Thursday, 17 April 2014

Critical Thinking 9: Denying the Antecedent

Higher Philosophy Podcast
Critical Thinking: Denying the Antecedent

This is available as an MP3 or to download as a podcast through iTunes
for Desktop and Apple devices, as well as PodcastHD for Android Devices.

Consider the following:

If Frodo is a Hobbit then he has hairy feet, Frodo is not a Hobbit, so no hairy feet for him.

Reconstruction of the argument reveals its invalidity:

P1      If Frodo is a Hobbit (P) then he has hairy feet (Q).
P2      Frodo is not a Hobbit (not-Q).
C        Frodo does not have hairy feet (not-P).

We can see that the argument is invalid. Again every Hobbit may have hairy feet but the argument does not establish that only Hobbits have hairy feet. We can imagine another creature with hairy feet. As we refer to P as the arguments antecedent and the second premise denies this the fallacies title is denying the antecedent. Therefor the structure P→Q,not-P∴not-Q is both invalid and a formal fallacy.

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