The loneliness of the aardvark

Empirical science must have its objects.  Notoriously, it cannot observe the unobservable, or detect the undetectable.  Only objects are material, and therefore it must have them.

It is for this reason, it incessantly reminds us, that it cannot find evidence consistent with the existence of God.  Less often it admits that neither can it find any against her.  Though the empirical claims of God’s believers are easily refuted, God herself is unobservable and undetectable. God has by definition no length or width or depth, no mass and no duration – unless one considers her everywhere and all the time. But by the laws of mathematics, a ubiquitous God is nowhere at all, for such a creature can be factored out of our equations without any loss of explanatory power.  We divide both sides by God, and so remove her as a variable.

For this mathematical reason, God lacks at least one awesome power she bestowed on her creation: the power to be empirically seen. And this is why, if we must still have her, we must have her through faith alone. God cannot be inferred.  She must simply be believed.

From this singular failure, many seculars have extrapolated.  Unobservables and undetectables can never explain anything.  And so we make lists of such things – fairies and elves and garden gnomes and Santa Claus and unicorns.  Seeing that none of them explain anything either, we proceed to generalize.  All of science, we say, from soup to nuts, is empirical.

This is not true, of course. Realism has its metaphysics, and science has its unobservables.  It is merely that ours are clothed in grandeur, not red suits and flying sleighs. It is not, perhaps, a good defense that we simply do not know it.

Last month I was walking through the halls at Columbia’s Psychiatric Institute when I bumped into a friend of mine, a scientist I will not name – BA, MD, PhD, tenure track, several top-tier publications. She asked me where I was going, and I held up a book on the philosophy of science and told her to return it to the library. “Ugh,” she said, making a face. “I just like empiricism!”

I teased her back – or so I thought. “So then how do you handle the problem of induction?”

She furrowed her brow.

Sensing that we do not all, perhaps, walk around with such questions on the tips of our tongues, I clarified.  “How do you build theory out of a bunch of brute facts – or are the brute facts theory-dependent to begin with? How do you see your neurons, how do you know their roles?”

She furrowed again, and I began to understand that I was embarrassing us both.  To save two faces, I waved off my question, removed it from the air like so much sulfur, and rolled my eyes at my absurdity. “See what you’re missing?” I asked laughing, as though ashamed.  Relieved, she laughed back and went on her way.

But I was not ashamed. I do not believe that science should have done what it has done: to raise a generation that can, from memory, recite the second law of thermodynamics, or Hebb’s, or Ohm’s, but which does not recognize the problem of induction that marks them all.  It is not that it is wrong, but merely foolish. For the relationship of theory to fact, concept to percept, is not some idle concern for Sunday afternoons, but the stuff of our professional lives.

More, we are, in practice, wriggling around the problem of induction every day, and trafficking in unobservables.  No – it is more than this – we are swimming in them, drowning. Unobservables – those very things we claim we cannot see – are the great indulgence of the field.  We are the dieter who professes abstinence while munching bon bons as she speaks. We have beside us at our bench an infinite assortment of immaterial, unobservable, undetectable allies without whom we could not do our work.

We call them numbers.  And it is not merely the irrational ones, as I discussed last post, or those overtly influenced by theory, as I implied in the one before that.  It is all of them.

It takes some time for us to wrap our heads around the undetectable nature of numbers, for we seem to see them everywhere: one firecracker, two aardvarks, three pounds of cheese, four months of community service. (Long story – don’t ask).  One, two, three, four: how could anything be more objective, more observable, more detectable, than these numbers? They are as objective as anything can possibly get!

But even a rational number doesn’t exist in the world.  

Take those two aardvarks.

If numbers are a real thing in the world, an empirical thing that can be studied, then when you see two aardvarks you are seeing two classes of things superimposed upon or attached to or comprised somehow of one another: aardvarks and numbers.   Regardless of the precise nature of the connection, numbers and the aardvarks are perfectly correlated, so that every single time you see an aardvark you also see a number.  There are always aardvarks matched with a number – one, two, three, four – but this correlation disguises the fact that they are separate entities.

So take away the aardvarks and leave the number.

I can’t, you say – I need the aardvarks to have the number.  Try harder; imagine a case where you can.  So you try and try, but you can never get the aardvarks out without also getting rid of the number.  Some people say the number just changes to zero, but that’s cheating. Where’s the zero? And if it doesn’t exist, well then.

I have been beating this horse – or should I say, this aardvark? – for several posts now: that statistics don’t exist in nature, that the world cannot be counted.  There are no bounded objects in the world.  

So where are they? Where is pi? Where are medians? Where are t-tests? Where is one zebra and two aardvarks?

This tiny little question is our gateway to a huge conceptual problem in the everyday metaphysics of science.  Because it leads us, inevitably, to understand that my friend in the hall was wrong.  Empiricism cannot function without rationalism. You begin to realize in your own way the thing that Kant realized in his.  That number two is in you. As is Chad Orzel’s median in him, and Jonah Lehrer’s cherry in him, and Derek Jeter’s batting average in his fans.

These numbers are not in the world.  You, in the case of these aardvarks, are projecting them onto the world.  The world does not contain, objectively, two aardvarks.  Or five aardvarks.  Or one you.  The world contains, perhaps, aardvarkness.  Or aardvark potential.  This raw stuff may – just may (though I think not, but may) be a “thing in the world.”  Or what Wittgenstein called a “natural kind.”  Or what Buddhists call “from its own side.”  But the number itself is coming from you.

Which leads us back again to the overwhelming concern of this site.

Who, again, are you?


  1. In any case, you’re stuck on reification again.

    If you can do geometric calculations and on their basis build a bridge, it’s silly to say that numbers have nothing to do with the world. Where, then, do they exist, you ask? Where anything exists: in a state of constant arising and extinction — that is, in a state of radical contingency and relatedness. There is one me, but the metaphysical ground of that “me” is literally incomprehensible; so, too, then, am I. But once you let go of the urge toward perfect comprehension, that intellectual grasping, then you are freed to act within the quotidian, where if you have two apples and get two more apples, you have, lo and behold, four apples — and no need to ask what appleness or fourness might be. There is no thing; therefore there are things. Ta da.

    1. Hey Greg! But *where* is this arising and extinction within the empirical paradigm? Isn’t that question important or at least worthwhile or at least sensible? Or is the universe a brain in a vat – or rather, is the universe the mind produced by an unknowable brain in an unknowable vat, so that we cannot know our own location?

      1. I think it stands to one side of that empirical paradigm, with empiricism being useful but metaphysically shallow.

    2. Greg can I say one more thing? I don’t think that numbers have nothing to do with the world. But I think they aren’t physically embodied in the world as per scientific dogma

  2. And here’s a real Scholastic quibble for you: is it a power “to be . . . seen”? I would call it a condition; in Scholastic terms, an accident.

    1. Well, per se it’s not a power, you’re right. But God did not make the universe with the accidental quality of being empirically verifiable. What is the Catholic position on why god didn’t make himself knowable empirically? Or is there none?

      1. As standing above, so to speak, the natural order, God will not be knowable – that is, comprehensible – through natural means. The empirical order is a material one; God is not material.

        Though not exactly an answer to your question, there’s some consideration of ways in which one may know God in the Catechism:

  3. Two comments, then we’ll read the post (lol)
    – Damn boy! You can tell a story and write. Very rare.
    – It is a sad state of affairs when grade A American road kill meat gets disrespected with leprosy! “Side of plague with that mam? Excuse me? Yes, Black Plague. Why yes, just like the best caviar.”

  4. How is this anything more than a verbal puzzle? First, it is really the “chacter” formerly known as a “god.” How is that different from the Great Pumpkin?

    2. “science has its unobservables.” – like what? Isn’t what we call science, by definition , measurable.

    3. “How do you build theory out of a bunch of brute facts – or are the brute facts theory-dependent to begin with? How do you see your neurons, how do you know their roles?”

    The answer is simple – we make stuff up. But stuff that can either predict other stuff or not. We “know” essentially nothing. Well, a little. But the more we know the more we know, really, we don’t know. But that doesn’t open the way for everything to be possible or true or predictable. We do have our (severe, dual hemispheric, limits apparently.

    All predictive claims are probabilistic and local. Yes, even the “laws of thermodynamic and maybe even gravity. Aren’t numbers just like a stick – just a tool? How do we define “exist” and “world” or any verbal term for that matter?

    The observer cannot be separated from the observed. Sure, unless it’s a bullet or bacteria, etc.

    We have no ability to answer many (most) questions. Our brains evolved in close-in forests. That’s it.

    Don’t think you’re saying there is no stimuli or photons reaching “me?” Hyper relativism and subjectivity is fine but likely an artifact of our language more than anything in the “world.”

    How do we separate this argument from just language usage? In moments like this I bop over to the visual cognition myspace page and brush-up on how our brains process that stimuli and ignore the verbal stuff.

    Where did I leave my bloody car keys?

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