Logic

If the saying "nothing is impossible" were correct, then wouldn't it be impossible for something to be impossible?

Comments

I also find that saying suspicious, though I'm not sure I accept your suggested argument against it (more on that in a moment). I disagree with the saying because there seem lots of clearly impossible states of afffairs: that 2 and 2 could equal 5; that I could both win and not win the tennis match (in a fixed sense of "win"), and, pehaps more controversially, that I could have had different biological parents than I did. (For more on the different senses of "possible" see Alex George's answer to question 71: Is nothing impossible?) In fact, though, I particularly dislike the saying when people use it to generate false optimism. It is not, alas, possible (in the relevant sense) for me to win the olympic marathon, to be an international multi-billionaire, or to be a wildly successful tabloid heart-throb (well, maybe there's still time for that...). And no snake-oil or course of instruction on the internet will change this, even if the packaging proclaims that everything is possible.

Now to your argument: that if nothing is impossible then it would be impossible for something to be impossible, and that seems implausible. The argument seems plausible, but that's because I think you're construing "impossible for something to be impossible" simply to mean that (or to be true if and only if) nothing is impossible. That's fine, but then the argument doesn't really take you anywhere. And you're better off complaining with me about snake-oil salesmen and objecting directly to the claim that nothing is impossible.

An alternative (and perhaps more natural) way to construe "impossible for something to be impossible" would be that it holds if and only if none of the possible situations relative to us allows that there are impossibilities relative to it. This is a more substantial argument. But if we're allowing that nothing is impossible, then it's unclear why we shouldn't allow that one of the many things that is possible is that there are impossibilities--though, of course, these would not be impossibilities relative to us. This reply only makes sense if we allow generally that we can and should talk of what's possible relative to a given situation, and we allow specifically that what's possibly possible is not always possible (or in this case, that what's possiblly impossible is not always impossible). Philosophers have indeed developed "modal" frameworks and logics that support talking in this way.

Huh? Really? The best example I can think of in which one might apply the type of modal thinking I have in mind is due, I believe, to Nathan Salmon. (I hope I get it right.) My vase is composed right now of a given collection of molecules, call it A. My vase might have been composed of a different collection, B, that contains most of the same molecules as A, in fact just enough so that we still hold that B would compose my vase and not a different vase that looks just like it. Consider a third collection of molecules, C, that contains even fewer of those in A, but more of those in B. If we set things up just right we might well want to say that it's possible that my vase be composed by B, not possible that my vase be composed by C, but nevertheless possible that it be possible that my vase be composed by C, since if my vase were composed of B it would have been possible for it to be composed of C.

I leave it to you or others to judge whether this example works, and whether the modal framework it might motivate plausibly applies to your argument.

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