Ideas from 'Logic in Mathematics' by Gottlob Frege [1914], by Theme Structure
[found in 'Posthumous Writings' by Frege,Gottlob (ed/tr Hermes/Long/White etc) [Blackwell 1979,0631128352]].
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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

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
16863

Does some mathematical reasoning (such as mathematical induction) not belong to logic?

16862

The closest subject to logic is mathematics, which does little apart from drawing inferences

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

16870

Axioms are truths which cannot be doubted, and for which no proof is needed

16871

A truth can be an axiom in one system and not in another

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 / 3. 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 / 4. 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 / B. Meaning / 4. Meaning as Use
16879

A sign won't gain sense just from being used in sentences with familiar components

19. Language / E. Propositions / 2. Nature of Propositions
16874

The parts of a thought map onto the parts of a sentence

16873

Thoughts are not subjective or psychological, because some thoughts are the same for us all

19. Language / E. Propositions / 4. Support for Propositions
16872

A thought is the sense expressed by a sentence, and is what we prove
