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 1979,0-631-12835-2]].
green numbers give full details |
back to texts
|
expand these ideas
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
|
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
|
16871
|
A truth can be an axiom in one system and not in another
|
|
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
|
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
|
16872
|
A thought is the sense expressed by a sentence, and is what we prove
|
|
16873
|
Thoughts are not subjective or psychological, because some thoughts are the same for us all
|
19. Language / D. Propositions / 5. Unity of Propositions
|
16874
|
The parts of a thought map onto the parts of a sentence
|