Sunday, January 27, 2008

Follow-up: "Interesting but Inconsistent?"

While looking at the discussion after my last post--for those who missed it, I made a really dumb attribution mistake that was thankfully corrected, and it was forcefully brought to my attention that my original example relied on an understanding of conditionals deeply controversial among precisely the same sort of people likely to find Impressive Scientist X examples compelling, but I argued that the same point could be made without bringing in the material conditional, and that there are simpler explanations of e.g. Bohr's failure to derive random crazy things from his inconsistent atomic theory than that he was somehow unknowingly working with an "underlying paraconsistent logic"--something closely related occurred to me.

There's a phrase that's used a lot in these discussions as if we all knew what it meant. I'm not sure that it's so clear. That's "interesting but inconsistent theory."

(The phrase "non-trivial," often appended to "interesting but inconsistent," adds bupkis. All it means is that not everything will follow from the theory, i.e. that interesting but inconsistent theories should be reasoned about paraconsistently or not at all. OK. If you believe that the moon is both made of green cheese and not made of green cheese, that theory will be "non-trivial" in precisely the same sense, but I doubt anyone would call it "interesting" in the relevant sense.)

Well, what is an 'interesting' theory? I mean, I think I know what it means before modified with "but inconsistent," but after that's there, I'm not so sure any more. Normally, when talking about consistent theories, I would take "interesting theory" (in the sense that seems to be driven at, not "interesting" as in "crazily unexpected" or anything like that) to mean "plausible theory," i.e. one that might very well turn out to be true. Or, applied to out-dated theories, one that it would have been rational to regard as quite possibly true given the evidence available at the time, even if we now understand that it is false.

Now, full-blown dialetheists banding about the phrase "interesting but inconsistent theory" might mean exactly this, since they think it's possible in principle for something to be inconsistent but true. What I'm interested in at the moment is what this "interesting but inconsistent phrase" means to people who bandy it around who are on the 2nd Grade of Paraconsistent Involvement discussed in the last post, the "I'm not a dialetheist, but..." crowd who are still holding back from the 3rd Grade where you admit that some of these theories may be true.

So, if you aren't a dialetheist, you still believe in the Law of Non-Contradiction, hence you believe that it is categorically impossible for an inconsistent theory to turn out to be true and there has never been a situation where it would have been rational on the basis of any sort of empirical evidence to believe that an inconsistent theory was true, what does "interesting but inconsistent theory" mean?

Interestingness also can't just boil down to a degree of predictive accuracy*, right? If so, interesting-but-inconsistent theories would be too easy to generate and lose the aura of respectability they gain from Bohr-type examples. After all, for any hotly disputed scientific area, where one theory predicts a bunch of effects with a certain amount of experimental support, and an obviously logically inconsistent competitor theory predicts a bunch of other effects, and there are a certain amount of experimental support for those two, if someone blandly asserted that the disputed phenomenon both existed and didn't exist, and was thus able to claim the experimental successes of both competitors for this claim (like, "if X exists, we expect to see some Y's and if it doesn't, we'd expected to see some Z's, so I expect to see both Y's and Z's..."), would that make the new conjunctive theory "interesting"?

Anyway, I'm throwing this open to the floor. On the assumption that it's never rational to believe an inconsistent theory to be actually true, what does it mean to call one 'interesting'?

*...although why we'd be interested in predictive accuracy, except as an indicator of truth, is for the most part mysterious to me.


Daniel Lindquist said...

I suspect that "interesting but inconsistent", in the second grade of paraconsistent involvement, means the same as it does in the third grade -- with the caveat that at the second grade, one says to oneself "But of course an inconsistent theory can't be true!" And so when all of your evidence would lead you to believe that some particular inconsistent theory is true (or at least is a plausible candidate for truth, deserving of further consideration), the second-grade paraconsistentist backs down, and assumes that there has been a mistake somewhere along the line. The inconsistent theory cannot become a real candidate for truth -- it's inconsistent, and that is bad.

Maybe "interesting" means the theory can be a place to build off of -- perhaps the theories which the second-grade paraconsistentist considers as plausible candidates for truth are just the various ways of making the inconsistent theory consistent. And what makes him a paraconsistentist is just that he doesn't think the inconsistent theory is crazy; he doesn't think it logically entails that Graham Priest is a fried egg, or that the moon is made of cheese. He thinks the theory is false, because inconsistent, but he doesn't think it's trivial (=entails everything). (I am not sure if this could ever be a difference which makes a difference -- a partisan of classical logic could also find an inconsistent theory "interesting" in that he tries to find a true theory by making the inconsistent theory consistent. The question of whether the inconsistent theory was trivial (in addition to false) seems to matter not a whit, if this is what "interesting" means. And it seems doubtful that anyone could disagree that there are "interesting and inconsistent" theories in this sense -- Russell's set theory before he discovered the paradox which bears his name, for instance. But then the difference between the second-grade paraconsistentist and the partisan of classical logic is just whether or not we want to call such a theory trivial -- they both handle the theory the same way, in trying to modify it.)

Hrmph. Now I am not sure what the difference between first- and second-grade paraconsistentists can amount to. If one is a first-grade paraconsistentist, then one won't claim that a theory is trivial just because it's inconsistent. (You're right to claim that "non-trivial" in this context adds bupkis. If one doesn't hold that there are non-trivial inconsistent theories, then one holds Explosion valid.) Presumably even non-paraconsistentists hold that there are inconsistent theories. So it looks like the only difference between the first-grade paraconsistentist and the second-grade paraconsistentist is that the second-grade paraconsistentist thinks some of these theories are "interesting" (but they can't be true, or else the second grade would collapse into the third grade).

So, I seem to have covered the same ground which you did in your post, in attempting to answer it: What the devil can "interesting" mean here? (I swear, I thought I had an answer at the start of this comment!). Hrmph again.

This strikes me as perhaps ad hoc, but maybe the answer is that the second grade in Priest's hierarchy just is a really unstable position -- Priest views the landscape from the position of his fourth-grade dialetheism, and maybe he really did describe the lower-grade paraconsistent positions as being a muddled mess. It would not surprise me to find that Priest views the "I'm not a dialetheist, but..." crowd with mild disdain -- from his dialetheic vantage point, they are wafflers in the battle against the (so-called) "law of noncontradiction." And so the earlier grades of paraconsistency are supposed to be bad positions. This would leave mysterious what the "I'm not a dialetheist, but..." crowd take themselves to hold, but I think they are mysterious. I can make sense of the dialetheists, and I can make sense of just thinking Explosion is a violation of relevance, but whatever's supposed to lie between those positions is ??? to me.

Colin Caret said...

I'd assume that 'interesting' in this sense can be given whatever reading you'd prefer from standard variations on this theme in the theory-choice literative predominant in phil. science. For instance, you might think there are a bunch of markers of 'interestingness' such that...

1) theory A is more interesting than theory B if it has greater predictive power

2) theory A is more interesting than theory B if it is less ad hoc

3) theory A is more interesting than theory B if it explains the target phenomenon better

4) theory A is more interesting than theory B if it is simpler

5) theory A is more interesting than theory B if it is more ontologically parsimonious


Ben said...


I think you're probably basically right, but given that some very bright people situate themselves on the "I'm not a dialetheist, but..." second level, I'm willing to grant that its possible that something less muddled than it initially looks like is going on here.

...but ultimately, yeah, I'm agreeing with Priest here that once you've started to climb the paraconsistent-commitment ladder, it might make be harder than it looks to justify the decision to stop climbing halfway up.


Well, sure, but what you're listing off there are theoretical virtues that we use to choose between theories that we think might be true, that in fact are each supported by enough evidence to make it otherwise reasonable to believe that they are true. If you are a non-dialetheist paraconsistentist, way down there on the 2nd Grade, who rejects the possibility of true contradictions and so doesn't think it would be rational to actually believe these theories to be true, what does the interesting-ness then amount to? Is it just a way of saying something like "a theory that, although inconsistent and hence necessarily false, possesses features that, if it weren't inconsistent, would make it rational to believe that it was true?"

Colin Caret said...

"a theory that, although inconsistent and hence necessarily false, possesses features that, if it weren't inconsistent, would make it rational to believe that it was true?"

sure, why not?