How come these instances of modus tollens seem so weird?
January 23, 2013 8:23 AM Subscribe
Basic logic question. The validity of modus tollens is intuitive when the antecedent and consequent in the first conditional premise aren't negative statements. But whenever the argument begins with something like "If not-p, then q", the whole thing seems less intuitive to me. Can someone explain to my very rusty brain why those instances of modus tollens are still valid?
posted by Beardman to Religion & Philosophy (16 answers total) 4 users marked this as a favorite
I don't have any trouble with arguments that assume the generic form of modus tollens:
If you’re murdered, you’re dead. (If p, then q.)
You’re not dead. (Not q.)
So you’re not murdered. (So not p.)
But this seems weirder, even though it's still modus tollens (correct?):
If you’re not murdered, then you’re alive. (If not-p, then q.)
But you’re not alive. (Not q.)
So you’re murdered. (So p.)
If you’re not a racist, you like Jim. (If not-p, then q.)
But you don’t like Jim. (Not q.)
So you’re a racist. (So p.)
Any thoughts on why the validity of 2 and 3 isn't as apparent? (In each of them, my brain starts tossing out other ways you could have died, other reasons you might not like Jim...) Would translating them into sentences about necessary and sufficient conditions help?