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Single Idea 9991
[filed under theme 5. Theory of Logic / G. Quantification / 2. Domain of Quantification
]
Full Idea
For Frege the variable ranges over all objects.
Gist of Idea
For Frege the variable ranges over all objects
Source
report of Gottlob Frege (Begriffsschrift [1879]) by William W. Tait - Frege versus Cantor and Dedekind XII
Book Ref
'Philosophy of Mathematics: anthology', ed/tr. Jacquette,Dale [Blackwell 2002], p.59
A Reaction
The point is that Frege had not yet seen the necessity to define the domain of quantification, and this leads him into various difficulties.
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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