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

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
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