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A quantifier shift is a logical fallacy in which the quantifiers of a statement are erroneously transposed. The change in the logical nature of the statement may not be obvious when it is stated in a natural language like English.

Definition

The fallacious deduction is that: For every A, there is a B, such that C. Therefore, there is a B, such that for every A, C.

\forall x \exists y Rxy \vdash \exists y \forall x Rxy

However, an inverse switching:

\exist y \forall x Rxy  \vdash  \forall x \exist y Rxy

is logically valid.

Examples

1. Every person has a woman that is their mother. Therefore, there is a woman that is the mother of every person.

\forall

This article uses material from the Wikipedia article Quantifier shift, that was deleted or is being discussed for deletion, which is released under the Creative Commons Attribution-ShareAlike 3.0 Unported License.
Author(s): Bryan Derksen Search for "Quantifier shift" on Google
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x\exists
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Author(s): Largoplazo Search for "Quantifier shift" on Google
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y(Px →
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Author(s): Quondum Search for "Quantifier shift" on Google
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(Wy & M(yx))) therefore \exists
This article uses material from the Wikipedia article Quantifier shift, that was deleted or is being discussed for deletion, which is released under the Creative Commons Attribution-ShareAlike 3.0 Unported License.
Author(s): Largoplazo Search for "Quantifier shift" on Google
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y\forall
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Author(s): Bryan Derksen Search for "Quantifier shift" on Google
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x(Wy →
This article uses material from the Wikipedia article Quantifier shift, that was deleted or is being discussed for deletion, which is released under the Creative Commons Attribution-ShareAlike 3.0 Unported License.
Author(s): Quondum Search for "Quantifier shift" on Google
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(Px & M(yx)))

It is fallacious to conclude that there is a single woman who is the mother of all people.

However, if the major premise ("every person has a woman that is their mother") is assumed to be true, then it is valid to conclude that there is some woman who is any given person's mother.


2. Everybody has something to believe in. Therefore, there is something that everybody believes in.

\forall

This article uses material from the Wikipedia article Quantifier shift, that was deleted or is being discussed for deletion, which is released under the Creative Commons Attribution-ShareAlike 3.0 Unported License.
Author(s): Bryan Derksen Search for "Quantifier shift" on Google
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x\exists
This article uses material from the Wikipedia article Quantifier shift, that was deleted or is being discussed for deletion, which is released under the Creative Commons Attribution-ShareAlike 3.0 Unported License.
Author(s): Largoplazo Search for "Quantifier shift" on Google
View Wikipedia's deletion log of "Quantifier shift"
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y Bxy therefore \exists
This article uses material from the Wikipedia article Quantifier shift, that was deleted or is being discussed for deletion, which is released under the Creative Commons Attribution-ShareAlike 3.0 Unported License.
Author(s): Largoplazo Search for "Quantifier shift" on Google
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y\forall
This article uses material from the Wikipedia article Quantifier shift, that was deleted or is being discussed for deletion, which is released under the Creative Commons Attribution-ShareAlike 3.0 Unported License.
Author(s): Bryan Derksen Search for "Quantifier shift" on Google
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x Bxy

It is fallacious to conclude that there is some particular concept to which everyone subscribes.

It is valid to conclude that each person believes a given concept. But it is entirely possible that each person believes in a unique concept.


Formal fallacies
In propositional logic
In quantificational logic
Syllogistic fallacy
This article uses material from the Wikipedia article Quantifier shift, that was deleted or is being discussed for deletion, which is released under the Creative Commons Attribution-ShareAlike 3.0 Unported License.
Author(s): WOSlinker Search for "Quantifier shift" on Google
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zh:量化詞移位
This article uses material from the Wikipedia article Quantifier shift, that was deleted or is being discussed for deletion, which is released under the Creative Commons Attribution-ShareAlike 3.0 Unported License.
Author(s): Timtrent Search for "Quantifier shift" on Google
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