The Aristotelian Pathway to the Modern World and Beyond

I’m just back from a week of seminars in Maine: an overview of Aristotle’s world-view, based on a sequence of selected readings.  Although I’ve long been curious about Aristotle’s thinking, and written about this to some extent on this website, I’ve never before caught the full coherence and impact of his world-view. I’ll leave details to future posts to this blog, but here’s an overview of a few highlights. Tradition has misleadingly titled many of Aristotle’s works. His “Physics” is not limited to what we today call “physics”, but actually addresses the foundations of the entire natural world, of all things that move, from stones to living creatures, including ultimately ourselves. Aristotle’s “Physics”, then, lays the foundation for his other works, and in the “Metaphysics”, of the cosmos itself. We ourselves he will say, are rational by nature.

What is “nature”?  An inner principle of motion, Aristotle says; things move not because they are pushed or pulled, but through inner tendencies. This is by no means nonsense. Within what we call “physics”, think for example of the second law of thermodynamics, which asserts, in more formal terms, that heat “tends” to flow downhill. Within our own lives, think of fear or love, and our innate desire to know. Thus in Aristotle’s inclusive world-view, there’s no occasion for the infamous split which today appears to divide our sciences from the humanities.

Such unification need not threaten the integrity of the sciences. Remarkably, within this encompassing perspective Aristotle lays a secure foundation for a fully valid alternative approach to modern science. Key is his concept of “energy” (the word, energeia, is his!); motion consists in the unfolding of energy from potential to kinetic form. Importantly, energy belongs primarily to whole systems, so wholeness and living, organic unity are foundational in Aristotelian science.

In the 17^th century Leibniz, who knew his Aristotle, put this into mathematical form. He introduced, in open opposition to Newton, a version of the calculus which served to open alternative path into not just modern physics, but modern thought more generally.

As a result, we can discern two very different, parallel pathways through the history of western thought – one leading to Newton, Descartes, and a world of force, competition and mechanism; the other, prefigured by Aristotle, leading to wholeness, cooperation, friendship and life.

The path through Newton, Locke and Hobbes is very familiar to us; it has led t the world we know today, a world of strife, competition, and ever-escalating warfare. That other thread, which runs from Leibniz, Euler, Lagrange, Hamilton, Faraday, Maxwell and Einstein, bespeaks unity and intelligent cooperation. Within physics, this appears especially in the concept of the field; but more generally, it looks to a society of intelligent cooperation in the solution of our common human problems. It is easy to see, I believe, which is better suited to address the problems of warfare and environmental catastrophe which beset human society today.

Nobody, of course, is offering us this choice of roads into the future.  But we have independent minds, and it would be good to know that there is a difference in principle even if we see no way at present to pursue it in practice. I propose to write more about this in upcoming postings – and it will be good to know what others think of this Aristotelian way I’m convinced I’m seeing.

"Faraday's Mathematics"

“Faraday’s Mathematics” is a lecture I gave at at a conference on Faraday at St. John’s College in Annapolis.  Its subtitle is “On Getting Allong Without Euclid”, for Faraday had neither studied Euclid, nor taken on board the plan of formal demonstration which most of us learn from the study of geometry.  In short, Faraday thought in his own way, following the lead of nature and experiment.  He was in effect  liberated from the presuppositions about thought and physical theory with which others in the scientific community were encumbered. 

 The result was that Faraday hit on a fundamentally new way of understanding the phenomena of electricity and magnetism – by way of the new concept of the “field”. Maxwell deeply respected Faraday’s way, and dedicated much of his own life to comprehending how Faraday worked, and what it was that Faraday had done.  The field is a fully connected system, and fields interact, not by way of their parts, but as wholes.  This was clear enough to Faraday, but it required recourse to a new sort of mathematics – Lagrangian theory – and a major reversal of conventional thinking, to articulate a formal theory in which the whole is primary, and with it a new rhetoric of explanation.   This was Maxwell’s accomplishment in his Treatise on Electricity and Magnetism, a transformation I trace as a rhetorical adventure in my book Figures of Thought.

  In the end, Maxwell emerged with the astonishing claim that of them all, it was the uneducated Faraday who was the real mathematician.  If that could be so, what is mathematics?   That’s the question pursued in this lecture, which aims to find out what Maxwell could have meant.

Maxwell was clearly in earnest, and seems to be pointing to a mathematics embodied in nature, which lies deeper than either its symbolic or its logical forms.

"Reason", Old and New

Somewhere in the course of our western history, something fundamental has been lost: we have lost track of the wholeness of the psyche, and its membership; in a world which was whole and in which it might feel at home.   

Where did this happen?  The psyche was whole in Athens – its membership in the family, the polis and the cosmos were so presupposed that there were perhaps no words to express the separation and fragmentation so vivid to us today.   I don’t think there was a word for “objective” or “subjective”, nor was there a mind which might be thought of as a blank tablet, upon which an outside world might write. In society there was work, but no word for “job”, with the radical alienation that term implies.  I’m not suggesting life was in any sense idyllic – only that for better or for worse, the psyche was intact, and seated in the world. 

I’ll leave it to others to explain how this has come about, but somehow we now find ourselves equipped with a mind which is well-furnished with knowledge, indeed, but all too easily likened to a calculative engine, with a memory bank stored with data from an “outside” world.  We understand the mind better and better – but only as a marvelously equipped machine.  

What is missing would seem to be that faculty once called “intellectual intuition” – the power to see directly and immediately, without the intervention of words, truths which are timeless and fundamental.  That old intellect -- for which the Greeks did have a word: NOUS -- was inherentlyi drawn to beauty, which it deeply loved. 

I don’t see this as an exercise in nostalgia: there are ways open to us today by which we can recover this power, which is perhaps rather hidden than lost.  Other cultures have preserved it in ways we haven’t, and we have much to learn from them.  To a large extent it is our conception of “modern science” which denies the evidence of intuitive reason, and reduces the concept of “reason” to accurate symbolic calculation.  But there is another way within modern science, equally mathematical and rigorous, but founded in a concept of wholeness, and looking to the whole rather than the parts as the ground of “explanation”.  I have spoken about this way – the “Pinciple of Least Action” -- in my lecture, “The Dialectical Laboratory”, elsewhere on this website.   

Nothing prevents, I believe, our mending this split between that classic concept of intuitive reason, seated in the world and knowing and loving truth directly -- and the concept current today of reason as a calculative engine making what it can of an “outside” world.   We need only retrace our steps and pick up that thread of truth wherever we dropped it.  Not easy to do, of course, but worth every effort!

Any suggestions as to how to begin? 

The Deep Roots of “Western Science”

I’m very excited to have been invited to participate in the Cosmic Serpent project, which will be exploring the relationships – likenesses and differences – between Indigenous views of Nature, and the world-view of “western science”.

My first thought about this is that what we are accustomed to calling “western science” is not one well-defined, monolithic structure, but rather a growing and changing, organic body including strongly contrasting strands and a deep tap root which reaches far back in history to ancient Greece and beyond.

It is this richness and diversity of our present notion of “science”, together with its vigorous signs of growth, which make the Cosmic Serpent conversation something far more than a confrontation of two distinct ideas. Whether there’s the same degree of diversity and growth within Indigenous approaches to Nature is something I don’t pretend to know, but the coming conversation may reveal.

I feel impelled to say something more about that deep “tap root” of modern science, as it lies close to my heart and has been the subject of much that I’ve thought about and written. (I wrote about one aspect of it in the lecture “The Dialectical Laboratory”, elsewhere on this website.) For me, as we look backwards from our present stance toward a distant past, it is Leibniz who’s the key. Between Leibniz and Newton lay a split far more important than the question of prioty in laying the foundations of the calculus usually referred to. In ways not always recognized, Newton was looking to Christian scripture, especially the Old Testament, when he placed the notion of “law” at the foundation of his Principia. Leibniz, by contrast, was looking to Aristotle and saw intelligible principle – not “?law” – as the basis of our approach to Nature. Two of Leibniz’ crucial terms: energy – potential and actual – come straight from Aristotle’s Physics, and remain to this day beacons of an alternative path in physics. Not forces between particles, the dominant concept of the mechanical view of Nature – but motions of whole systems guided by principles rightly thought of as holistic – set this other course. It becomes formulated mathematically as the law of least action, which evolves in turn into the equations of Lagrange and Hamilton, and in general into the Variational approach to natural motions. It is an approach inherently compatible with the notion of TELOS, or goal. In a broader arena, it is at home, for example, with Gestalt theory in psychology and the theory – at once of art and science – which Goethe sets over against that of Newton in his Farbenlehre, the Theory of Color.

For the practicing physicist, the Newtonian and the Lagrangian methods may seem convenient alternatives to be called upon as occasion demands. But in truth they reach very deep into alternative conceptions of the natural world and its ways. As I explore in Figures of Thought, it was not for convenience but out of deep conviction that Maxwell chose the Lagrangian approach in his own development of the equations of the electromagnetic field in his Treatise on Electricity and Magnetism. That this is an issue for human thought in general, and not a problem whithin mathematical physics alone, is shown beautifully by the fact that Maxwell chose the Lagrangian method as the way to express within mathematics the insights of Michael Faraday, who knew, and wanted to know, no mathamatics.

I have to acknowledge that there’s a manifest contradiction in what I’ve just written: I spoke at the outset of one “tap root” of science, but this whole discussion has been of two: one Newton’s, and the other that of Leibniz. I’m convinced these two lead back, by way of Alexandria, to one lying still deeper – but that must be the subject of another “blog”!