The reasonable effectiveness of mathematics

by Neil Rickert

(This is part of my series of posts on evolutionary epistemology)

Perhaps it is a new meme in the ID world.  On several recent occasions, I have seen ID (Intelligent Design) proponents asserting that mathematics is evidence of an intelligent designer.  Sometimes it is a comment on the mathematics itself, and sometimes on the way that mathematics works so well within science.  A recent example of the latter kind is Karl Giberson’s essay “Mathematics and the Religious Impulse.”  The argument seems to be that there is no reason for the world to be mathematical, and that the useful of mathematics is therefore evidence of a divine intelligent design of the world.  Giberson is not alone in this view.  It is similar to the “Fine Tuning” argument that is sometime made in support of ID.  Others, including physicist Eugene Wigner, have thought the effectiveness of mathematics to at least be surprising and unexpected.  In this essay, I shall present my view on the issue.

So is the role of mathematics in the sciences evidence of intelligent design?  Well, yes, of course it is.  But we know who the designers were – they were the scientists themselves who were designing their theories.

I get strange looks when I say things that suggest that science involves design, invention or construction.  People seem to hear it as saying that scientists construct the world (something claimed by social constructionists).  However, I am not at all suggesting that scientists construct the world.  I suggest only that scientists construct ways of talking about the world.  And while there is not complete freedom in how we talk about the world, there is still a considerable amount of leeway.  To illustrate this, consider your stereo system.  We have two very different ways of talking about the output power that is fed to the speakers.  We can describe that in terms of Watts, a absolute linear scale.  Or we can describe it in terms of decibels, a relative logarithmic scale.  That we can such very different ways of talking about output power, shows that our ways of talking are not fixed by the problem we are talking about.

As I suggested in an earlier essay, the problem of knowledge is the question of how we can have facts at all.  Scientists solve this problem by creating a framework that allows us to express the facts of interest.  This is a bit like a builder constructing a scaffolding around a building.  The requirement for the scaffolding is that it fit the building, but that still leaves some flexibility in the scaffolding design.  Likewise for the scientist, the problem is one of fitting a framework of concepts to the problem, but the form of the resulting framework is underdetermined by the problem.  Scientists use this freedom of choice to give the framework a mathematical structure, wherever that is possible.

The trouble with traditional epistemology, is that it depicts the problem of knowledge as one of truth seeking and belief change.  However, most of the major scientific advances involve conceptual change, and the choice of conceptualization is mostly a pragmatic one rather than a veridical one.  Mathematics is effective in science, because scientists build mathematical ideas into their frameworks of concepts.  And physics is the most mathematical of sciences because physics has the largest role in defining new concepts.

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