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Single Idea 10536
[filed under theme 5. Theory of Logic / G. Quantification / 2. Domain of Quantification
]
Full Idea
For Frege there is no need to specify the domain of the individual variables, which is taken as the totality of all objects. This contrasts with the standard notion of an interpretation, which demands that we first fix the domain.
Gist of Idea
Frege's domain for variables is all objects, but modern interpretations first fix the domain
Source
comment on Gottlob Frege (Begriffsschrift [1879]) by Michael Dummett - Frege Philosophy of Language (2nd ed) Ch.14
Book Ref
Dummett,Michael: 'Frege Philosophy of Language' [Duckworth 1981], p.475
A Reaction
What intrigues me is how domains of quantification shift according to context in ordinary usage, even in mid-sentence. I ought to go through every idea in this database, specifying its domain of quantification. Any volunteers?
The
20 ideas
from 'Begriffsschrift'
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7622
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In 1879 Frege developed second order logic
[Frege, by Putnam]
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7729
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Frege replaced Aristotle's subject/predicate form with function/argument form
[Frege, by Weiner]
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9991
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For Frege the variable ranges over all objects
[Frege, by Tait]
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10536
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Frege's domain for variables is all objects, but modern interpretations first fix the domain
[Dummett on Frege]
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9950
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A quantifier is a second-level predicate (which explains how it contributes to truth-conditions)
[Frege, by George/Velleman]
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13609
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Frege produced axioms for logic, though that does not now seem the natural basis for logic
[Frege, by Kaplan]
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7730
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Frege introduced quantifiers for generality
[Frege, by Weiner]
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7742
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Frege reduced most quantifiers to 'everything' combined with 'not'
[Frege, by McCullogh]
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13824
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Proof theory began with Frege's definition of derivability
[Frege, by Prawitz]
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17855
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It may be possible to define induction in terms of the ancestral relation
[Frege, by Wright,C]
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10607
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Frege's logic has a hierarchy of object, property, property-of-property etc.
[Frege, by Smith,P]
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11008
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Existence is not a first-order property, but the instantiation of a property
[Frege, by Read]
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22280
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Frege's account was top-down and decompositional, not bottom-up and compositional
[Frege, by Potter]
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7741
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The predicate 'exists' is actually a natural language expression for a quantifier
[Frege, by Weiner]
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22270
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Frege changed philosophy by extending logic's ability to check the grounds of thinking
[Potter on Frege]
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8939
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We should not describe human laws of thought, but how to correctly track truth
[Frege, by Fisher]
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17745
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For Frege, 'All A's are B's' means that the concept A implies the concept B
[Frege, by Walicki]
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7728
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Frege has a judgement stroke (vertical, asserting or judging) and a content stroke (horizontal, expressing)
[Frege, by Weiner]
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4971
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I don't use 'subject' and 'predicate' in my way of representing a judgement
[Frege]
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16881
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The laws of logic are boundless, so we want the few whose power contains the others
[Frege]
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