Cognition and Will

I see mathematics as associated with a searching, instinctual will, whose direction is shaped by our biology.   I find some of its roots in the way our visual system constructs what we see, or in the way grid cells (neurons lit by location) tell a rat where it is, or the way ants can find their way home with a kind of internal vector analysis.  In the past, I’ve thought of mathematics as somehow making unconscious processes like these, available to the needs of a conscious will.  But I also see the emergence of mathematics as one of the body’s actions, something the organism just began to do, like language.  Why would our nervous system begin to build something like mathematics?

One can find a meaty collection of essays on mathematics in the book: 18 Unconventional Essays on The Nature of Mathematics edited by Reuben Hersh.  In one of the essays (Philosophical Problems of Mathematics in the Light of Evolutionary Epistemology), Yehuda Rav says that we should not just accept the mystery of the effectiveness of mathematics in the natural sciences.  It “is the task of any epistemology” to furnish some explanation for it.  And Rav proposes something consistent with my own ideas:

The core element, the depth structure of mathematics, incorporates cognitive mechanisms, which have evolved like other biological mechanisms, by confrontation with reality and which have become genetically fixed in the course of evolution.  I shall refer to this core structure as the logico-operational component of mathematics.  Upon this scaffold grew and continues to grow the thematic component of mathematics, which consists of the specific content of mathematics.

Rav makes the observation that

When we form a representation for possible action, the nervous system apparently treats this representation as if it were a sensory input, hence processes it by the same logico-operational schemes as when dealing with an environmental situation.

He quotes biologists Humberto Maturana and Francisco Varela who said:

all states of the nervous system are internal states, and the nervous system cannot make a distinction in its processes of transformations between its internally and externally generated changes.

These observations support the idea that the nervous system treats mathematical objects the same way it treats objects of the senses.  And with this idea we can understand why it feels like mathematics is being discovered.

But Maturana and Varela also made the following statement

Living systems are cognitive systems, and living as a process is a process of cognition. This statement is valid for all organisms, with or without a nervous system.

Clearly Maturana and Varela defined cognition far more broadly.  Cognition, in this sense, is like interaction or adaptation.  This school of thought associates cognition with life in the most fundamental way.  But, as Rav considers, this has implications for how we characterize knowledge itself.

This equivalence between what we mean by cognition and what we mean by living systems calls to mind (for me) Schopenhauer’s will – to which I should devote another blog.  Shopenhauer’s Will is fundamental and ubiquitous, like Maturana’s cognition.  I will just quote from translation of The World as Will and Representation (first published in 1819) that can be found here.

Here we already see that we can never get at the inner nature of things from without. However much we may investigate, we obtain nothing but images and names

The act of will and the action of the body are not two different states objectively known connected by the bond of causality; they do not stand in the relation of cause and effect, but are one and the same thing, though given in two entirely different ways, first quite directly, and then in perception for the understanding. The action of the body is nothing but the act of will objectified, i.e., translated into perception. Later on we shall see that this applies to every movement of the body, not merely to movement following on motives, but also to involuntary movement following on mere stimuli; indeed, that the whole body is nothing but the objectified will, i.e., will that has become representation.

I would also like to note that Rav proposes that the fact that the nervous system responds to representations in the same way it responds to sensory input can account for what he calls the Platonic illusion.  But, as I see it, there is reason to wonder about this neutrality of the nervous system.  I still think Plato’s intuition was correct.  There is something behind or beneath the objects of our experience, even if it is the pure commonality of everything. And mathematics helps us see that.

……Best wishes for the upcoming holidays!