Tuesday, August 31, 2004

So Many Possibilities...

What's really possible? I'm deeply confused by modality - though whether that's due to the subject's intrinsic incoherence, or simply my ignorance, I'm not sure. So I'll ramble about it a bit here to try to sort my thoughts out, and hopefully someone a bit more knowledgable can leave a comment and help me out.

Here's my current position: modal notions (i.e. possibility versus necessity) cannot be applied simpliciter. Instead, they need to be assessed against some background framework of stipulated limitations. Some examples would be:
  • Epistemic possibility - Whether a state of affairs is consistent with our current state of knowledge.

  • Physical possibility - Whether something contradicts our actual (practical) physical capabilities and such. E.g. it is physically impossible for a human to run a mile in ten seconds.

  • Natural possibility - Whether something contradicts the 'natural laws' (or laws of physics) that govern our universe. E.g. travelling faster than light is impossible in this sense.

  • Logical possibility - Whether something is logically consistent. E.g. it is logically impossible for my cat to be both alive and not alive (at the same time).

One might also extend this template to interpret deontic possibility (or rather, permissibility) in terms of what is consistent with (or allowed by) some particular set of rules - e.g. a moral or legal code.

But what about metaphysical possibility? What's really possible? What could have existed? I don't think we can answer this question. I'm not even sure if it's asking anything meaningful.

Some might equate metaphysical possibility with what people can imagine or conceive of. But conceivability merely tells us about the limits of human cognition, and doesn't necessarily imply anything deeper about the possible nature of reality. I have difficulty conceiving that time and simultaneity could be relative, not absolute. Yet this is not only possible, but indeed true!

Others might simply equate metaphysical with logical possibility. But I'm not sure that this is justified either. After all, what reason is there to think that logical impossibilities are metaphysically impossible? We cannot conceive of them, sure, they seem "absurd". But, as suggested above, this cannot be reason enough.

Besides, it might (this is an epistemic 'might') be the case that some logical contradictions are in fact true. [Update: I reconsider and indeed retract this claim, here.] Quantum physics is the most serious contender here (did the photon go through the left slot or the right? Is Schrodinger's cat dead or alive?). Some also argue that the Liar's Paradox is best understood as being both true and false. If we adopt a paraconsistent (rather than classical) logic, then this is not a disastrous result.

And this then brings up another reason for doubt: namely, that there are many different logics! "Logical possibility" is (I think?) bound by classical logic. But there's no reason to think that reality is, when there are so many alternatives to choose from. For those who think it "obvious", and the alternatives "absurd", the fall of Euclidean geometry provides a handy precedent. For centuries, mathematicians and philosophers thought that Euclidean geometry was "absolute truth". But in actual fact, it merely applies to flat planar surfaces, and if we instead consider curved surfaces, then non-Euclidean geometries (complete with different laws and a priori 'truths') result. So although people in the past took it as a necessary truth that exactly one line can be drawn through a point, such that this new line is parallel to some other given line, in actual fact this axiom isn't even always contingently true!

Don't get me wrong, I think the idea of "possible worlds" can be a useful heuristic. But if they're merely defined by logical possibility, rather than metaphysical possibility, then we should be clear on that. For example, the usually-sharp Maverick Philosopher attempted to refute the idea that laws of logic are empirical generalisations (and hence only contingently true), by equating contingency with logical contingency. But of course this is quite blatantly question-begging. Of course if you assume that metaphysical possibility simply is (or implies) logical possibility, then the laws of logic are necessary and not merely contingent. He reached the conclusion by (implicitly) assuming it as a premise, which is a rather cheap (and unconvincing) move. [Update: see here and here for more detail.]

To change tack slightly, I was also struck by the problem of (categorical) possibility when writing my essay on Van Inwagen & Free Will. For if determinism is true, then given the current state of affairs and the laws of nature, there is only one categorically possible future. And that seems to be an awfully limited understanding of possibility! Indeed, even if we ignore determinism, the fatalist's "argument from truth" would seem to establish this categorical uniqueness.

The Fatalist's Argument From Truth:
1) Let E be any event that occurs in the future
2) Then, the proposition that E will occur is true.
3) So, nobody can bring it about that E does not occur.
4) That is, E is inevitable.

In my essay above, I argued that adopting a categorical notion of 'could' (i.e. possibility) commits one to the soundness of this absurd fatalist argument. After all, one presumably could not (categorically) bring about a logically inconsistent state of affairs.

I conclude, then, that categorical possibility is so empty as to be effectively meaningless - we are better off adopting a hypothetical understanding of choice and modality.

Modal notions seem to arise from a certain sort of counter-factual thinking. We establish some particular limitations, and then we consider what states of affairs are allowed within our chosen framework. But divorced of any such framework, modal notions strike me as meaningless. If you take away the limitations, then we're stuck with the empty truism: "anything is possible".

Am I missing something here?


  1. "But divorced of any such framework, modal notions strike me as meaningless."

    Exactly! What if you extend this idea beyond the discussion of possibility? What if you consider the limitations that are imposed in order to make any sense out of assertoric claims or truth evaluation?

    This is what I have attempted in my post. I agree with the logic of your argument, I’m not sure how far along the relativist chain you have travelled thus far.

    I intend to develop the idea further by suggesting that we have no access to a noumenal reality where truth claims might be assessed, instead we have a phenomenal reality which is made up of raw sense data which in itself is incomprehensible and conceptual thinking which actively interprets this sense data and constructs the ‘knowable’ reality as it occurs to us. If concepts necessarily dependent upon language, then we might inquire further in the role language plays in interpreting the sense data and constructing reality.

    If I can show this, then it makes sense that someone embedded in the language of classical logic would perhaps be entirely restricted from entertaining this view of possibility and reality… 

    Posted by Illusive Mind

  2. Richard,
    I don't get what epistemic possibility is. I see it as a combination of some of the other notions of possibility you list along with it. I would say that a claim is epistemically possible (def) if and only if it is logically possible within our most advanced scientific theories, given the (non-law) statements we accept about the actual state of the world. Incidentally, given Heisenberg's uncertainty principle and the use of possible worlds in quantum mechanics, I can't think of something that is epistemically impossible and logically possible (including a person running a ten-second mile, or something travelling faster than light). But maybe you mean something else by "epistemic possibility".
    Second, note that logical possibility is also, in a sense, the kind of absolute framework for possibility that you reject. Granted that there are different logics, which is why I put the "kind of" in the last statement. But as long as we accept some system of logic, we never call anything possible that is logically impossible. The other frameworks for understanding modality that you propose all rest on some sort of previously agreed upon system of logic, with the addition of some non-logical axioms (although again, the non-logical axioms afforded by quantum mechanics don't seem to place any extra-logical restrictions on what is possible). As long as we agree to a system of logic (and, in reality, this is going to be classical logic 99% of the time), for any statement about my physical capacities P, "P and not P" is never going to be possible. Period. You don't need to qualify or relativize that statement to a more specific framework.


Visitors: check my comments policy first.
Non-Blogger users: If the comment form isn't working for you, email me your comment and I can post it on your behalf. (If your comment is too long, first try breaking it into two parts.)