Beware arguments from possibility

by cousin_it1 min read3rd Feb 201814 comments



For any claim X, exactly one of these is true:

1) X is possible - compatible with the evidence so far.

2) X is impossible - there's a contradiction between X and the evidence so far.

That means asserting the possibility of something is harder than you think. For example, if Bob says: "Epiphenomenalism is possible, therefore <far reaching conclusions>"

Wait, Bob, did you just say it's impossible to find a contradiction between epiphenomenalism and anything else you know? That's an awfully strong claim! You got any evidence?

Bob pulls back: "I meant only that X sounds plausible to me." But that's a fact about Bob's limits of reasoning, it doesn't support the far-reaching conclusions anymore. For that you need to justify (1) over (2), not just assert it.

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I'm in two minds about this.

On the one hand: yes, there's a philosophical failure mode where someone says "X is possible" meaning only that X seems plausible, and then draws far-reaching conclusions that would only follow from a much stronger notion of possibility. (Arguments from the alleged possibility of "philosophical zombies" are typically like this, for instance.)

On the other hand: prima facie, saying "X is impossible" is also an awfully strong claim: it means there's no, er, possible way to reconcile X with the other things we know. And I'm not sure both P and ~P can rightly be regarded as very strong claims in the relevant sense. I think Bob's feeling that X is plausible is evidence that X is possible, albeit sometimes very weak evidence, and in many cases there's an implicit (and not terribly bad) argument along the following lines: "For X to be actually impossible, there would need to be an actual logical contradiction between X and the other stuff we know, and there obviously isn't because there's too much vagueness in both X and the other stuff we know for a watertight argument to be available."

As we get smarter, it often turns out that past evidence wasn't in fact vague, and watertight arguments were available all along. So it seems wrong to make positive claims because the evidence looks vague to us now.

"possible" in this usage is always a fact about Bob (or whoever), and supports whatever conclusions in Bob's mind to the degree that Bob is correct.

Keep in mind that "evidence" is what you know on your map, not what's true in the territory. "the evidence" doesn't exist in an objective shared pool of observations, each agent has a set of evidence they use to form beliefs. "possible" in this sense, like "probability", is a statement about one's knowledge, not about the universe.

There are other uses of the word which mean closer to "a configuration of the universe that's reachable from the current state", but we probably can never access that level of truth.

Yeah, my post talks about possibility w.r.t. a shared set of scientific evidence.

I think you're holding Bob to an impossible standard. When you say things like " it's impossible to find a contradiction between epiphenomenalism and everything else we know ", you're implying that Bob is overreaching unless he knows and indexes "everything else we know". Bob's description of plausible (compatible with everything I know, and with everything you can point out to me that I should know) seems closer to a reasonable colloquial use of "possible".

I'd still want to see some actual arguments that X is compatible with A, B, C etc. before accepting Bob's far reaching conclusions.

Of course. Neither you nor Bob is rational enough to just invoke Aumann agree. Arguments and explanations about HOW it's compatible with A, B, and C are necessary for you to understand why he claims something is possible. But remember that arguments aren't evidence - that's just bob helping you rearrange your knowledge, not new knowledge. It doesn't change whether something is "possible" for him, or whether it's "possible" in the world, only whether it's "possible" for you.

Thinking more about this, I think I'd rather use "plausable" than "possible" when talking about beliefs and evidence. It's more accurate and doesn't carry an implication of objective truth. So arguments and explanations don't change plausability for Bob (unless you present arguments showing incompatibility), they change it for you, and have zero impact on physical possibility.

I remember hearing an anecdote about a philosopher making this kind of argument for intuitionistic logic: you can think about dropping the law of excluded middle, therefore the law must not hold universally; after all, logic is about our thoughts themselves, and whatever logic governs thoughts about the possiblity of discarding the law of excluded middle must not include the law, if it is taking the hypothesis seriously. Therefore, the law of excluded middle is no law at all.

If this way of arguing worked, you could discard any law of logic you could name.

In my math school we called it "proof by lack of contradiction": assume X is true, we haven't reached a contradiction, therefore X.

Moved to frontpage.

did you just say it's impossible to find a contradiction starting with <...>?

Isn't this often trivially true though? Such claims are called unfalsifiable. To the contrary of your point, Bob is wrong because it is impossible to find a contradiction, not because it might in fact be possible.

I don't think epiphenomenalism is unfalsifiable.

Note that I explicitly removed the word "epiphenomenalism" from my quote, because I didn't want to make claims about it. My point was that if you started with the assumption that X is unfalsifiable and derived that Y is true, then I don't care about Y.

Where did your other comment go? I think it was a more accurate counter to my point.

Ah, ok. I changed it because I thought I misread you.

Anyway, yeah, if Bob has a valid argument against (2) - if he can prove that X is compatible with all evidence so far - that seems useful and non-vacuous to me. I've edited the post to make this clearer.