Against the axiom of nature’s infinite precision

Working at any art gives us an experience of what might be called the stubbornness of matter: you have an idea in your head for a picture or a melody or a paragraph, then in trying to make it work you find the materials have a mind of their own. Those who make things end up expecting some divergence between what they set out to make and what gets made, and whether this is a disappointment or a pleasant surprise involves a changing ratio of luck and skill. I’m literally having this experience right now in trying to get this paragraph to work.

From Galileo until now, we’ve taken it as an axiom that the totality of natural causes does not have to deal with the stubbornness of matter since they are infinitely precise. If I am trying to cut a straight line but get a crooked one, we assume this is because there were competing forces that account for these slight deviations. My line is crooked because I only account for a part of the forces that gave rise to it. The total forces are infinitely precise and perfectly mathematical since any deviation from absolute precision requires us to posit another force to explain what caused the deviation. At this point we are supposed to humbly say we can never know all these forces and so science does the best it can with degrees of approximation.

But even total awareness of forces would not suffice to explain the end result since even an infinite intelligence would not suffice to make nature a math problem. Forces act only so far as they are given mathematically, and math is non-temporal. You can imagine formal or mathematical quantities taking time to execute a process, but they don’t take time as mathematical: how long does it take to sum all the parts of an integral? How long does it take to add 2 and 2? For that matter, how long is a yardstick as mathematical? One doesn’t need three feet of space to use the “yard” that gets used in an equation.

Trying to sufficiently explain either time or distance by purely mathematical considerations ends up leaving off the very motion and time we are trying to explain in the first place. Actual motion can’t be just an instance or concretion of mathematical “motions”. There is a non-formal element in them making them temporal, mobile, and therefore unintelligible to us. Some theory of hylomorphism or participation seems inevitable.



  1. dsthorne said,

    January 20, 2016 at 2:54 pm

    Do you mean to merely point out the distinction between the mathematical description of a process (always an abstraction) and the actual process thus described (always concrete), or something above and beyond this distinction?

    In expressing the inevitability of hylomorphism, do you mean it as the only candidate for harmonizing a given thing and its formal features, i.e. features that are universals?

    Or have I missed something?

    • January 20, 2016 at 3:26 pm

      Something over and above. I’m arguing that even a totality of formal specifications would not suffice to explain the structure of something arising in nature. Ever since Newton, we’ve wanted a purely formal nature – which concludes to Wheeler’s “it from bit” universe or Tegmark’s mathematical universe.

      Notice I said hylomophism or participation. Plato’s theory of the world as a sort of screen or receptacle of forms is still a logically possible account.

  2. Josh said,

    January 23, 2016 at 2:06 pm

    Is the recognition of this interval between formal/mathematical and non-formal/temporal what Lonergan is talking about when he uses the concept of “empirical residue”?

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