex can be defined; what is simple must be pointed to
|
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / b. Types of number
9886
|
Cardinals say how many, and reals give measurements compared to a unit quantity
|
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / g. Real numbers
9889
|
Real numbers are ratios of quantities [Dummett]
|
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / c. Fregean numbers
10553
|
A number is a class of classes of the same cardinality [Dummett]
|
10020
|
Frege's biggest error is in not accounting for the senses of number terms [Hodes]
|
6. Mathematics / C. Sources of Mathematics / 7. Formalism
9887
|
Formalism misunderstands applications, metatheory, and infinity [Dummett]
|
8751
|
Only applicability raises arithmetic from a game to a science
|
9. Objects / B. Unity of Objects / 3. Unity Problems / e. Vague objects
9891
|
The first demand of logic is of a sharp boundary
|
18. Thought / E. Abstraction / 3. Abstracta by Ignoring
9890
|
The modern account of real numbers detaches a ratio from its geometrical origins
|
18. Thought / E. Abstraction / 8. Abstractionism Critique
11846
|
If we abstract the difference between two houses, they don't become the same house
|