Experimental Logic

Consider the sentence: 

(1) The circle is near the square, and it isn't near the square.

This sentence appears to be a contradiction, and it therefore seems that defenders of classical logic would have to say that it was false. However, there are other logics -- Graham Priest's dialetheist logic LP, for example -- in which sentences like this one can turn out to be true. 

A question now arises as to what ordinary folks think of sentences like (1). Do people take the apparently classical view that such sentences have to be false, or do they think that sentences like (1) can actually turn out to be true? 

In a surprising new paper, David Ripley shows that people are actually extremely willing to express agreement with apparently contradictory sentences like this one. In cases at the vague borderline between 'near' and 'not near,' people felt that it was perfectly acceptable to consider an object 'both near and not near.' In fact, they were just as willing to say that an object was 'both near and not near' as they were to say that it was 'neither near nor not near.' 

This is one of the first studies to systematically examine people's ordinary intuitions about the status of contradictions, and so far, it is looking like people think that contradictions can actually be true!

Comments

[jonathan weinberg]

Very interesting! I'm also glad to see the engagement with the relevant cross-cultural work.

[Greg Frost-Arnold]

I found this paper very interesting. A couple of comments:

1. One explanation of the data that was not directly considered (it might be thought of as a combination of the error theory (3.4) and non-compositional (3.5) interpretations) is that the informants might be using a strictly false sentence to _pragmatically imply_ true information. I'm thinking of an analogy or converse case with logical truths. The standard semantic line is that logical truths carry no information in virtue of their semantics. But English speakers _do_ communicate content by uttering logical truths, e.g. "It is what it is." Although this sentence is carries no content semantically, an utterance of it can pragmatically impart content (about accepting the current situation/ the futility of trying to change the situation).

2. I wonder to what degree the data actually do support dialethism, as the author (with reasonable reservations) suggests. In LP and kindred logics, a true contradiction is (I think) always _BOTH_ true _and false_. And in the paper, the author points to informants' agreeing (to some degree) with a contradictory sentence as evidence that the speakers consider that sentence true. But if agreement signals holding-true, and disagreement signals holding-false, then it seems like the experimental evidence that would be required to show that English speakers operate with LP is actually that informants both agree _and disagree_ with the contradictory sentence. Or have I misunderstood something? (Perhaps the fact that speakers did not often mark '7', for highest level of agreement, could be interpreted this way -- but that's not usually the way we understand Likert scales like this, I think.)

[Dave Ripley]

Howdy!

Greg:

I think the "pragmatic implication" line is very much worth considering. While it might not be a straight-up noncompositional explanation, I think it'll need similar supplementation to a noncompositional explanation. In particular, something about these sentences would have to pragmatically imply borderline-case-ness, and that should be explained. My bet---and so far, it's just a bet---is that the explanation for why this pragmatic implication holds is going to appeal to contextualism, or fuzziness, or dialetheism. (Really probably contextualism, since if you're already revising logic, you're probably not appealing to a pragmatic line on these sentences.) But even if I'm wrong in my bet, the pragmatic line needs to offer some answer to: what about contradictions suggests borderlineness?

As far as LP and agreement/disagreement: the traditional line for dialetheists about assertion/acceptance/agreement/other attitudes and actions of this general sort is that these attitudes are appropriate when (and only when) the thing being asserted/accepted/agreed to/whatever is true. Typically, falsehood isn't seen as taking away from a sentence's acceptability; it just means the sentence's negation is also acceptable. So if p is both true and false (as any true contradiction will be, in LP), we should agree with p and we should agree with ~p.

Short picture: the standard dialetheist doesn't think disagreement suggests holding-false, but instead that it suggests holding-not-true. If the dialetheist about vagueness adopts this line (as I think she should), she can stick to the ordinary interpretation of the Likert scales.

This suggests, though, a direction for further study: what do people in fact say about "It's not both near and not near", or "It's either near or not near"? Since the dialetheist thinks the contradictions studied in the paper are both true *and false*, she should predict agreement to these sentences as well. In fact, if the cultural bias I suggest in the paper is on the right track, the dialetheist should predict higher agreement to these sentences than to the sentences in the paper. I haven't yet checked these sentences, though, so I don't know whether that prediction holds up or not.

Thanks much for the comments!

[leslie glazer]

Interesting. The logic of ordinary language can perhaps allow for what analytic philosophy considers a contradiction because it includes acceptance of ambiguity and plurovocality, metaphors and other figurative language. Something can sensibly be said to be near and not near as one gropes for a better way of expressing oneself, or gropes for a better understanding of what is said, looking for the language to guide one's eyes toward where the actually thing may be located, looking for context cues to further determine the sense expressed, asking the further questions in the give and take of dialogue or inquiry. In more analytic terms, the expression isn't a contradiction because the meaning of the first term 'near' is different than the meaning of the second term 'near' [in not near]. Only the process of questioning, contextualizing, looking, feeling one's way toward the thing meant determines the sense.

[Dave Ripley]

Leslie:

Thanks very much! The strategy you point to is absolutely one way of explaining the current data; note, though, that there are a lot of constraints on such a theory. (One key constraint: the theory had better not appeal to there being two occurrences of "near", since the results remain unchanged when participants see only one occurrence, as in "The circle both is and isn't near the square".) If this sort of contextual story is right, seeing the details of those constraints should help us understand how models of context-dependency fit (or don't) with speakers' real responses.

[Blake Myers-Schulz]

Very fascinating! After reading this, I started thinking about how people might respond to contradictory statements about mental states.

Here are some interesting preliminary results regarding contradictory statements about an agent’s intentions. I'm wondering what others think about this

Piloting data from 16 subjects:

8 subjects received Knobe’s environmental harm scenario. They were then presented with this question:

Is the following sentence true or false?
The chairman intentionally harmed the environment, and he didn’t intentionally harm the environment.
True False (circle one)

The other 8 subjects received Knobe’s environmental help scenario. They were then presented with this question:

Is the following sentence true or false?
The chairman intentionally helped the environment, and he didn’t intentionally help the environment.
True False (circle one)

Here are the results:
Out of the 8 that received the harm scenario: 1 subject answered ‘true’, and 7 subjects answered 'false'.
Out of the 8 that received the help scenario: 5 subjects answered ‘true’, and 3 subjects answered 'false'.

So, only 12.5% of the harm-subjects were willing to agree that the chairman intentionally harmed the environment and didn’t intentionally harm the environment. But surprisingly, 62.5 % of the help-subjects were willing to agree that the chairman intentionally helped the environment and didn’t intentionally help the environment.

Any thoughts?

[Dave Ripley]

Wow!

My first thought (probably because I'm vagueness-obsessed) is to try to chalk it up to the help-CEO's action being a borderline case of "intentional".

I'm thinking of a model along the lines of the one in Josh Knobe & Dean Pettit's paper at http://philpapers.org/rec/KNOTPI which maps representations of pro-attitudes (like intentionality) onto a linear scale, and predicts CEO-case-like effects whenever the case in question is of an "intermediate" character. If that's right, maybe what we see in CEO cases is not the difference between a clear-intent harm case and a clear-non-intent help case, but rather a clear-intent harm case and a borderline-intent help case.

[Natalia]

Hi, how can I contact you?

I want to start, a list of philosophy BLOGS. A small presentation of the thing, a library or address book. But one question I don't know is, how to contact people through blogs, I'm not familiar with this medium.

If time permits, I want you to make a post here,

http://dissidentphilosophy.lifediscussion.net/conversation-f8/

It will get stickied and start a list of philosophy blogs. You could write a small intro too, like "Here is a index and library of PHILOSOPHY blogs ...."

Already an index of BBS is here,
http://dissidentphilosophy.lifediscussion.net/conversation-f8/the-community-of-ephilosophers-philosophy-bbs-sites-t9.htm

Kind regards,

- Niki

[Max Deutsch]

This was, for me, a very interesting and provocative paper, as the length of my comments below will show. The talented Mr. Ripley! (Bet you’ve never heard that before.)

1. Seems like the results could be skewed by the ‘what does the experimenter want me to say?’ bias, especially if the order of presentation was Pair A to G (or pair G to A) for each subject. Sample reasoning: ‘In pair A, the circle is clearly not near the square, so it’s clearly not both near and not near the square. But now, in pair B, the circle is nearer to the square! What am I supposed to say? Perhaps the experimenter wants me to say that I’m less confident that the sentence is false of pair B.’ Assuming Ripley is after what people think about the sentences as opposed to what people think Ripley wants them to think about the sentences, this could be a problem.

2. Some of the sentences Ripley presented were not borderline contradictions, they were just contradictions. So there’s a worry about ‘contrast effects’ (as I think they’re called). If I show you a clearly red color patch and then, just after, one that’s red, but not so clearly, you might be less inclined than you would have been if I had shown you just the not so clearly red patch to describe it (the not so clearly red patch) as red. Not sure what this means (if anything) for Ripley’s method. Perhaps judgments in the midst of contrasting cases reveal a person’s true view of a particular case? I don’t know. Might be nice to get data on judgments about single cases, i.e. show subjects just Pair A and ask them for their level of agreement about the sentence, show a different group just Pair B, etc. Maybe Ripley has this already?

3. My intuition (no chuckles now) is that a borderline contradiction such as ‘The circle is near the square and not near the square,’ said of Pair C, pragmatically conveys the proposition that, in Pair C, the circle is a borderline case of being near the square. Since this proposition is true, if it is conveyed by the contradiction, that would explain an increase in agreement level while leaving open the question of whether the proposition semantically expressed by the contradiction is true. In his reply to Greg, Ripley admits this, but asks for an explanation of how contradictions ‘suggest borderlineness.’ I presume the demand is for how _borderline_ contradictions suggest this. But how could they _not_ suggest it? Surely one thing a person is trying to say, when she says that a both is and isn’t F (when a is a borderline case of F) is that a is a borderline F. Even if its obscure what the precise Gricean mechanism here is, I think it’s pretty plain that there is this suggestion in such cases. In fact, even if this isn’t true in general, it seems that in Ripley’s experimental setting, in which a subject is exposed to some plain old contradictions and some borderline ones, it’s even more plausible that, when a subject increases her agreement level upon exposure to the borderline ones, part of what she is doing thereby is letting Ripley know that she sees that the circle in such cases is a borderline case of being near the square. Add to this that agreement never rises very far above the midpoint level and I think we have a fairly strong case against the view that there’s evidence that ordinary (Western) speakers accept some contradictions as true. The qualified nature of the agreement suggests that, at best, the humpers (ahem!) are borderline cases of people who (partially) accept that some contradictions are true.

4. I worry that the experimental design itself encourages subjects to think that truth/agreement comes in degrees and hence that a sentence can be more or less true. Once you think this, it seems to me a short step to the thought that a borderline contradiction might be more true than a plain old one, but it’s not clear that the folk would think this _before_ being exposed to a study that tells them to reflect their amount of _agreement_ with a sentence on a scale from 1 to 7. This seems different from reflecting one’s _confidence_ in the truth of a sentence. For I might fully agree/disagree with a sentence without confidently doing so. Or is that too much conceptual analysis for y’all?

5. I think the issue of whether someone who theorizes about the semantics and truth-values of borderline contradictions is committed to predictions about the speech behavior of ordinary speakers is (a) one of the more interesting issues and (b) not explored in sufficient detail by Ripley. At one point, Ripley says, “few logically-minded theorists of vagueness, then, have bothered being very explicit about what their theories predict about ordinary speakers.” Could this be because such theories don’t make predictions of that kind? The theories in question have something to say about the truth-conditions and truth-values of ordinary speakers’ sentences, but they are silent, it seems to me, about what ordinary speakers will say about these same issues. And their silence is no defect; they are theories about the sentences, not about what ordinary speakers will say about the sentences. Of course we (I) want to know why Ripley’s subjects behave as they do. But I’m not sure it’s fair to demand this explanation from philosophical theories of vagueness. At another point, Ripley says that he doesn’t mean his experiment or his interpretation of its results to bear on any theory that is “explicitly not about ordinary speakers.” But this isn’t enough of a concession. If I have a theory about apples, you don’t get to criticize it for not explaining various facts about oranges just because my apple theory is not “explicitly not about” oranges. I imagine Ripley might reply by saying that the speech behavior is at least evidence for/against the predictions of a theory. But this is a very significant difference. If the speech behavior is only evidence for/against the predictions, then, for example, a prediction might be true despite the speech behavior evidence against it, and there might be other, better evidence in favor of the prediction. In the phil of lang there are quite a few theories that make predictions for which speech behavior, if evidence at all, would be counterevidence. (Think Millianism about names or straight Russellianism about definite descriptions.) The proponents of these theories seem bothered only a little that ordinary speakers don’t accept the predictions of their theories. And maybe this is the right attitude, methodologically speaking.

6. I like that Ripley admits that the content _Dave likes to dance_ is (very) true. Breakdancing I hope?

[Greg Frost-Arnold]

Just to follow up on Max Deutsch's 5.:

Logicians don't take the fact that naive informants embrace the argument forms of denying the antecedent and affirming the consequent to be evidence against their theories of conditional entailment.

Why should the cases of contradictions discussed in this paper be different from denying the antecedent? =Is there a principled difference between informant responses about denying-the-antecedent and these informant responses about contradictions involving borderline cases?

[jonathan weinberg]

I'm highly sympathetic to the first part of Max's point #5 -- in general, the x-phi community needs to get more developed accounts (probably a number of rival accounts should proliferate) of just how to suss out the testable implications of different philosophical theories.

But the problem with the "hey, I'm all about the sentences, man" line, I take it, that what we end up using when we theorize about sentences is, well, our takes on the sentences. So as a matter of practical fact, there's no theorizing about sentences without theorizing about people's takes on sentences.

E.g., Russell's account of definite descriptions seems to me to be trying to accommodate both a fair amount of actual linguistic use, and the demands of the formal logic he was working with. If we all used definite descriptions rather differently, then the motivation for his theory might drop out altogether.

One answer to Greg's question is with the question: are there logics that make good sense out of affirming the consequent? (As opposed to, e.g., theories of confirmation that try to make sense out of people's card-selection behaviors as not really instances of affirming the consequent. And is there any evidence for ordinary subjects denying the antecedent, btw?) The dialetheist is, after all, offering us just such a candidate for making sense of some true contradictions. So perhaps with the logic of indicative conditionals, we let the demands of the formal system trump ordinary usage. There's a whole lot of other reasons to take the non-affirming-the-consequence choices as normatively correct, too; see e.g., Stanovich & West. We might not have any such reasons for reasoning about contradictions, though I suspect that maybe the work just hasn't been done one way or the other.

[Dave Ripley]

To Max's 1 and 2: a follow-up experiment that mixed things up, presenting clear cases and borderline cases out of order and the like, could help address these. One such is in the works; I'll be sure to spread the data around once I have it. One thing to note: the responses I call "slope" responses in the paper may well best be explained by something like the process you propose in 1. But I think the humps less so---unless something about "both near and not near" (and the other sentences) somehow conveys borderlineness---and that itself is the phenomenon to be explained here.

To 3: Everyone (let's pretend) agrees that contradictions suggest borderline-ness. But the mechanism by which they suggest it might be either semantic or pragmatic. I don't think it's enough for the defender of a pragmatic line to simply say that the suggestion must be pragmatic, even if we don't know how it could work---because we have not just one, but two models of how the "suggestion" could happen semantically. Both the contextualist and dialetheist models account for contradictions' getting the idea of borderlineness across, and they both appeal to semantic theories to do so. If a pragmatic theory is to compete with these, I think it does need to fill in the gap, as its semantic counterparts have done.

(And note that agreement often rises quite far above the midpoint level: just under half of the participants agree fully---7 out of 7---with at least one of the contradictions, and over half agree at level 6 or 7 with at least one. The reason for the relatively low mean responses is that these maxima didn't line up with each other across participants.)

To 5 and ensuing discussion: This is where a lot of the action is, of course. In this paper, I mean simply to present a phenomenon and canvass possible explanations for that phenomenon. If a theory of vagueness really makes no predictions about how ordinary speakers use our language, then I really (in this paper) have nothing to say about it.

Widening the focus, though, I think philosophical theories of vagueness aren't so divorced from speakers' actual practice. Especially recently, there's been a shift in the vagueness literature towards attending to experimental results. (Examples: Smith lays out potential experiments in his recent book, and provides fuzzy explanations for potential results, Raffman has run a number of fascinating experiments confirming predictions her contextualist(-ish!) theory straightforwardly makes, Bonini et al. look for similarities between speakers' behavior w/r/t vagueness and w/r/t ignorance, in support of epistemic theories.)

I don't think this shift is misguided. If we weren't concerned with describing the language we actually speak, there would be no problem of vagueness; we could simply describe an ideal, non-vague language instead. It's the focus on our actual language that drives much research, empirical and otherwise, on vagueness, and empirical research is one way to learn about our language.

All of this is to respond just as Max predicted I would; that is, to say that experimental evidence is (just) evidence. (This is why, for example, I consider error theories in the paper.) But I think that it's not enough for a theory to simply shrug off evidence against it. At the absolute least, it's better for a theory if it can explain why apparent evidence against it isn't so worrying after all.

To 6: Alas, my breakdancing career was cut short in a tragic funk accident.

[Jon Cogburn]

For what it's worth, my paper in the Graham Priest, J.C. Bealle dialetheism anthology (J. Cogburn, "The Philosophical Basis of What? The Anti-Realist Case For Dialethism," in The Law of Non-Contradiction, ed. Graham Priest, J.C. Beall, and Bradley Armour-Garb, Oxford University Press, (2004). ) argued: (1) that Dummettian anti-realism leads to true contradictions for discourses with paradigmatically defeasible warrants, and that (2) the person on the street's view of tragic choice ethical situations is at least consistent with them being described as true contradictions.

I don't know if I'm the one who hypothesized this first, but I'm the only one to defend dialetheism for situations that neither involve vagueness (actually the paper was written before glut approaches were in print) or self-referential paradoxes. So I doubt anyone hypothesized in print that one of the virtues of dialetheism about non-self referential contradictions is that makes sense of the manifest image.

[David]

"David Ripley shows that people are actually extremely willing to express agreement with apparently contradictory sentences like this one."

The emphasis should be on "apparently." I don't see that anything about attitudes toward bivalent logic is made clear by merely apparent contradictions.

[seth Edenbaum]

Came to this from Leiter's page. He introduced it thus:
"What's so bad about contradictions?
Not so much, according to the 'folk.'[sic] "
Leiter's a leftist and a snob. Contradiction or no?

To paraphrase Sartre: The folk are other people.

[Dave Ripley]

Just to keep the recent history in view: at least Priest and Routley have both argued for dialetheism in situations that involve neither vagueness nor self-referentiality.

For example: impossible objects, motion, change, and multicriterial terms are all argued to be sources of dialetheia in the 1989 Priest, Routley, Norman volume. Some of these arguments I think are more convincing than others, but they're definitely there. I think you're right (if I remember correctly) that none of them involve appeal to the "manifest image", though.

[seth edenbaum]

"The circle is near the square, and it isn't near the square."
What does "near" mean without context?
Is the Earth near the moon? compared to what?
People tend not to reason abstractly without context.

Thinking abstractly it is simply a fact that the circle without reference to any other element is both near and not near the square.

Also: Are Jews in America white or non-white [A or Not-A]?
Again, there's no answer outside of context.

[Max Deutsch]

I still like the 'borderlineness as an implicature' idea. If borderlineness is suggested in the relevant cases (as it seems to me to be) then, prima facie, a pragmatic explanation is more plausible. Reason: ‘a is F and a is not F’ just doesn’t look like the sort of sentence capable of semantically expressing the proposition that a is a borderline F. (I take Dave himself to be elaborating something like this reason in his complaints against ‘non-compositional’ theories.) So if it’s expressed at all, it’s pragmatically expressed. Dave says that contextualism and dialetheism both _semantically_ account for the suggestion of borderlineness. Those two theories explain how the borderline contradictions (or ‘contradictions’) can be true, but it’s not clear that this explanation, in either case, involves appealing to the idea that it’s part of the semantic content of ‘a is F and a is not F’ that a is a borderline F. Maybe I’m (definitely probably) missing something here…

If it’s implicature, Dave wants a story about mechanism. Leave aside the issue of whether, generally, borderline contradictions suggest borderlineness. The story about how humpers’ agreement to the borderline contradictions in Dave’s study is used by humpers to convey borderlineness may be something very roughly like: A humper knows, and knows that Dancing Dave knows that he knows, that the only way to convey the fact that (he recognizes that) Pair C involves a borderline case of ‘near the square’ is to increase agreement level to the contradictory sentence applied to Pair C.

I still like the ‘I’m all about the sentences, man’ idea (and that way of putting it). You can be all about the sentences, man, without admitting that your theory is “divorced from speakers’ actual practice,” or that it floats completely free from “peoples takes on sentences,” or that it is not a theory of “the language we actually speak.” You can also say that your theory makes no predictions about ordinary speakers’ truth-value judgments, without denying that ordinary speakers’ truth-value judgments figure in somehow (as highly defeasible evidence for example). The way people use a language is of course relevant to a semantics for that language. That’s trivially true. But ‘the way people use a language’ covers a wide range of practices. The danger is taking the trivial claim about use to imply that a theory is in serious jeopardy if some speakers make truth-value judgments that conflict with the theory. Dave considers ‘error-theories’ and so is sensitive to this point, but I guess I think he’s not sensitive enough (to the point—I’m sure he’s a sensitive guy). I get the sense that Dave thinks that every theory of borderline contradictions owes an explanation of the phenomenon he’s uncovered in the study he ran. I think this is wrong. Dave _says_ that if a theory really makes no predictions about speech behavior then he’s got nothing to say about it. But my sense (_I’m_ a sensitive guy.) is that Dave thinks the proponent of such a theory has her head in the sand.

Brief reply to Jonathan on me on Russell on dds: Though I wasn’t especially clear in the original post, the thought was not that Russell’s theory ignores “actual linguistic use.” It was rather that there are a fair number of cases in which ordinary speakers and the theory will diverge on truth-value judgments. ‘Actual linguistic use’ has a much broader extension than ‘ordinary speakers’ truth-value judgments.’

[Dave Ripley]

I don't necessarily think that all theories of borderline contradictions owe an explanation of the present results, but I do think there must be some explanation of the results, and going theories of borderline contradictions seem to be the best places to start. Theories that antecedently predicted this result get a gold star of some sort; true novel predictions are a good thing. That's far from supposing that other theories are in serious, or even any kind of, jeopardy.

Note, though, that a semantic theory that doesn't predict this result takes on certain commitments: at the very least, it's committed to the claim that something non-semantic (perhaps pragmatic, perhaps experimental design, perhaps something else) produced the result. Whether that's plausible or not depends on the plausibility of the non-semantic theories that do predict the result.

Of course, this will all be much better examined in the light of a huge amount of data we simply don't have yet. It's hard to conclude much of anything at the moment, except things along the lines of "X predicted this, and Y didn't".

As I've said, though, I don't yet see a fully pragmatic explanation: the core question yet to be answered by such an explanation is "Why would these contradictions convey borderlineness?" How is it that the humper and Dancing Dave understand each other to mean borderlineness by a contradiction?

Contextualism and dialetheism both can answer this question. On the dialetheist theory, the borderline cases of "near" are precisely the cases where "both near and not" is true. It's not simply that dialetheism predicts that contradictions can be true; it goes farther, and predicts that contradictions are true in all and only borderline cases.

The contextualist doesn't think any contradictions are true, but thinks that these apparent contradictions can be true, because "near" can have different extensions in different contexts. On the usual contextualist line, only some cases are such that they can plausibly be filled in either way: the borderline cases. So like the dialetheist, the contextualist not only explains how the sentences in question can be true, but also offers an explanation that only holds for borderline cases.

If these sentences can only be true in borderline cases, we have a straightforward (semantic) explanation for why speakers would take the sentences to indicate borderlineness. So for the time being, I still think the contextualists and the dialetheists are a leg up on the pragmatic explanation.

[jonathan weinberg]

"Though I wasn’t especially clear in the original post, the thought was not that Russell’s theory ignores “actual linguistic use.” It was rather that there are a fair number of cases in which ordinary speakers and the theory will diverge on truth-value judgments. ‘Actual linguistic use’ has a much broader extension than ‘ordinary speakers’ truth-value judgments.’"

Who is supposed to be saying something inconsistent with any of that, though? All Dave (et al.) need is that the speaker's judgments are relevant. That other things will also of course be relevant is not a point in contention.