I finally got my internet connection back up at home now. Turns out I had a bad cable out on the side of the appartment building. Now all I have to do is get to the backlog of super interesting comments! I hope I’ll have some time to do that this weekend.
In the meantime here is something I was puzzeling about today. Consider the following argument
If P then P
So, not P
Is this a valid argument? That would depend on whether it is an instance of modus tollens or denying the antecedent; but how can we tell which one it is an instance of? We have the same problem for modus ponens and asserting the consequent.
If P then P
So what are we supposed to say about this? I suppose one could deny ‘p –> p’ since it is equivelent to the law of the excluded middle (~p v p) and there are those who would deny that it is true but that doesn’t seem to solve the problem. We still won’t be able to tell what argument form this is an instance of and so can’t know if it is valid or not. But if that is the case then we may be commiting a fallacy when we infer that a sentence must be true because its negation can’t be true and that would mean that reductio arguments have a deep problem.
So, any thgoughts on whether these are valid arguments or not?