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Single Idea 11219
[filed under theme 2. Reason / D. Definition / 10. Stipulative Definition
]
Full Idea
Frege has defended the austere view that, in mathematics at least, only stipulative definitions should be countenanced.
Gist of Idea
Frege suggested that mathematics should only accept stipulative definitions
Source
report of Gottlob Frege (Logic in Mathematics [1914]) by Anil Gupta - Definitions 1.3
Book Ref
'Stanford Online Encyclopaedia of Philosophy', ed/tr. Stanford University [plato.stanford.edu], p.4
A Reaction
This sounds intriguingly at odds with Frege's well-known platonism about numbers (as sets of equinumerous sets). It makes sense for other mathematical concepts.
The
20 ideas
from 'Logic in Mathematics'
11219
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Frege suggested that mathematics should only accept stipulative definitions
[Frege, by Gupta]
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16863
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Does some mathematical reasoning (such as mathematical induction) not belong to logic?
[Frege]
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16862
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The closest subject to logic is mathematics, which does little apart from drawing inferences
[Frege]
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16864
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If principles are provable, they are theorems; if not, they are axioms
[Frege]
|
16866
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Tracing inference backwards closes in on a small set of axioms and postulates
[Frege]
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16865
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'Theorems' are both proved, and used in proofs
[Frege]
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16867
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Logic not only proves things, but also reveals logical relations between them
[Frege]
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16868
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The essence of mathematics is the kernel of primitive truths on which it rests
[Frege]
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16870
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Axioms are truths which cannot be doubted, and for which no proof is needed
[Frege]
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16871
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A truth can be an axiom in one system and not in another
[Frege]
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16869
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To create order in mathematics we need a full system, guided by patterns of inference
[Frege]
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16873
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Thoughts are not subjective or psychological, because some thoughts are the same for us all
[Frege]
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16872
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A thought is the sense expressed by a sentence, and is what we prove
[Frege]
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16874
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The parts of a thought map onto the parts of a sentence
[Frege]
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16876
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We need definitions to cram retrievable sense into a signed receptacle
[Frege]
|
16875
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We use signs to mark receptacles for complex senses
[Frege]
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16877
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A 'constructive' (as opposed to 'analytic') definition creates a new sign
[Frege]
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16878
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We must be clear about every premise and every law used in a proof
[Frege]
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16879
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A sign won't gain sense just from being used in sentences with familiar components
[Frege]
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9388
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Every concept must have a sharp boundary; we cannot allow an indeterminate third case
[Frege]
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