Monday, January 25, 2010

Dialetheism and Scientific Reasoning

As paraconsistentists of all stripes are fond of pointing out, historically well-accepted scientific theories have often entailed various inconsistencies. There seems to be some sense of “accept” in which working scientists are often willing to accept implicitly inconsistent theories (or pairs of mutually inconsistent theories, like classical formulations of relativistic and quantum physics) while they search for consistent alternatives. Partisans of what one can call “paraconsistency-lite”—the view that classical logic is wrong in holding that everything follows from every contradiction, but not because this “explosion” of inferences has true counter-examples (i.e. not because any contradictions are true)—are particularly fond of these sorts of examples. After all, by their lights, the scientists’ attitude is exactly the rationally correct one: accept the inconsistency, don’t accept triviality, and don’t lose sight of the fact that the inconsistent theory you’ve provisionally accepted must ultimately be wrong, because contradictions are never true. People who, for example, accepted Bohr’s theory of the atom in the formulation that relied on Maxwell’s equations, were, implicitly and without having the logical formalism to explain why they were right, proto-paraconsistentists.

Or so goes the argument. I have a lot of issues with the whole line of thought, not least of which is the fact that, while I’m as naturalistic in my epistemic stance as the next guy (actually, in my Department, I tend to be way more naturalism-friendly than the next guy), I think that this sort of thing tends to devolve into a sort of exaggerated hyper-naturalism where the empirical sciences are taken not just as pretty good tools for getting to the truth in the long run, but as nearly flawless paragons of rationality in all of their day-to-day epistemic practices—the speed at which the scientific community actually arrives at a conclusion must be the correct speed, etc. There’s a lot to be said about this—I’ve blogged here about these sorts of “retroactive implicit paraconsistency” arguments more than once before, and I certainly will again—but right now I want to focus on another subject entirely.

From the perspective of the paraconsistency-lite crowd, the attitude of those scientists willing to temporarily swallow inconsistency while looking for the right theories (which they assume must be consistent) makes perfect sense, but what about dialetheism? (To switch from beer to cigarettes, we can think of the views we’ve been discussing as Paraconsistency Lights and dialetheist positions as Paraconsistency Reds.) I’ve read many passages in which Graham Priest basically makes the classical Paraconsistency Lights argument and leaves at that, but only one where he makes the obvious Paraconsistency Reds twist on it.

It comes on pp. 149-150 of my edition of Doubt Truth To Be A Liar:

“It is here that the impact of paraconsistent logic is revisionary—indeed, revolutionary. The Law of Non-Contradiction has been well-entrenched in Western thought—and so science—since the canonization of Aristotle, whose defence of the Law has rarely been challenged. Hence, scientists and philosophers have not been prepared to brook the thought that an inconsistent theory of any kind might be true. But subscribing to the law is not rationally mandatory, as I argued in Chapter 7, and as the development of paraconsistent logics has played a large role in showing. Once this fact is digested, scientists may—justifiably—take a different attitude to inconsistent theories of the appropriate kind. Indeed, they may even develop inconsistent theories, if these have the right empirical consequences, just as paraconsistent logicians have developed inconsistent theories of semantics to handle the paradoxes of self-references.”

…and that’s pretty much all he has to say about it. (To be fair, in a couple of other places in DBTL he gives a couple of hypothetical examples of ways this might happen, but this is pretty much what he has to say on the epistemic issue.) So, to sum up:

(1) Scientists have been in the thrall of the Aristotelian dogma of non-contradiction, which explains their bias that inconsistent theories can never be true, but
(2) Philosophical work on the self-references paradoxes, the development of inconsistency-tolerant formalisms, etc., shows us that this dogma should be rejected, so
(3) Now, one hopes, they'll start being less dogmatic.

This is certainly a far cry from the extreme deference to scientific practice you tend to get with the paraconsistency-lite foks, and it raises a lot of strange and awkward questions. Given that, as his less radical comrades are always pointing out, temporary inconsistency is not that rare a situation in the history of science, and that these are presumably situations where inconsistency is pulling in one direction (showing that the theory must be false) but happy empirical consequences are pulling in the other (giving the scientific community good reason to continue to provisionally accept the theories in question), what sort of retroactive advice should someone who agrees with Priest give scientists in this position? What scientific progress would have been lost by researchers agreeing with Priest, and what future progress would be lost if the contemporary scientific community were to be won over to his position?

To switch gears for a second, consider a traditional criticism that defenders of neo-Darwinian biological orthodoxy level against “Intelligent Design” creationists: that, if their views were generally adopted, researchers would be content to put God in the gaps in their understanding, and future explanatory progress would be stunted.

Now, here’s my question for readers more sympathetic to dialetheism than I am:

Does an analogous criticism apply to what Priest is advocating here? If not, why not? What’s the difference?

Certainly, as a sociological matter, most dialetheists are atheists (although, as I’ve mentioned before, I think that the appropriation of dialetheism by at least some philosophically aware Christian theologians is a historical inevitability), so part of their answer here might just be that there is no good reason to believe that God exists (the central philosophical arguments for God all being fairly spectacularly unconvincing), whereas the paradoxes of self-reference do give us good reason to believe in true contradictions.

Fair enough. If so, though, how about the counterfactual? If there were a good, convincing argument for the existence of God (e.g. some bright young grad student at Notre Dame came up with an absolutely unanswerable re-formulation of the Ontological Argument), would Intelligent Design theory be a rationally acceptable option for biological science, or would the stunting-future-inquiry objection still be a good one, and as such would the stance of those theologically liberal Christians who accept God but categorically reject ID be the right one? If so, is there an epistemically relevant difference between the ID creationist’s suggestion that gaps in our understanding should at least sometimes simply be accepted as evidence of divine intervention and Priest’s suggestion that inconsistent theories should at least sometimes not just be provisionally accepted while everyone assumes they can’t possibly be true and tries to find a consistent alternative, but actually accepted as true? If so, what is it?

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