Invisible Unicorns

Apology for Invisible Unicorns:

Post-positivist Ponderings on Empiricism and Meaning

 

The Logical Positivists were actually petty negative.  They gathered in Vienna cafes in the ‘20s to pooh-pooh all the traditional problems of philosophy, especially metaphysics, and tried to build a new picture of the world out of nothing but stern logic and incontrovertible evidence.  On their view, metaphysical claims like Heidegger’s ‘The Nothing itself nothings’ or even Descartes’ comparatively sensible ‘I think, therefore I am’, were not false—no, falsehood was too good for them.  They were meaningless—pure Jabberwockian gibberish spawned of logical and grammatical errors.  The Positivists admitted that, like Lewis Carol’s “Jabberwocky”, metaphysics might have some poetic or artistic value, but only that, and not much of it.  Rudolph Carnap, their most ambitious warrior, scathingly compared metaphysicians to “musicians without musical talent”.

The Positivists’ influence was vast.  The winds of war and genocide dispersed them across the West, and their sensibility, if not their theses, came to dominate philosophy in Anglophone universities and even seeped into the broader culture.  (Surely Mr. Spock is their nephew, and New Math partly their fault.)  Today their doctrine is part of the standard philosophical curriculum, though mainly as another cautionary example on philosophy’s long record of failures. 

Their view fell into disfavour for a number of reasons, one being that it was false.  But falsehood played only an indirect role.  There was no definitive refutation of Positivism, only challenges that it never managed to meet.  For one, the Positivists never pinned down exactly which statements were meaningful and which weren’t.  Every attempt at a precise criterion seemed to legitimize too much metaphysics or condemn too much successful science.  And in 1951, Willard Quine shocked philosophy (to hear some tell it) by arguing that there was no real difference between meaning and fact.  On his view, even statements like ‘All bachelors are men’, widely thought to hold in virtue of the meanings of words alone, could be overturned if we encountered enough empirical anomalies (and surely by now we have).  So if there was really no difference between questions of meaning and questions of truth, how could the Positivists call metaphysics meaningless? 

But even Quine’s argument wasn’t a knock-out punch.  It was a challenge:  Explain the difference between meaning and fact without falling back on other distinctions that amount to essentially the same thing.  And not surprisingly, no one managed it.

But my purpose here isn’t to review the history of Logical Positivism’s failures.  I want to explore a more general and intuitive objection to the whole idea of an empiricist criterion of meaningfulness.  The key concept is a slippery one:  understanding.  But slippery as the idea may be, it seems clear that we can understand claims that have no empirical implications.  On the other hand, metaphysics may face a great challenge in making itself understood. 

            Suppose I sit down in a London Underground train, and the woman sitting next to me whispers to me, “There are invisible unicorns all around us.  They’re completely undetectable.  They have absolutely no effect on anything that we can see, feel, or otherwise sense, but they’re here.”  Clearly this woman is mad (one of the perennial charms of public transportation).  But I don’t feel inclined to say her claim is meaningless.  I would say it’s false, and I suspect that many readers would, too.  And yet, it seems to have no empirical implications whatsoever.  The claim itself even says as much:  The unicorns have absolutely no effect on anything we can sense.

            So why am I inclined to regard this claim as meaningful?  And I don’t mean meaningful in some vaguely expressive way, like poetry or a Jackson Pollack or Mingus’s “Goodbye Pork Pie Hat”.  I think it actually asserts something about how the world is.  Something very false, no doubt, but something.  Why?  It seems to me this is because I can situate the claim within my picture of the world, i.e., within the network of concepts that I already grasp.  I know what unicorns are supposed to be, and I assume they’re supposed to be made of some sort of matter.  I have some sense of what matter is, at least insofar as I can normally tell when there are big hunks of it around, and I know roughly what to expect of it.  As well, I can imagine there being two kinds of matter in the same place that have no effect on each other.  (We have neutrinos, which hardly do anything to other particles, so why couldn’t we have further particles that interact with each other but don’t interact with the particles we are made of at all?)  I can picture the shapes of the unicorns, and locate them in space and time.  I imagine them now loping up and down the tube car forlornly.  I don’t see any reason to believe there are such things, and given the arbitrariness of the proposal, it seems extremely unlikely, to say the least.  It’s just one ridiculous, random hypothesis out of billions.  But I seem at least to understand it.

            So far this is just introspective intuition.  But we can give it a bit more backbone by finding other ways the stranger’s claim can be connected with a model of the world and how it works.  Suppose these unicorns are indeed made of some kind of matter that doesn’t interact with the matter we know.  But now imagine a third kind of matter that affects and is affected by both the unicorn matter and ours.  If such mediating matter existed, maybe I could use it to “feel” the unicorns, the way one can feel things with a stick.  Or the unicorns might reflect a special kind of radiation that doesn’t affect ordinary matter but which could be transformed into visible light by another special material.  And then maybe I could fashion spectacles from this material and see the unicorns.  Of course, my travelling companion did not say that such mediating materials exist, but the point is, the presence of the unicorns implies some counterfactual conditionals about observations —statements about what we could observe empirically if things were different.  If we had the right tools, or if things were different in some other helpful way, we could be affected by the unicorns and detect them. 

In fact, the unicorn story is in this respect not much different from statements about ordinary objects on the dark side of the moon or on a planet in a distant galaxy.  We can’t sense them, but we could in principle detect them under the right circumstances.  Positivists like the English spokesman A.J. Ayer wanted to admit statements that were empirically confirmable “in principle”—how embarrassing it would be to claim that statements about rocks on the far side of the moon were meaningless!—but what doesn’t count as empirically confirmable in principle?  Our invisible unicorns could be detected if certain helpful things happened to exist.  Anything could be detected if things were a little different.

            But it isn’t just these empirical counterfactuals (such as the fact that we could detect the unicorns if conditions were favourable) that make the invisible unicorn hypothesis comprehensible.  Suppose next my new friend says, “And they’re in terrible pain.  Because we don’t brush our teeth enough.  If we don’t brush at least every two hours, the unicorns suffer horribly.”  Again, this is mad, but it seems to give her story more bite in two ways.

First, it implies that, thought the unicorns have no effect on us, we can affect them.  Take another example:  Suppose the unicorns can’t pass through our bodies.  Every time we move, we nudge them around without being affected ourselves.  (This might violate our laws of physics, but never mind.)  Then the unicorns would be a bit like people of the future:  We can affect them, but they can’t affect us.  And surely we don’t think that claims about what will happen in the future, once you and I are dead or all of humanity is gone, are meaningless.  In any case, the fact that we can affect the unicorns would constitute a further connection between them and the world familiar to us, in this case a causal connection, without giving them any further empirical significance. 

But more interestingly, I think, if I believed the unicorns were in agony, I would feel terrible for not brushing my teeth more.  So for me, there is a significant difference between the unicorns existing (and being in pain) and their not existing, despite the lack of any empirical difference.  And I think, if the tortured unicorns existed, we would be morally obliged to brush our teeth more regularly.  (Of course, these are fully conscious, self-reflexive moral-agent-unicorns, and they don’t like pain.  So even if you think it’s ok to hurt “dumb animals” or masochists, we’re obliged not to hurt these unicorns.)  More generally, if our actions affect the unicorns, then even though they have no empirical significance for us (except the logically possible, counterfactually empirical significance already mentioned), their existence imposes moral obligations on us. 

The funny thing is, it seems to be a matter of fact whether we do have such a moral obligation.  Surely, either it’s true that we should brush more than we would be obligated to if the unicorns didn’t exist, or it isn’t.  Hence it seems to be a question of fact whether any such unicorns exist.  At first blush this argument may seem to presuppose some form of moral realism—the view that moral obligations and the like are objective facts, whatever we may think.  But really it doesn’t.  Even if there aren’t any objective moral facts, many people will just have a strong personal preference not to hurt the pretty unicorns if they can help it.  And again it seems like a question of fact whether they ought to brush their teeth more in virtue of that preference or whether they needn’t bother.  Of course, if you’re really a committed Logical Positivist, you might argue that we are definitely not obligated to any such unicorns precisely because their existence isn’t a question of fact.  But it would seem really short-sighted and even potentially cruel to go around blithely yuck-mouthed just because we can’t see the suffering unicorns.  (Cf. Dr. Suess 1954, Horton Hears a Who!)

So, there are various ways the hypothesis of undetectable unicorns can be meaningful besides having actual empirical significance.  It proposes entities similar to familiar ones, and located in space and time.  It implies empirical counterfactuals, and it can be amended to imply causal connections and moral obligations.  All of these observations involve the unicorns bearing some relation, possible or actual, to matters that we already understand to some degree, i.e., to existing elements of our conception of the world. 

We might suggest, then, that understanding, or one important kind of understanding, consists in being able to draw such connections with one’s model of the world—spatiotemporal correlations, counterfactual empirical implications, causal influence, moral obligation, and perhaps lots of other kinds.  But let’s make two clarifications.  First, a meaningful proposition shouldn’t have to be fully comprehensible by any one individual.  If we have a definition that’s too complex to be understood all at once, that’s OK, as long as we can understand its parts individually and how they’re put together.  Personally, I can never grasp all at once the definition of a discretely ordered semi-ring, for example, but I can understand each bit of the definition separately and the basic unifying structure, and that suffices for the meaningfulness of ‘discretely ordered semi-ring’.  Secondly, ‘one’s model of the world’ has to be very broadly construed to include purely abstract objects like numbers and propositions and so on.  For example, we certainly understand some mathematical objects that have no direct connection with our models of physical reality.   (I like to describe philosophy as the study of how “things”, very broadly construed, “are”, very broadly construed.  But I’ve probably nicked that from someone.) 

In any case, there’s a rough, naïve account of what it means to understand a statement:  It means we can connect it with our representation of how things are, in the broad sense of ‘how things are’.  In particular, we can see ways in which things that we already understand would be affected by its truth or falsity.

Now I admit, analysing meaningfulness in terms of understanding invites a heap of objections.  What mainly concerned the Positivists about meaning was whether a given statement had a truth value (true or false), and arguably that is a matter of fact, independent of anything psychological like understanding.  But the fact that I can make sense of a claim—give it a place in my picture of the world—seems to be some reason to say that the sentence is either true or false.  It communicates a representation that might or might not correspond to reality.  And a representation doesn’t have to be consistent or describe a metaphysically possible state of affairs.  Even if the claim that I am a female bachelor is absurd and necessarily false, it is perfectly comprehensible.  We know what female means, and bachelor, and if indeed there is no one thing that fits both descriptions, we can only know that if we understand the terms.  The important thing for understanding is just that the claim should communicate something about how matters are supposed to be (in the physical world, or in mathematics, or whatever), however impossible it may be.  If I couldn’t draw any tenuous connections between the world and the putative unicorns, I would worry that my mad companion wasn’t saying anything at all.  But I can.

But wait wait—representations and correspondence—that draws a boatload more objections, including many of those raised by the Later Wittgenstein.  He pointed out that there’s no one special relation between a picture and what it represents; various mappings could be drawn between any representation and any object.  Hilary Putnam argued in a more technical way for a similar point about theories:  Any given theory could be taken to say just about anything.  But it’s obvious that we do form accurate and inaccurate representations, mental and otherwise.  Picture your bedroom.  Now picture it different.  You could also draw a picture or describe it verbally.  The question isn’t whether we represent, only how.  And maybe the fact that a given expression somehow induces certain mental pictures or models is not exactly what meaning consists in, but it is at least one important function of language.

It’s an old-fashioned an unpopular view:  Statements convey ideas about how things are, and either they are that way or they’re not.  They don’t have to make a lot of sense just to be false.  On the other hand, there are statements that don’t seem to convey anything.  What after all does it mean to say that universals exist, or that numbers don’t?  How would things—the world, logic, mathematics—be any different if they did or didn’t?  I can’t imagine.  This is why I say that, even if there is something right in what has been said above and meaningfulness doesn’t require any empirical significance, still, metaphysics, or some metaphysics anyway, still faces a challenge:  To make itself understood.  But that’s an issue to explore another time.        

Ayer, Alfred J.  1936.  Language, Truth and Logic.  London: Victor Gollancz Ltd.

Carnap, Rudolph.  [1931] 1959.  “The elimination of metaphysics through the logical analysis of language,” in A.J. Ayer, 1959, Logical Positivism, Glencoe, Ill.: Free Press.

Hempel, Carl G.  1950.  “Problems and changes in the empiricist criterion of meaning,” Revue Internationale de Philosophie 41, 41-63. 

Putnam, Hilary.  1980.  "Models and reality," Journal of Symbolic Logic 45, 464-482.    

Quine, Willard V.O.  1951.  “Two dogmas of empiricism,” The Philosophical Review 60, 20-43.  Reprinted in 1964, From a Logical Point of View, Cambridge, Massachusetts:  Harvard University Press.

Wittgenstein, L.  1953.  Philosophical Investigations.  Oxford: Blackwell.

A Moral Paradox of Infinity

God is kind. He has promised that humanity will forever flourish. Over time, an infinity of people will live.

Satan is cruel. He is going to torture infinitely many of those people. And crueler still, he has charged you with choosing which ones he will torture. You have three choices:

(1) Satan will torture everyone born on a Monday after January 1st 2012.
(2) Satan will torture everyone born on a Wednesday after January 3rd 2012.
(3) Satan will torture everyone born on a Monday after January 8th 2012.

Each victim will suffer the same amount of pain, and that amount will be the same whatever your choice.

Here is the paradox:

(1) is no worse than (2), as these choices apparently concern equal sets of people being tortured equally. Similarly, (2) is no worse than (3).

So it follows that (1) is no worse than (3).

But this is obviously false, since in case (1), all the same people are tortured as in case (3) and others as well. Contradiction.