Modus Tollens Conundrum

A Random Interesting Conundrum……

P1: If a modus tollens argument has true premises, then it is sound. P2: The argument is unsound C: Therefore, its premises are false.

(The above argument is not my own, but was taken from some internet site ages ago when I was looking up random stuff. Unfortunately I can’t remember which site, but I suspect that it was from Wikipedia.)

What is going on here?

Modus Tollens arguments are deductively valid. So for the argument above to be sound, then the premises must be true.

P2 is true, if the argument is unsound. But for the argument to be unsound then (since it is presumably valid), one of the premises must be false.

P1 is true (seemingly).

P2 cannot be false since, for it to be false the argument must be sound. But the argument cannot be sound whilst P2 is false. Hence it is logically impossible for P2 to be false. So, P2 must be true.

If the premises are true and the argument is deductively valid, then the truth of the conclusion should be guaranteed. But C is seemingly false.

How intriguing! Does anyone have any thoughts? Is this just a version of the liar or does it involve additional issues?

Cool - My first edit! Emily Bye

[[green It’s a very nice argument. I think it’s a version of the liar and doesn’t involve any additional issues. I wonder whether there’s a simple definition of what counts as a version of the liar and what doesn’t. Not sure.

This has made me think about classifying paradoxes in general. I guess the most important issue is the one you’ve already raised: does paradox A raise new issues over and above those raised by paradox B? (And in this case I think it probably doesn’t … although I’m not a professional logician, so I might ask around about this.)

I expect that a few things have been written on classifying paradoxes. The only one I know that says anything non-obvious is Graham Priest, Beyond the Limits of Thought, which you can get in the library: ]] {[blue SS&H B C 199L 54 P75 1995 ]}. Jason

Ps. How do you do colors?

{[orange Here’s ]} {[red how ]} {[olive you ]} {[blue do ]} {[pink colours ]}. {[green Edit this page to see how I did that, and/or see the link on the right called “Instructions” for more details. ]}