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?