Overstepping the limits of conscious judgment

I’ve thought about mathematics as a reflection of hard-wired cognitive processes, or even as our own consciously rendered image of them.  In this light, mathematics’ conceptual weaves look particularly organic, even fleshy.  I’ve pursued this perspective because I find that it helps me see two things better:  mathematics itself and what qualifies as physical.  What I realized today is that it also contradicts reductionist views of human experience and what has come to be called biological determinism because we have yet to characterize its imaginative power.  It demonstrates the unexplainably, inexhaustible range of what can be thought.

All of this came to mind more clearly while I was reading a recent Scientific American blog by John Horgan. Horgan is writing in defense of Stephen Jay Gould’s “ferocious opposition to biological determinism,”  a view characterized by claims that “social and economic differences between different groups – primarily races, classes and sexes – arise from inherited, inborn distinctions…”

Horgan’s blog focuses on an article in PLoS Biology that critiques Gould’s critique of the work of Samuel George Morton, a 19th century physician, who compared the sizes of skulls, collected from around the world, and concluded that, on average, whites had larger skulls.  This was used as evidence that white’s and black’s did not share a common ancestry.  In his blog, Horgan also referenced the work of evolutionary biologist Jerry Coyne and neuroscientist Sam Harris, who Horgan says insist:

that free will is an illusion because our “choices” are actually all predetermined by neural processes taking place below the level of our awareness.

I’m always fascinated by the extent to which the body is built to do what it does and the extent to which it is living outside of our awareness.  But I have yet to find that seeing this in any way diminishes the significance of willful action.  In fact, what it calls into question, is the integrity or the soundness of conscious judgment (like Coyne’s that free will is an illusion).

When action becomes understood as interaction, as happened in the discovery of the classical laws of physics, it’s easy to be tempted by a deterministic view, or a purely mechanical view of cause and effect.  But physics has already found the error in this reasoning.  And, as I see it, mathematics consistently reveals the limits of conscious judgment by unveiling exotic, counter-intuitive, yet fully meaningful possibilities that consistently broaden scientific horizons.  It replaces judgment with necessity and, in the sciences, manages to correct perspectives that are largely molded by expectation, instead of the laborious introspection that is managed with mathematics.

I would also like to suggest that while mathematics can look almost spontaneous or emergent (with abstraction being fundamental to vision and learning) it is also directed.  We’re very far from understanding the nature of the will. But from the interaction of the will, the senses, and the world that shapes them, comes profoundly imaginative vision and insight, that are often first given shape in mathematics.


5 comments to Overstepping the limits of conscious judgment

  • Joselle

    I like this very much and would like to read more but I don’t read French! I think this captures an important intuition that has likely been expressed before in different forms.

  • Benoit

    Joselle what do you think of the following I took from an article by Claude Tresmontant? “Le problème de l’âme”(I can give you the article if you read French)

    The key is to have a word[soul,principle,pyche] for that reality which is the structure that is not an element, not a material thing, which integrates multiple hardware, and remains for a lifetime while the integrated subject is changed.

  • Thanks, I’m working on it! I’m happy you found my blog. Looks like our thoughts overlap.

  • happyseaurchin


    i have been wandering a bit on the net
    looking for the maths of emergence
    and your site popped up 🙂
    and i was particularly taken by the first sentence of this post
    “I’ve thought about mathematics as a reflection of hard-wired cognitive processes, or even as our own consciously rendered image of them.”

    i’ve been exploring this over the last few years
    after my first deep dive in 2008 which resulted in a book
    the extracts of which can be found here under the XQ headings

    have you made any further progress regarding your — to me — very insightful statement?

    be well

  • John Horgan

    Joselle, thanks for mentioning my piece on Gould. You’ve got a really interesting blog, connecting math to all these other fields of human science. Keep up the good work. John

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