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WillowOne's Positions

Argument from Mathematical Intelligibility

Form

Built on Eugene Wigner's 1960 essay "The Unreasonable Effectiveness of Mathematics in the Natural Sciences", and used by William Lane Craig and John Lennox:

  1. Mathematics, often developed with no application in mind, turns out to describe the physical world with astonishing accuracy (complex numbers in quantum mechanics, Riemannian geometry in general relativity, group theory in particle physics).
  2. On naturalism this is a happy accident with no explanation: there is no reason why the products of human minds should match the structure of a mindless universe.
  3. On theism it is expected: a rational mind made both the world and the minds that study it, and made them to fit.
  4. Therefore the applicability of mathematics is evidence for God.

My Positions

  1. Mathematics was built by looking at the world. Counting, geometry, and the calculus were developed to handle quantities, land, and motion. It is not a surprise that a language refined for two thousand years against physical regularities describes physical regularities. The "unreasonable" cases (complex numbers, non-Euclidean geometry) were extensions of that language by the same rules, and the rules were abstracted from the world in the first place.
  2. We remember the mathematics that worked. Most mathematics describes nothing physical and is never heard of outside mathematics departments. The handful of structures that found a use are selected for the anecdote; the thousands that did not are not counted (Survivorship Bias, Texas Sharpshooter). The fit is also far less exact than the story suggests: the three-body problem has no closed solution, quantum field theory needs renormalisation to give finite answers, and most of physics is approximation.
  3. Effectiveness is what regularity looks like from the inside. Mathematics is the study of structure and pattern as such. If the universe has any regularities at all, then whatever describes regularities will describe it. The deep fact is that the world is regular, which is a presupposition of all enquiry (My Presuppositions) and is not something theism explains better than anything else: a god could have made an irregular world, and we would not be here to describe it (Anthropic).
  4. "Theism predicts it" is written after the result. Nothing in any theology predicted complex Hilbert spaces or gauge symmetry. Had mathematics applied only roughly, the apologist would have said God made a world of mystery to keep us humble. A hypothesis compatible with every outcome predicts none of them (Popper's Razor).
  5. Wigner did not draw the inference. His essay ends in puzzlement, not in God, and Richard Hamming's reply in 1980 gave four naturalistic reasons: we see what we look for, we select the mathematics that fits, science answers only the questions it can, and evolution built brains that model regularities.
  6. Even granted, "a rational structure" is not a person. The argument reaches, at most, that reality is intelligible. That is as consistent with Pantheism, Deism, or a Platonic order as with a god who answers prayer.

Sources

  • Wigner, E., "The Unreasonable Effectiveness of Mathematics in the Natural Sciences", Communications on Pure and Applied Mathematics 13 (1960)
  • Hamming, R. W., "The Unreasonable Effectiveness of Mathematics", American Mathematical Monthly 87 (1980)
  • Steiner, M., The Applicability of Mathematics as a Philosophical Problem (1998)
  • Plantinga, A., "Two Dozen (or so) Theistic Arguments", in Walls and Dougherty (eds), Two Dozen (or so) Arguments for God (2018)

Also see