Wednesday, May 19, 2010

A Few Thoughts On Logical Fallibilism

Imagine that Aristotle had had Graham Priest's position that some (but not all) contradictions are true, and the first big treatise suggesting the impossibility of true contradictions wasn't published until 1987. Largely unquestioned academic orthodoxy held that some contradictions are true, mainstream probability theory reflected this assumption and so on. Everyone taking introductory logic classes slaved through the construction of long truth tables reflecting the three options T, F and B (for "Both"). The instructor might devote perhaps five minutes to illustrating the possibility of "Both" with a Liar sentence. Doubtless some Beginning Logic and Intro to Philosophy students would find it all a bit confusing--"how can it be *both* true and false?"--and smug TAs would sit around the bar and trade snotty jokes about the inability of undergraduates to understand basic logic.

Surely, nothing about the world described in the last paragraph is, y'know, impossible or unimaginable. (Nothing about the truth of orthodox ideas about logic makes it impossible or unimaginable for most people to be wrong about them. If you think that there are no true contradictions or truth-value gaps, etc., classical logic is the One True Logic and so on, you therefore think that in the actual world some actual people *are* mistaken about these matters. It's hard to see what possible basis there could be for arguing that it would have been impossible for things to be the mirror image of the way they are, and for the mistaken opinions to be the overwhelmingly popular ones.) Equally surely, from our perspective as residents of the actual world, we can all agree that it would be rational for denizens of the possible world in question to take that 1987 polemic against the possibility of true contradictions seriously, to (at the very least) seriously weigh the arguments and have a serious debate whether or not they should abandon dialetheist orthodoxy. After all, in the actual world, everyone with a position on the subject either thinks that (a) it's completely obvious that true contradictions are impossible, or that (b) far from being trivially obvious one way or the other, there's an interesting and important philosophical debate to be had on the matter. (No actual dialetheist that I'm aware of thinks that the existence of true contradictions is too obvious for it to be worth arguing about it.) If you have position (a), presumably you think that it would be rational for people in the possible world described above to question their belief in true contradictions. If you have position (b) in the actual world, presumably you'd advise the same position to people in the possible world where the debate was being held with a different balance of forces.

For (some) people with position (a), though, contemplation of the hypothetical might raise some sticky problems. After all, some people with position (a) brush off the very notion of taking the debate about these matters seriously by saying things like...

"You need logic to argue about logic. The very idea of arguing about it is ridiculous."

or

"What could be more basic than logical truths on the basis of which you could argue for them?"

or

"The denial of obvious logical truths is so nonsensical that I really don't care if I am begging the question."

Etc., etc., etc. I've heard variations on all of the above many times over the last couple of years of writing and thinking about dialetheism, and there are some famous and well-respected philosophers who've written sophisticated variations on the theme. For example, in a famous response to an invitation to contribute an essay to an anthology debating the Law of Non-Contradiction, David Lewis wrote:

"I’m sorry; I decline… My feeling is that since this debate instantly reaches deadlock, there’s really nothing much to say about it. To conduct a debate, one needs common ground; principles in dispute cannot of course fairly be used as common ground; and in this case, the principles not in dispute are so very much less certain than non-contradiction itself that it matters little whether or not a successful defense of non-contradiction could be based on them."

(Lewis, in other words, felt that dialetheism could be refuted with an incredulous stare.)

Now, consider the clearly possible world discussed above where dialetheism was orthodox and the camp that wanted to revise away the view that everyone else considered to be one of the most obvious and basic logical truths that there could be (that there are three possible truth-values that statements fall into, 'true', 'false' and 'both') was a tiny minority. Imagine that the David Lewis counterpart of that world (let's call him Bizarro-Lewis) responded to a similar invitation in the same way. Granted that Bizarro-Lewis' position (that the existence of the third standard truth-value was too obvious and epistemically basic to be debatable) would be *false.* That's not the issue. The question, for those who agree with the Lewissian position in the actual case, is whether Bizarro-Lewis' dogmatic refusal to even consider the opposition's arguments would be in some way irrational or unreasonable? (Rationality is, obviously, distinct from success. The history of science is littered with theories that we would now all agree are false, despite the fact that we would all agree that belief in them was, at one time, rationally justified.) If not, if the Bizarro-Lewissian position would be rational, does that mean that the philosophical community of that world would be entitled to remain in blissful ignorance of the truth of these matters, never learning better because they never seriously engaged with the debate? That seems like an....odd...position to take.

It's one that, however, it's terribly hard to see how actual-world Lewissians can avoid. If anyone can explain why we (orthodox logicians in the actual world) are justified in being dogmatically unwilling to engage in debate with dialetheists, whereas they (Bizarro-Lewissians) would *not* be justified in being similarly dogmatically unwilling to engage in debate with the dissenters of their world (who correctly deny the possibility of true contradictions), I'd like to hear it. My suspicion, however, is that any remotely satisfying answer to that question* would amount to a substantive defense of the truth of the Law of Non-Contradiction....

....or, in other words, it would amount to a contribution to the debate.



*"Any remotely satisfying answer" means, at the very least, "any answer which was such that the Bizarro-Lewissian couldn't easily offer up its exact mirror image as an answer to the mirror image question."

8 comments:

Emil said...

Very interesting. One should almost think that you are a dialetheist. But your thesis was a defense of monoaletheism, right? Maybe you are both a dialetheist and monoaletheist. :)

Also, what is the source of the Lewis quote?

Ben said...

Nah. I'm definitely not a dialetheist. My dissertation was indeed a defense of monaletheism and classical logic.

But, as far as the topic of the post, if I wasn't in the (b) camp--if I didn't think there was an interesting, tricky and not entirely obvious philosophical debate to be had about all this--I wouldn't have bothered to spend two years writing a 266-page response to the case for dialetheism.

Lewis Powell said...

I think the incredulous stare line is an unfair criticism of Lewis's position. Taking the quote piecemeal:

"I’m sorry; I decline… My feeling is that since this debate instantly reaches deadlock, there’s really nothing much to say about it."
I take this part of the quote to stress a perceived futility to the debate. Presumably, Lewis would have thought those who deny LNC should feel similarly: if it is utterly futile to engage in debate as to whether LNC, then it would be foolish for parties on either side of the issue to debate.
I am not sure I am in agreement with Lewis on the complete futility of the debate here, but it seems like the basic consideration, if applicable on one side would also be applicable on the other.


"To conduct a debate, one needs common ground; principles in dispute cannot of course fairly be used as common ground;"
This is a substantive (though sensible) position on some necessary conditions for engaging in debate, and, again, seems neutral between the two sides of any given debate (excepting, perhaps, debates about whether disputed principles may be fairly used in the common ground).

"and in this case, the principles not in dispute are so very much less certain than non-contradiction itself that it matters little whether or not a successful defense of non-contradiction could be based on them."
Note that, since Lewis does not deny that there are some principles constituting a common ground between proponents and deniers of LNC, he is not suggesting that it is impossible for them to engage in debate. Rather, Lewis is claiming that any such debate would be futile. Presumably, it is futile because (according to Lewis) defenders of LNC would more readily abandon every element of that common ground than give up LNC.

This is probably the part of Lewis's claim that is most apt for an asymmetry. At least, in the actual world, the relevant asymmetry seems likely: Dialetheists probably do not actually take ~LNC to be more certain than all of the elements of the common ground they share with defenders of LNC. It is also plausible that even in a world where Dialetheism is orthodoxy, the denial of LNC is not enshrined as an irrefutable law of logic (for instance, it is existential rather than universal, and the relevant instances are "weird" edge cases).

Not sure this answers your challenge, but I'm also not sure how critical it is to answer, since differences would have to be a lot greater between this world and the world in your suppositional for ~LNC to be the entrenched orthodox position.

Emil said...

"Presumably, it is futile because (according to Lewis) defenders of LNC would more readily abandon every element of that common ground than give up LNC."

That seems highly questionable. Ben, would you really give up any other belief to maintain LNC? That would not be rational.

Ben said...

Lewis,

"it seems like the basic consideration, if applicable on one side would also be applicable on the other."

Right. To my mind, this is the nub of the problem. If Lewis is right (and I see no reason to suppose that he is, and excellent reason to suppose that he isn't, particularly given the actual state of the thriving debate that exists on the LNC, an interesting literature that most definitely does not immediately reach deadlock), it seems like no possible rational procedure could help undecided people make up their minds about this issue. Certainly, Lewis' rightness wouldn't give any aid and comfort to the classical logician.

"Presumably, it is futile because (according to Lewis) defenders of LNC would more readily abandon every element of that common ground than give up LNC."

I don't know if Lewis thought that, but if so, it doesn't seem terribly plausible. Personally, I defend the LNC, but I certainly wouldn't dogmatically hold onto it come what may, no matter what evidence and arguments I was presented with. I'm far from alone in that, so it's definitely not true of *all* defenders of the LNC. The question, I guess, is whether it's true of all defenders of the LNC with the rationally correct attitude or some such. Even there, though, I don't see even the prima facie case for thinking so. For example, intuitively, it's not obvious why, if one were to be convinced that the only way to hold onto the LNC was to jettison a number of other equally obvious-seeming logical principles (e.g. Excluded Middle, Identity), we should favor the LNC at the expense of the others.

"It is also plausible that even in a world where Dialetheism is orthodoxy, the denial of LNC is not enshrined as an irrefutable law of logic (for instance, it is existential rather than universal, and the relevant instances are "weird" edge cases)."

Well, I don't know that the LNC is enshrined as an "irrefutable" law of logic in our world. Certainly, given the influence of Quine's universal revisability thesis on mainstream philosophy in the last several decades, any tradition that holds the LNC as irrefutable at least has serious competition these days. That said, it is widely viewed as too obvious to bother worrying about, and it's not clear why, if the balance of power were reversed and people were trained from their first logic class to fill out dialetheist truth tables, etc., the situation shouldn't be reversed.

Certainly, the position of most major actually existing dialetheists (Priest, Beall), is that the existence of true contradictions is an analytic truth, the truth value of e.g. Liar sentences determined by the logical rules regulating the meaning of the terms. Now, even among those who believe that there is such a thing as "analytic truth" (and I'm not one of them), opinions vary about whether analyticity implies irrefutability in some sense, but I'm sure that in a world where dialetheists were in the vast majority, quite a few would take the "analytic truths are irrefutable" line. The question, as with our world, would be whether that's a terribly rational stance.

"Not sure this answers your challenge, but I'm also not sure how critical it is to answer, since differences would have to be a lot greater between this world and the world in your suppositional for ~LNC to be the entrenched orthodox position."

Really?

Why?

Are introductory classrooms or departmental meetings that different in the places in Australia where dialetheists are a dominant element of the local philosophical scene than they are over here that it would be that difficult to imagine them being the norm, but damn near everything else was the same? Which large things do you think would have to be different, and why, for this fairly obscure esoteric philosophical issue to be thought about different by most of the profession?

Lewis Powell said...

"Are introductory classrooms or departmental meetings that different in the places in Australia where dialetheists are a dominant element of the local philosophical scene than they are over here that it would be that difficult to imagine them being the norm, but damn near everything else was the same? Which large things do you think would have to be different, and why, for this fairly obscure esoteric philosophical issue to be thought about different by most of the profession?"

First a few questions: Is dialetheism actually the dominant antipodean position, or is it just the position of a sizable minority there? If they are dominant, is that dominance among logicians only, or among philosophers generally?

To address your question: I think it is a non-accidental feature of many philosophical projects that are classified as "naturalist" or "empiricist" that they enshrine LNC in fundamental assumptions about the nature of belief or about the assignment of content to given mental states. Hume's position was that it is impossible to believe a contradiction, and Lewis/Stalnaker possible worlds framework pretty much hard-codes something like logical consistency in the possible objects of belief. Now, it may be that these are not good assumptions, or that they should be called into question (after all, some dialetheists at least purport to believe some contradictions), but it strikes me as reflecting a deep entrenchment of LNC among philosophers with strong empiricist/naturalist tendencies.

Of course, all I wanted to suggest was that it may not be that one's position on LNC can plausibly be excised and reversed independent of other substantive alterations to one's outlook (and thus, that we might not be very good at imagining what the world would be like in which dialetheism was taken for granted).

Ben said...

Lewis,

"I think it is a non-accidental feature of many philosophical projects that are classified as "naturalist" or "empiricist" that they enshrine LNC in fundamental assumptions about the nature of belief or about the assignment of content to given mental states."

Do you think this is more true of naturalists and empiricists than it is of their philosophical opponents? That seems backwards to me.

I mean, yes, although Lewis always seemed like the opposite of an empiricist to me, what with his claimed armchair discovery of spatio-temmporally existing worlds, it's certainly true that some people who could be called naturalists or empiricists say things like "it's impossible to believe a contradiction." Then again, so does Kant.

Certainly, something like foundationalism seems to be the epistemic position from which it makes the most sense to hold logical claims totally immune from the possibility of revision--think about Bonjour's claim that we know the truth of such claims from "transcendent rational intuitions," not arguments--whereas the corner of the philosophical world where people have, in the last few decades, been most open to at least the in-principle revisability of logical principles has been naturalism of the Quinean flavor.

Ben said...

OK. That said....

""

....is an excellent point. I was probably (at least implicitly) overstating the case like crazy.

Actually, the more I think about this, I think the way the discussion has drifted on both our parts might really be pretty orthogonal to the original point.

Let's say that the most likely and plausible scenarios for dialetheism being an academic orthodoxy involve a lot of other things being very different than they actually are. Granted that. Still, would you concede that there are possible worlds--maybe, in some sense, very different ones, ones that our world was very unlikely to happen to turn out like--where dialetheism is orthodox, but just about nothing else is different?