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Single Idea 8689
[filed under theme 6. Mathematics / C. Sources of Mathematics / 6. Logicism / a. Early logicism
]
Full Idea
After the problem with Russell's paradox, Frege did not publish for fourteen years, and he then tried to re-found arithmetic in Euclidean geometry, rather than in logic.
Gist of Idea
Eventually Frege tried to found arithmetic in geometry instead of in logic
Source
report of Gottlob Frege (works [1890], 3.4) by Michèle Friend - Introducing the Philosophy of Mathematics 3.4
Book Ref
Friend,Michèle: 'Introducing the Philosophy of Mathematics' [Acumen 2007], p.66
A Reaction
I take it that his new road would have led him to modern Structuralism, so I think he was probably on the right lines. Unfortunately Frege had already done enough for one good lifetime.
The
26 ideas
from 'works'
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13473
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Frege thinks there is an independent logical order of the truths, which we must try to discover
[Frege, by Hart,WD]
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6076
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For Frege, predicates are names of functions that map objects onto the True and False
[Frege, by McGinn]
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3319
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Frege gives a functional account of predication so that we can dispense with predicates
[Frege, by Benardete,JA]
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9871
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Frege always, and fatally, neglected the domain of quantification
[Dummett on Frege]
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16884
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Basic truths of logic are not proved, but seen as true when they are understood
[Frege, by Burge]
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3331
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If '5' is the set of all sets with five members, that may be circular, and you can know a priori if the set has content
[Benardete,JA on Frege]
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16880
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Frege aimed to discover the logical foundations which justify arithmetical judgements
[Frege, by Burge]
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5657
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Frege's logic showed that there is no concept of being
[Frege, by Scruton]
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16882
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The building blocks contain the whole contents of a discipline
[Frege]
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3318
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Frege made identity a logical notion, enshrined above all in the formula 'for all x, x=x'
[Frege, by Benardete,JA]
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16885
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To understand a thought, understand its inferential connections to other thoughts
[Frege, by Burge]
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16887
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Frege's concept of 'self-evident' makes no reference to minds
[Frege, by Burge]
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16894
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An apriori truth is grounded in generality, which is universal quantification
[Frege, by Burge]
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5816
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Frege said concepts were abstract entities, not mental entities
[Frege, by Putnam]
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7307
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A thought is not psychological, but a condition of the world that makes a sentence true
[Frege, by Miller,A]
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7309
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Frege's 'sense' is the strict and literal meaning, stripped of tone
[Frege, by Miller,A]
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7312
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'Sense' solves the problems of bearerless names, substitution in beliefs, and informativeness
[Frege, by Miller,A]
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7725
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'P or not-p' seems to be analytic, but does not fit Kant's account, lacking clear subject or predicate
[Frege, by Weiner]
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7316
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Analytic truths are those that can be demonstrated using only logic and definitions
[Frege, by Miller,A]
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3307
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Frege put forward an ontological argument for the existence of numbers
[Frege, by Benardete,JA]
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13455
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Frege did not think of himself as working with sets
[Frege, by Hart,WD]
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16895
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The null set is indefensible, because it collects nothing
[Frege, by Burge]
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3328
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Frege proposed a realist concept of a set, as the extension of a predicate or concept or function
[Frege, by Benardete,JA]
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8689
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Eventually Frege tried to found arithmetic in geometry instead of in logic
[Frege, by Friend]
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22317
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Truth does not admit of more and less
[Frege]
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9179
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Frege frequently expressed a contempt for language
[Frege, by Dummett]
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