Friday, February 22, 2008

Squaring the Circle, in Malcolm's Dreams

Few works of philosophy are more perverse than Norman Malcolm's (1959) Dreaming, in which he argues that dreams do not occur when one is asleep and contain no feelings, imagery, sensations, or the like. Malcolm's view, rather, is this: When we wake, we're inclined to confabulate stories of a certain sort. Telling such a story is what we call "relating a dream", but there is no sense in which the dream exists independently of or prior to the story we tell about it, and no sense in which such a story can be evaluated as an accurate or inaccurate description of occurrences during sleep.

Malcolm knew about the then-recent REM research that most people think creates serious problems for his view. He cites and dismisses, on what seem to me flimsy grounds, Dement's research suggesting that reported dream duration on waking matches duration of REM sleep and his very suggestive finding that horizontal movements of the eyes during REM sleep correlate with dream reports of horizontally-salient events (such as a tennis match) and vertical movements of the eyes correlate with reports of vertically-salient events (such as climbing a series of ladders, looking up and down them).

So I don't recommend trusting Malcolm on dreams. But here is an interesting remark of his:

In a dream I can do the impossible in every sense of the word. I can climb Everest without oxygen and I can square the circle (p. 57).
So here's my question: What does it mean to say one can "square the circle" in dreams?

Surely Malcolm doesn't mean that the dreamer can actually coherently conceive of a square circle. That, I take it, is straightforwardly impossible. Somewhat differently, can one violate the laws of math and logic in fiction? Can I coherently tell a story in which 2 + 2 equals 5 (like I can coherently tell a story in which pigs fly)? I'm not particularly well read in the metaphysics of fiction, but my impression is that few philosophers of fiction would grant that -- though if we do grant it, we might be able to use it (with some additional assumptions) to give sense to the idea of squaring a circle in a dream.

More likely, Malcolm is expressing the idea that we can reach incredibly stupid judgments in our dreams, even baldly contradictory judgments. I have also long thought this (see section v. of this essay).

If we accept this view, it gives more juice to the dream skeptic than she is usually accorded. For if this right now might be a dream, then mightn't also my thinking be so baldly contradictory that I can't even trust my simplest-seeming judgments? The dream possibility calls, then, not only sense experience but also reasoning into doubt. If we allow ourselves the assumption that a faculty frequently unreliable is not to be trusted, there would be no hope that I can rely on my reason to establish the hypothesis that I actually am awake, or indeed anything else.


Jonathan Jenkins Ichikawa said...

Here's how I think of it. (I make no claims to Malcolm interpretation.)

Dreams are a lot like fictions -- in particular, the contents of dreams are closely analogous to the contents of fictions. I'll even go out on a limb and suggest the strong thesis that all and only propositions that could be the contents of fictions can be the contents of dreams.

There could be a fiction in which someone squares the circle. I'd be an incoherent fiction, but fictions have incoherent contents all the time -- witness Back to the Future. Likewise, I could have a dream in which I square the circle. Why not?

That's not to say that I can "actually coherently conceive of a square circle." But I can imagine that I square a circle. Heck, someone might even believe that he's squared a circle. Some people have had this false belief. It's possible to have incoherent beliefs, imaginings, fictions, and dreams.

Justin (koavf) said...


Asking what can be done in fiction is a bit dicey because I'm not sure what you mean by your question. In "fiction" as a broad literary genre, then you can "do" anything that is grammatical and intelligible as language, including creating a little universe in which 2+2=5. It's "done" once it is written. As for whether or not we can conceive of what that means, that's really our shortcoming as a logical persons.

It is certainly the case that a universe can exist that has a different set of historical accidents (e.g. Nazis won World War II) or physical laws (e.g. e=mc.) So, why not logical laws? Why can't an illogical or self-contradictory universe exist? We say that we can't imagine it; that's fine, I'll buy that. There was a time when it was literally impossible for anyone to conceive of flying machines and horseless carriages as well. Those sorts of transportation "problems" are overcome by technology and we have the capacity for that. We may simply not have the capacity to overcome the "problem" of conceiving of self-contradictory universes as well. That does nothing to make them more or less real, just like airplanes and automobiles were "unreal" thousands of years ago.


Nicholas Shackel said...

Eric, just as a matter of information, 'to square the circle' means to construct a square with the same area as a given circle (not to make a square circle), sometimes by restricted means, such as by use of compass and ruler alone.

bjb76 said...

I was going to make Nick's point, but he beat me to it. And it's an important point, because it clarifies what Malcolm is talking about. There's nothing inherently contradictory about the idea of finding a square with the same area as a circle. For millennia mathematicians struggled to find a geometrical means of doing so. But here's the relevant point: in 1882, mathematicians proved that it was impossible:

Ben Bayer

Anonymous said...

A few things:

1. Now I am very curious to read Malcolm's book. I think his idea is profound but I'll take your word for it that psychologists have disproved it.

2. Last night I had a lucid dream in which I flew a lot. I forgot about the dream, until I read this blog post. So I'm not completely sure the dream happened. I also have a vague recollection that DURING the dream I was thinking about this blog and lucid dreaming, which was discussed previously.

3. As far as whether we can imagine was is logically impossible (or physically impossible, or what we believe to be physically impossible), people care too much what people can conceive of. Some day we will program computers to "understand" things that are just beyond our comprehension, and that's just going to be the way it is going to be.

4. The idea of 2+2=5 is that you can't have a story where that happens because then you'd have a story that no one could understand, because you can't really conceptualize that, because it's too simple. Squaring the circle is equally "wrong" in some ethereal mathematical sense (it is proved impossible), but it's not obvious, so we can imagine a world where it happens. Even though in some sense (some views of mathematics) there can be no such world.

Jonathan Jenkins Ichikawa said...

Nick and Ben,

The challenge of squaring the circle was an open mathematical challenge for some time, until it was proven impossible, as Ben points out. So there is a literal incoherence in supposing that one has squared a circle: it entails a contradiction. Dreaming that one squares the circle is like dreaming that one proves the completeness of arithmetic.

(Malcolm is surely NOT suggesting merely that one can dream about finding a circle and a square with the same area.)

Unknown said...

Hi Eric,

If you're interested in the possibility of fiction which violates the laws of logic, you might want to check out Graham Priest's short story "Sylvan's Box", which attempts to show that an "essentially inconsistent" story is intelligible and non-trivial. It's available here (The link is broken up so it will fit in the window):




Jonathan Jenkins Ichikawa said...

Yes, ditto QQ. There are also a number of nice cases in the literature on 'imaginative resistance'. Tamar Gendler has a delightful story in which five and seven don't make twelve, Stephen Yablo has one where a five-fingered maple leaf shape is an oval, and Brian Weatherson has a whole bunch of neat cases.

Anonymous said...

jonathan ichikawa, thanks for pointing out that paper by Tamar Gendler, it is very interesting. I think her 5+7 story is unintelligible. I can pretend it makes sense, but I can't really make sense of it, even with a superficial reading. On closer reading I think it's completely nonsensical.

Anibal Monasterio Astobiza said...

Malcolm distinguished between three different kinds of memory: factual memory (associated with the use of verbs like " remember" uttered as propositions with a what-clause, where if the thing remebered is true, then, what follows after the clause is a "fact"), perceptual memory (those rememberings associated with images) and finally personal memory (those rememberings in which one has been involved)

Dreams are laid down, principally, in the category of perceptual memories but share every mayor aspect with the rest of the categories.

Why in dreams, according to Malcolm, is even possible to square the circle is, i think , a matter of the seemingly paradoxical standpoint in which old-classical and ortodox behaviourists are when confonted with pure experiential phenomena like dreams, because dreams don´t fit with any of his memory divisions and explanations.

Dreams are, in this sense, like intermediate phenomena with one foot in our confident world of reason and justifications and the other foot in the world of the total scepticism of the fantastic sect, as David Hume would say.

Eric Schwitzgebel said...

Thanks for all the comments, folks -- and especially for the help with what "squaring the circle" is and the contemporary literature on incoherence in the philosophy of fiction.

Jonathan and Justin and Quine: I see that the word "coherently" in my remark about "coherently" telling a story in which 2+2=5 was doing a lot of work for a little adverb -- more work than it should have been doing, obscuring the option that we can (as seems plausible) have incoherent dreams.

And yes, Anibal, I agree that Malcolm's behaviorism is what's forcing him into such a strange view!

But all this doesn't directly address what I take to be the core question: Can we reach utterly stupid, incoherent judgments in our dreams; and if so, does this give the dream skeptic ammunition to disarm reason as well as perceptual judgments if he can establish that it's possible, in some important way, that you're dreaming right now?

Jonathan Jenkins Ichikawa said...

Well, maybe we can make such crazy judgments in dreams. Suppose this is so. Does this introduce a new kind of skepticism? Plausibly not. For the relevant crazy things that I might do during dreams might well be the kinds of things that I can know via introspection not to be doing.

The idea would be: even if I can't prove I'm not having a realistic dream, I can definitely prove that I'm not having a dream like that.

Anibal Monasterio Astobiza said...

We are circulating and wandering around the bequest cartesian legacy of the epistemology of the first-person, and, how we can be confident of our self-servings perceptions, memories, reasons, justifications... and the like. In this sense, is very difficult to disregard the arguments of the skeptic.

I wonder if the skeptic has not the burden of proof?

Is it possible that a third-person approach erode the possibility of being dreaming right now?

Eric Schwitzgebel said...

So, Jonathan, it seems to me to get to some delicate issues about grounds. If reasoning in dreams can be utterly incoherent without our recognizing that fact, I can presumably think I'm thinking coherently when I'm not at all -- not even close. Can I know through introspection that I'm not in a dream, thinking absolutely incoherent thoughts? Well, maybe so, just as I can know through perception that I'm in my office (which I wouldn't be, if I were dreaming). But if one is skeptical enough not to grant the latter knowledge, is there some disanalogy between the cases that still allows one to grant the former knowledge?

Eric Schwitzgebel said...

Anibal, I wonder if the third-person perspective presupposes rather than establishes the falsity of dream skepticism.

I agree the skeptic has the burden of proof -- or at least the burden to show us why we should take the skeptical possibilities seriously.

I think it's illuminating to consider a parallel case of a skeptic about deduction, who challenges us to prove that deduction is a deductively valid method without using deduction. This appears preposterous and impossible. Why we should care about such a challenge or be troubled if it's impossible to meet? The same goes, perhaps, for the skeptic about induction, or perception, or other minds....

Genius said...

I'd say that dreaming or conceiving of a square circle in it's simple form (as opposed to ideal conceivability) is just having an object in mind that fits into your mind's "square" category and your "circle" category.

It implies that your mind is ignoring an important factor (although I'm not entirely sure this isn't contingent on physics) - but that isn't entirely surprising because your mind isn't a super computer - it almost always ignores important factors.

Like one of those impossible stairs drawings - it looks possible...

Unknown said...

I definitely disagree with Malcolm where he states dreams are formulated when the individual is waken up. First of all there have been numerous studies and brain scans that has prove certain brain activity when a person in deep sleep and in a dream by testing the person's heart rate while in a dream.

Secondly I also agree with Jonathan in stating that dreams are contents of fiction. While in a dream the part of the brain that makes sense in life is turned of which I do not recall the name of it exactly as of now and literally anything that is illogical can make sense in a dream. So squares can be circles, numbers can add up to anything and fishes can fly in a dream world that's made up by the person sleeping.