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Single Idea 9874
[filed under theme 5. Theory of Logic / G. Quantification / 4. Substitutional Quantification
]
Full Idea
The contradiction in Frege's system is due to the presence of second-order quantification, ..and Frege's explanation of the second-order quantifier, unlike that which he provides for the first-order one, appears to be substitutional rather than objectual.
Gist of Idea
Contradiction arises from Frege's substitutional account of second-order quantification
Source
comment on Gottlob Frege (Grundgesetze der Arithmetik 1 (Basic Laws) [1893], §25) by Michael Dummett - Frege philosophy of mathematics Ch.17
Book Ref
Dummett,Michael: 'Frege: philosophy of mathematics' [Duckworth 1991], p.217
A Reaction
In Idea 9871 Dummett adds the further point that Frege lacks a clear notion of the domain of quantification. At this stage I don't fully understand this idea, but it is clearly of significance, so I will return to it.
Related Idea
Idea 9871
Frege always, and fatally, neglected the domain of quantification [Dummett on Frege]
The
23 ideas
with the same theme
[quantifiers range over expressions instead of objects]:
9874
|
Contradiction arises from Frege's substitutional account of second-order quantification
[Dummett on Frege]
|
10800
|
The values of variables can't determine existence, because they are just expressions
[Ryle, by Quine]
|
21642
|
If quantification is all substitutional, there is no ontology
[Quine]
|
9025
|
You can't base quantification on substituting names for variables, if the irrationals cannot all be named
[Quine]
|
9026
|
Some quantifications could be false substitutionally and true objectually, because of nameless objects
[Quine]
|
10801
|
Either reference really matters, or we don't need to replace it with substitutions
[Quine]
|
10793
|
Quine thought substitutional quantification confused use and mention, but then saw its nominalist appeal
[Quine, by Marcus (Barcan)]
|
10785
|
Maybe a substitutional semantics for quantification lends itself to nominalism
[Marcus (Barcan)]
|
10795
|
Substitutional language has no ontology, and is just a way of speaking
[Marcus (Barcan)]
|
10798
|
A true universal sentence might be substitutionally refuted, by an unnamed denumerable object
[Marcus (Barcan)]
|
10009
|
Substitutional quantification is just a variant of Tarski's account
[Wallace, by Baldwin]
|
10792
|
The substitutional quantifier is not in competition with the standard interpretation
[Kripke, by Marcus (Barcan)]
|
18123
|
Substitutional quantification is just standard if all objects in the domain have a name
[Bostock]
|
9469
|
Substitutional existential quantifier may explain the existence of linguistic entities
[Parsons,C]
|
9468
|
On the substitutional interpretation, '(∃x) Fx' is true iff a closed term 't' makes Ft true
[Parsons,C]
|
15533
|
We can quantify over fictions by quantifying for real over their names
[Lewis]
|
9465
|
Substitutional universal quantification retains truth for substitution of terms of the same type
[Jacquette]
|
9466
|
Nominalists like substitutional quantification to avoid the metaphysics of objects
[Jacquette]
|
12222
|
Substitutional quantification is referential quantification over expressions
[Fine,K]
|
13674
|
We might reduce ontology by using truth of sentences and terms, instead of using objects satisfying models
[Shapiro]
|
15136
|
Substitutional quantification is metaphysical neutral, and equivalent to a disjunction of instances
[Williamson]
|
8475
|
The substitution view of quantification says a sentence is true when there is a substitution instance
[Orenstein]
|
17988
|
Quantification can't all be substitutional; some reference is obviously to objects
[Hofweber]
|