Sunday, June 25, 2006

Bootstrapping Possibility as Conceivability

I previously introduced epistemic modality as effectively involving the familiar space of possible worlds under a different mode of presentation. (I hope that's not too misleading a summary; do read the linked post if you're not familiar with it.) This view assumes a plenitude of metaphysical possibilities, which is very plausible but might be denied by some. For example, a theist who holds that God's existence is metaphysically necessary but not a priori thereby admits more epistemic scenarios than he does possible worlds, and so must insist that the two modal spaces are distinct. To accommodate such views, Dave Chalmers (see, e.g., section 5 of his epistemic space paper) describes how we could construct epistemic modal space from purely epistemic notions. Say, P is (deeply) epistemically possible iff P is ideally conceivable (i.e. ~P is not knowable a priori). But what kind of modality is involved in those "ables" (knowable, conceivable)?

Metaphysical modality won't do, since that would defeat the stated purpose. For example, one might hold that ideally rational agents are brutely impossible. But we require such an idealization for this epistemic modality nonetheless. ~P might be a priori even if there is no brute metaphysically possible world containing an agent who a priori knows ~P. So this is not the appropriate sense of "a priori knowable".

Given our independent grasp of apriority (as demonstrated in the previous paragraph), we might simply take as a modal primitive the kind of possibility involved in something's being "a priori knowable". That seems the safest option.

Intriguingly, Chalmers hopes that we might instead be able to take it to be epistemic possibility. This seems circular: P is epistemically possible iff it is not epistemically possible that an agent knows ~P a priori? Where has the idealization gone? Here Chalmers appeals to a kind of "bootstrapping" effect. The core idea is that although we're far from ideal reasoners ourselves, we can conceive of slightly more ideal reasoners, who in turn could conceive of even better reasoners, and so forth, until we reach ideal conceivability.

It's a neat idea, but still seems to rest pretty heavily on an independent primitive modality. We need it to fill out the claim that our imagined reasoners could do better than us, and to let their improved results be sufficiently "real" to contribute to modal reality. If our actual reasoning powers were bedrock, then it's hard to see how we could get beyond them. Second-order possibility (what we imagine our better reasoners could imagine) would seem to revert back to first-order modality, with all our limitations. The bootstrapping effect just can't get off the ground. It needs some independent modal element, so that the imagined agents could do more than we can conceive of them as being capable of.

We could then say that our non-ideal imaginings tap into this irreducible modal reality. It might even be traceable through the kind of bootstrapping procedure described above. Plausibly, we can imagine better reasoners, and they in turn also could imagine better yet, and tracing these conceptions through modal space would eventually map out the full idealization. But the "can" and "could" here presuppose the full idealization, and so cannot be used to reductively construct it. We can find our way to the end point only if we have its help right from the start.

(Disclaimer: I'm not entirely confident that I've understood Dave's position here. When I asked him about it after the conference, he suggested that we might be able to imagine a kind of general "blueprint" for a better reasoner, and that this would suffice to determine -- perhaps through some kind of mathematical necessity -- the stage-2 modal facts, even if the details go beyond what we can grasp in our ground position. So that doesn't sound entirely reductionist in any case. The modal properties of the blueprint must be grounded in something other than our actual epistemic capabilities. *shrug*)

P.S. This is all inspired by the recent Epistemic Modality conference -- Kenny offers a general overview.


  1. I don't know how much 'conceivable' adds to our understanding of this. What one person thinks is inconceivable, another may be able to conceive. Therefore 'inconceivable' may merely reflect a lack of imagination. And saying 'I can't imagine it' doesn't really impose anything onto the actual world. As you suggest, there is always the second-order 'imagined imaginer' who can conceive what we can't.

    I can't really see how 'better reasoners' is relevant to possibility either. Surely the truth and modality of statements are independent of the people making them, unless otherwise specifically stated (and thus not particularly interesting to anyone else).

  2. Yeah, this rests on an idealized notion of conceivability, concerning what can't be ruled out a priori by ideal reasoners. (So to call something "inconceivable" in this sense is stronger than merely claiming that I can't conceive of it. It is also to claim that no-one else could coherently conceive of it either.) The idea, then, is that this idealized notion fixes an interesting space of scenarios: i.e. scenarios which cannot be ruled out a priori. This makes them "live possibilities" in an interesting sense. We make genuine progress when we narrow this epistemic space down further through empirical investigation.

    For example, it isn't clear what we learn about the world when we learn that 2+2=4. There's not really any coherent alternatives that we've ruled out. (Any "alternatives" to this are simply incoherent.) But to learn that water = H2O is to learn something about the world itself: we can now rule out some further scenarios which we previously thought might obtain.

    So that's one rough way of getting at why idealized conceivability is relevant to a potentially interesting sense of (epistemic) possibility.

  3. Aw, I made a huge post on this and it got lost! I must have entered the word ID wrong and closed the window. I even had myself convinced. Never mind, I'll have another crack, since this is an interesting subject.

    I'm still not convinced 'conceivable' adds anything. It's either equivalent to 'can't be proved false logically' (in which case it is no improvement), or it's more restrictive (in which case I can't see that it's an improvement either).

    I suggest it could be more restrictive since the 'bootstrapping' technique doesn't guarantee that we can reach all 'possible statements'. There could be a jump that is not possible by that method, even though there are perfectly possible worlds beyond it.

    In your analogy, I guess I'm saying that *even if* bootstrapping can get us off the ground, there's no guarantee it can take us to the moon. And if we can get to the moon, there's no guarantee we can get to the stars, and if we can get to the stars there's no guarantee that we can get to other galaxies. And we still can't get out of a black hole, but that doesn't make what's in there 'impossible'. It's just 'unknown', and quite possibly 'unknowable'.


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