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