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Saturday, December 12, 2009

PhilPapers Survey: Classical or Non-Classical Logic?

For me one of the most surprising results in the PhilPapers Survey was the result of the logic question. In the target group 51.5% accept or lean towards classical logic, whereas 15.3% accept or lean towards non-classical logic. For all respondents, the distribution was: 44.3% versus 20.1%. I have seen people around the web say that they were surprised that so many accept or lean towards non-classical logic. So, let me explain why I was surprised that the numbers were not higher for non-classical logic.

First, as many commentators on the web have pointed out, philosophy undergraduate students often mistakenly believe that if you adhere to classical logic, you are required to treat corresponding English expressions accordingly, for example, they believe that you are required to treat the indicative conditional as a material conditional. Sometimes their logic teachers are responsible for inducing this belief in them. In any event, this belief often motivates undergraduate students (and some graduate students) to reject classical logic, or at least it has motivated many of my undergraduate students. What were the numbers, then, for undergraduate students? Hugely different from the target group: 37.3% accept or lean towards classical logic, whereas 26.7% accept or lean towards non-classical. But there is still a majority for classical logic.

Second, and more importantly, I would have thought that the target faculty had interpreted the question: "Logic: classical or non-classical?" as meaning "What do you believe is the correct logic for reasoning?". If you have a consistent premise-set, you will do well if you reason according to classical logic. But if you have an inconsistent belief-set, you will do terribly if you reason according to classical logic. Hence, classical logic cannot be the correct logic for reasoning in general. But perhaps the question was predominantly read as meaning: "What do you believe is the correct logic for reasoning, given a consistent premise set?". And, I am sure there are other more sophisticated ways of reading the question that can explain the attraction of classical logic.

Third, it's surprising that the numbers for the "other" category were so high. When I have talked to people in the target faculty about logic, a fair number have been sympathetic to logical pluralism. A common view is that we cannot narrow down the number of correct logics to one. But the question wasn't about whether or not we can narrow down the number of correct logics to one. The question was about whether classical or non-classical logic is correct in some respect, which was not specified. Perhaps if you are a logical pluralist, you will answer "neither". But even those who are logical pluralists could have read the question as "What do you believe is the correct logic for reasoning given some arbitrarily chosen premise set", in which case "non-classical logic" would have been an appropriate answer.

These are some of the reasons I was surprised by the results for the logic question. I want to raise a different, but not unrelated, point. At first I was very surprised that so many philosophers don't have determinate views about core issues. I think this mostly explains my errors in the metasurvey. But, on second thought, this is probably not what is going on. Rather, what is going on is that most questions have readings that will make a fair number of philosophers with determinate views say "other". The issue came up on the message board on PhilPapers discussing the surveys. David Bourget was surprised by the results for mental content. David Chalmers responded that one could hold that internalism about mental content is correct and yet think that some mental content is wide. But I bet some philosophers who hold the same views as Chalmers answered "other" to the mental content question, for this exact reason. I did not do that myself, but I considered doing it. In fact, for all of the questions, this sort of ambiguity may have explained the high numbers for the "other" category. For example, for the logic question, people might have thought that if they picked "classical", they would rule out the possibility that it sometimes might be preferable to reason in accordance with non-classical logic.

One final point: I have not yet mentioned the growing interest in the logical paradoxes as a factor. The logical paradoxes are sometimes used to motivate non-classical logic. However, it is not obvious to me that a significant number of philosophers take the paradoxes to motivate non-classical logic. Whether the paradoxes do do this is a very interesting and difficult question. It cannot be answered without saying what we mean by "correct logic". Perhaps languages come with a consequence relation. If this is so, then the Liar paradox may well be used to motivate the view that the consequence relation in English is non-classical. But there are lots of other options too. A recent attractive view is that the semantics for English, despite being inconsistent, is classically closed (variations on this view are held by, e.g. Kevin Scharp, Doug Patterson, Kirk Ludwig and Matti Eklund). Personally, I am more attracted to non-classical inconsistency views. I do not think non-classical inconsistency views entail dialetheism. I think one can take English to be inconsistent, closed under a paraconsistent consequence relation, and yet hold that all contradictions are logical falsehoods (but not logical truths). In terms of the "other" category on the survey, I suspect that if the growing interest in the paradoxes had any influence on the results at all, then it would have been in terms of placing more people in the "other" category.


jrshipley said...

"But if you have an inconsistent belief-set, you will do terribly if you reason according to classical logic."

This doesn't seem right to me. Logic is often regarded principally as a tool of inference. Accordingly, one is tempted to think of using it to make inferences from a fixed belief-set. On that picture, sure classic logic causes trouble if the set is inconsistent.

But logic is monotonic: all valid arguments are question-begging. Logic can be as much (and is, in virtue of monotonicity, perhaps more importantly) a tool of analysis as of inference. Thinking in those terms, classical logic simple dictates that the inconsistency needs to be resolved by abandoning at least one belief. I don't see that as "doing terribly". You only do terribly if, after analysis reveals the inconsistency, you go on reasoning classically from the inconsistent beliefs.

Maybe I'm missing the point though.

Aldo Antonelli said...

I thought the question about logic: "classical or non classical?" was just a silly question, as were almost all the other questions about realism etc. I do not know that I hold any specific views about these issues, but am rather more interested in exploring the consequences of adopting a position as opposed to another. Partly for these reasons, I declined to participate in the survey.

Brit Brogaard said...

jrshipley: This is definitely one way to look at it. I am sympathetic to the view that an inconsistent belief set ought to encourage revision rather than reasoning. However, I still think that it is interesting to explore the issue of how one ought to reason given an inconsistent belief set. Certainly one ought not reason in accordance with classical logic. I also think it is highly plausible that the semantics for English is not closed under classical consequence.

Brit Brogaard said...

Aldo: I thought a lot of the questions were informative. Some were easier to interpret than others in the simplistic format in which they were presented, for instance, atheism vs. theism, or Millianism vs. Fregeanism. But it occurred to me after seeing the results that the logic question was particular hard to interpret, because it is not clear what it means to accept classical logic vs. non-classical logic. Of course, you are right that exploring the consequences of adopting a position as opposed to another is where the hard work lies.

Gregory Wheeler said...

I was glad to see this post pop up in my reader, but Aldo Antonelli beat me to the punch: I was astonished that 188 target faculty answered the "classical or non-classical" question in particular, and that (apparently) every one of the 29 members in the sample who identified their specialty as logic and philosophy of logic responded to the question.

Brit Brogaard said...

Gregory: I agree that the logic question was one of the most difficult ones to interpret. I should have realized that during the beta-testing.

djc said...

See (scroll down) for some relevant thoughts on the logic question. We didn't include it on our original list of twenty for roughly this sort of reason, but lots of beta testers asked for it to be included. And of course respondents had the options of saying "Accept both" (my own answer), "The question is too unclear to answer", "There is no fact of the matter", and so on. But it's interesting that only 110 of the 931 target faculty, including 15 of the 92 logic specialists, took one of those three options. (N.B. Gregory Wheeler's lower figures appear to be drawn from the results of the Metasurvey.)

Brit Brogaard said...

Right, I see that. As I read the question, though, "accept non-classical" is consistent with "accept both". There are, of course, languages that are classically closed but I find it hard to believe that English is one of them (there may not be a fact of the matter about the semantics for English but if there is, then most likely it's not classically closed).

Anonymous said...

Classical or non-classical logic?
Accept both? Wtf. Dave, that doesn`t get you anywhere, man.

djc said...

...for different purposes.

Anonymous said...

Bullshit. Bingo!
Dave, that's one heck of an idea. You won that round. For different purposes. Yep, when I teach non-classical logic I am using non-classical logic too. Or when I am horsing around or telling somebody what Dave said the other day.
Note to self, think clearer before posting a comment.
N.B.: sticky stiffy stuff.