Ethics of Elfland

One danger in mathematical accounts of nature is that they can be taken as giving us the same insight into nature as we have into math: if you have values of 4, 3 and 2 in a combined gas law then you know that the gas your working on will always remain equal to (4 x 3) / 2, but you do  not have the same insight into nature as you have into the numbers. The relation of the quantities is known either by infallible insight or (if you follow Russell’s account of math) because the relation among quantities is tautological. But the reason why the gas preserves the constant is known neither by insight nor as a tautology. The quantity 4 X 3 over 2 = C is necessarily invariant and we can see why it is, but we see no reason for the connection among the things quantified. It might arise according to an invariant law or a historical one, with thought or without it. We can approach this sort of cause only by negating the insight we have into the connections among mathematical things. The necessity in the law is not in the thing we are describing but the way we are describing it. This isn’t even a very controversial claim: Comte was very clear about it, and it’s one of the simpler accounts of the Kantian denial of the thing-in-itself. If this is too abstract, one can simply reflect on the the problem of induction, or Russell’s chicken.

But insofar as physical law is known by way of negation of the sort of necessity we find in mathematics, logic, and the general truths of nature, then we fail to understand nature when we compare it to a machine. In fact, in this precise sense the machine is the worst possible metaphor for nature, since the machine is entirely transparent to our understanding. We understand its parts, its maker, its purpose, its historical antecedents, and everything else there is to understand about it. Nature is rather best understood as magic, that is, as a denial of our insight into how things work, caused by a simple trick of one who knows how we think and chooses to act in another way. Anyone can look at nature and see that somethings is doing something, but to project the hypothesis of a machine into this causal hiatus is to pretend to exactly the sort of insight that we need to deny in order to faithfully convey our experience of nature. Beyond the very general sorts of truths we know about nature, it doesn’t do what it does using the sort of things we have real insight into.

The analogy of nature to a machine or artifact is unavoidable and illuminating for any number of purposes: Aristotle uses it to show the composition and causes of natural things, and no pragmatic understanding of nature is possible without taking it as a sort of artifact. But no analogy is the thing itself – it’s just our lack of such a thing that forces us into analogy in the first place. Nature is magic too – the working of a cause that is at once simpler than what we are thinking and yet, for that very reason, baffling to us.

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1 Comment

  1. February 4, 2015 at 9:59 pm

    I’ve been noodling with a ‘practical calculus’ during my free time at work the past few days, seeing what it might be like to use a ‘mathematical’ formalism to, for instance, evaluate the action of any possible agent against that of some maximal agent within the domain of some ‘library’ (e.g.,the priciple of utility).

    One or two things I was quite pleased with, but studying action – so rigid, unidirectional and ordered – makes hash when combined with things one would want in a calculus, like commutability.

    Indifference to the order of some operations was hard to square with, among other things, the dependence of technical on epistemic knowledge; I was most successful when denying this distinction. And so many other denials would there be!

    But I can only wince so hard, so let it serve to illustrate the more successful the mathematicizing endeavor, the more likely it’s succeeded by redefinition. One might transmute the subject into something as radically different as Frege’s laws of thought are from Aristotle’s art of reasoning well, or do no better than to scrawl ‘can=open’ on the wall.


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