Illicit conversion

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Illicit conversion, or Affirming the consequent is the logical fallacy caused by the inversion of the subject and predicate in a proposition.

No P are Q.
Therefore, no Q are P.

The faulty logic which often leads to this fallacy goes something like: No dogs are cats, therefore no cats are dogs. While the conclusion is true, the premise does not necessarily lead to it. More often this will apply to something that happens to be observed now but does not apply to a condition: There is no metal in the air, therefore nothing in the air is metal. An airplane proves this conclusion false, there is nothing about being in the air that prevents an object from being metal. No cars are seven legged, therefore nothing with seven legs is a car. There is nothing about having seven legs that prevents an object from being a car.

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