### Ideas from 'Logic in Mathematics' by Gottlob Frege , by Theme Structure

#### [found in 'Posthumous Writings' by Frege,Gottlob (ed/tr Hermes/Long/White etc) [Blackwell 1979,0-631-12835-2]].

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###### 2. Reason / D. Definition / 3. Types of Definition
 16877 A 'constructive' (as opposed to 'analytic') definition creates a new sign
###### 2. Reason / D. Definition / 10. Stipulative Definition
 11219 Frege suggested that mathematics should only accept stipulative definitions [Gupta]
###### 2. Reason / E. Argument / 6. Conclusive Proof
 16878 We must be clear about every premise and every law used in a proof
###### 5. Theory of Logic / A. Overview of Logic / 3. Value of Logic
 16867 Logic not only proves things, but also reveals logical relations between them
###### 5. Theory of Logic / A. Overview of Logic / 8. Logic of Mathematics
 16862 The closest subject to logic is mathematics, which does little apart from drawing inferences
 16863 Does some mathematical reasoning (such as mathematical induction) not belong to logic?
###### 5. Theory of Logic / E. Structures of Logic / 8. Theories in Logic
 16865 'Theorems' are both proved, and used in proofs
###### 5. Theory of Logic / K. Features of Logics / 1. Axiomatisation
 16866 Tracing inference backwards closes in on a small set of axioms and postulates
 16868 The essence of mathematics is the kernel of primitive truths on which it rests
 16871 A truth can be an axiom in one system and not in another
 16870 Axioms are truths which cannot be doubted, and for which no proof is needed
###### 6. Mathematics / A. Nature of Mathematics / 1. Mathematics
 16869 To create order in mathematics we need a full system, guided by patterns of inference
###### 6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / a. Axioms for numbers
 16864 If principles are provable, they are theorems; if not, they are axioms
###### 9. Objects / B. Unity of Objects / 3. Unity Problems / e. Vague objects
 9388 Every concept must have a sharp boundary; we cannot allow an indeterminate third case
###### 18. Thought / B. Mechanics of Thought / 5. Mental Files
 16876 We need definitions to cram retrievable sense into a signed receptacle
 16875 We use signs to mark receptacles for complex senses
###### 19. Language / A. Nature of Meaning / 6. Meaning as Use
 16879 A sign won't gain sense just from being used in sentences with familiar components
###### 19. Language / D. Propositions / 2. Abstract Propositions / a. Propositions as sense
 16873 Thoughts are not subjective or psychological, because some thoughts are the same for us all
 16872 A thought is the sense expressed by a sentence, and is what we prove
###### 19. Language / D. Propositions / 5. Unity of Propositions
 16874 The parts of a thought map onto the parts of a sentence