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Single Idea 9871
[filed under theme 5. Theory of Logic / G. Quantification / 2. Domain of Quantification
]
Full Idea
Frege persistently neglected the question of the domain of quantification, which proved in the end to be fatal.
Gist of Idea
Frege always, and fatally, neglected the domain of quantification
Source
comment on Gottlob Frege (works [1890]) by Michael Dummett - Frege philosophy of mathematics Ch.16
Book Ref
Dummett,Michael: 'Frege: philosophy of mathematics' [Duckworth 1991], p.207
A Reaction
The 'fatality' refers to Russell's paradox, and the fact that not all concepts have extensions. Common sense now says that this is catastrophic. A domain of quantification is a topic of conversation, which is basic to all language. Cf. Idea 9874.
Related Idea
Idea 9874
Contradiction arises from Frege's substitutional account of second-order quantification [Dummett on Frege]
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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