Quantifier shift

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A quantifier shift is a formal logical fallacy in which the quantifiers of a statement are improperly transposed. While this cannot always be easily recognized in common language, it can be expressed in both formal and informal terms.

For every x there is a y such that R. Therefore, for every y there is an x such that R.

The classical illustration of this fallacy is as follows:

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

Use in Apologetics[edit]

This is most commonly illustrated in First Cause arguments for the existence of God.

Every event has a cause. Therefore, there is an event that caused all subsequent events.

v · d Logical fallacies
v · d Formal fallacies
Propositional logic   Affirming a disjunct · Affirming the consequent · Argument from fallacy · False dilemma · Denying the antecedent
Quantificational logic   Existential fallacy · Illicit conversion · Proof by example · Quantifier shift
Syllogistic   Affirmative conclusion from a negative premise · Exclusive premises · Necessity · Four-term fallacy · Illicit major · Illicit minor · Undistributed middle

v · d Faulty generalisations
General   Begging the question · Gambler's fallacy · Slippery slope · Equivocation · argumentum verbosium
Distribution fallacies   Fallacy of composition · Fallacy of division
Data mining   Cherry picking · Accident fallacy · Spotlight fallacy · Hasty generalization · Special pleading
Causation fallacies   Post hoc ergo propter hoc · Retrospective determinism · Suppressed correlative · Wrong direction
Ontological fallacies   Fallacy of reification · Pathetic fallacy · Loki's Wager
v · d False relevance
Appeals   Appeal to authority · Appeal to consequences · Appeal to emotion · Appeal to motive · Appeal to novelty · Appeal to tradition · Appeal to pity · Appeal to popularity · Appeal to poverty · Appeal to spite · Appeal to wealth · Sentimental fallacy · Argumentum ad baculum
Ad hominem   Ad hominem abusive · Reductio ad Hitlerum · Judgmental language · Straw man · Tu quoque · Poisoning the well
Genetic Fallacies   Genetic fallacy · Association fallacy · Appeal to tradition · Texas sharpshooter fallacy