### 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]].

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###### 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