Existential instantiation fallacy { Philosophy Index }

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Existential instantiation fallacy

Existential instantiation fallacy, or more simply the existential fallacy is a logical fallacy, committed by an invalid argument form “All P are Q, All R are P, therefore Some R are Q.”.

The affirming the consequent fallacy may be expressed formally as follows:

∀x(Px → Qx), ∀x(Rx → Px) ∴ ∃x(Rx ∧ Qx)

The fallacy occurs because one assumes that something of the set Rx actually exists.

Existential instantiation fallacy example

All undead creatures have superhuman abilities.
All vampires are undead creatures.
Therefore, there are vampires with superhuman abilities.

The conclusion is sometimes stated as “some vampires have superhuman abilities” but in either case, they take the form ∃x(Rx ∧ Qx), essentially affirming that such a thing exists.

However, even though the premises may be considered to be true on some interperetations, if you consider their definitions, the conclusion is not guaranteed to be true because neither undead creatures nor vampires actually exist.