Quantifier shift

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A logical fallacy in which the quantifiers of a statement are erroneously transposed.

[edit] Definition

For every A, there is a B, such that C. Therefore, there is a B, such that for every A, C.

x y(Rxy) therefore yx(Rxy)
OR

There is an A, such that for every B, C. Therefore, for every B, there is an A, such that C.

yx(Rxy) therefore x y(Rxy)

[edit] Examples

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

xy(Px (Wy & M(yx)) therefore yx(Wy (Px & M(yx))

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

xy Bxy therefore yx Bxy

v • d • e Formal fallacies Argument from fallacy • Fallacy of modal logic • Masked man fallacy • Appeal to probability • Bare assertion fallacy Fallacy of propositional logic: Affirming a disjunct • Affirming the consequent • False dilemma • Denying the antecedent Fallacy of quantificational logic: Existential fallacy • Illicit Conversion • Proof by example • Quantifier shift Syllogistic fallacy: Affirmative conclusion from a negative premise • Exclusive premises • Necessity • Four-term Fallacy • Illicit major • Illicit minor • Undistributed middle Other types of fallacy