Salvo 03.18.2021 15 minutes

How Modern Math Spawned Woke Ethics

A figure representing pythagorean theorem,  a right angled triangle formed with the joined vertices of three squares over a green colored black board

Philosophy is downstream from geometry.

In our era, ideas that until quite recently would have bordered on insane have become thoroughly entrenched in academia and, increasingly, government. The “woke” ruling classes implicitly understand—as in all the cultural revolutions of history—that their power depends on punitively enforcing falsehoods. How could this have happened, so rapidly and so pervasively? How could the accrued common wisdom of mankind have come so quickly to be regarded by so many as not only false, but deeply pernicious?

Insightful contemporary writers like Carl Trueman, Yuval Levin, and others have drawn on the resources of important 20th-century theorists like Charles Taylor and Philip Rieff to explain the rise of the “modern self” and its susceptibility to the delusions of woke politics. While their analysis is helpful, I believe that the true origins of these changes actually go much deeper and further back to the beginnings of modernity itself.

The radical claims of our fevered age are rooted in what might initially seem to be the unlikely soil of early modern philosophy. The radical way that the early moderns reconceived the possibility of knowledge itself made the later cultural and political changes possible. It is sometimes claimed that politics is downstream from culture, but it is also the case that culture is ultimately downstream from epistemology and metaphysics.  

For ideas to have long-lasting consequences, they must become embodied with a culture. The consequences of early modern philosophy lie not just in the ideas it produced, but in the transformation of society it enabled through the subsequent explosion of modern technology. We now live a new “ethics of modernity” that has habituated nearly all of us to modes of life and ways of being that are fundamentally alienated from human nature as traditionally understood. To see this, however, will require us to delve into the fundamental nature of the modern project, and then explore how that initially elite early modern philosophical ethos became fundamentally “democratized” through the pervasive expansion of technology throughout all of everyday life.

The late David Lachterman’s brilliant but now sadly neglected Ethics of Geometry is a particularly helpful resource for understanding the radical changes of the early modern period. In contrast with the earlier tradition, he argues that the early modern thinkers sought to re-establish the foundations of human knowledge on the model of “construction” borrowed from the (then) new mathematics.

For Descartes, the fundamental problem with the Aristotelian tradition of philosophy was its failure to live up to a mathematical standard of certainty. He compares that tradition to “magnificent palaces” built on “sand and mud” since its central principles fail to meet the standards of knowledge set by the new mathematics. In the First Critique, Kant tells a similar story, pitching his “transcendental philosophy” as the key to establishing metaphysics on the “secure path of a science.” Modern philosophy presents mathematics as the gold standard of human knowledge—indeed the only true examples of knowledge at all in the pre-modern history of the West.

While this is a familiar theme to students of the history of philosophy, Lachterman’s key innovation is to argue that the transformation of modern philosophy is actually secondary to the transformation of modern mathematics. Contrary to the standard histories that regard modern mathematics as simply a development of the ancient approach, Lachterman argues that modern mathematics “is essentially occupied with the solution of problems, not with the proof of theorems,” and so, for the moderns, “mathematics is most fertilely pursued as the ‘construction of problems or equations’—that is, as the transposition of mathematical intelligibility and certainty from the algebraic to the geometrical domain, or from the interior forum of the mind to the external forum of space and body.” In other words, where the old mathematics described what its practitioners saw as immutable and given in the world around them, in the new mathematics it is the practitioners’ ideas that are primary. The culmination of the modern project seek to conform the world to the mind instead of the mind to the world.

This marks a revolutionary break. For the Greeks, “the source of the intelligibility of the figure…is the nature of the figure in its own right.” For the moderns, “it is to be found in the strategies and tactics certain to bring the figure into visible or ‘bodily’ being. A distinction in the manner of knowing entails a difference in the mode of being” (emphasis added).

Shaping Thought

In the older tradition, the geometrical task was really geometrical; that is, it takes off from the physical reality of the figure available to us, at least in some important respects, through the senses. The new methodology, by contrast, seeks to reconstruct the “figure” as “represented” within the new science of analytical (algebraic) geometry. While most believe that the modern methods just give more precise expression to what the ancients had approximated, Lachterman’s suggestion is that the modern method of knowing actually “entails a difference in the mode of being.” That is, the subject matter of modern mathematics is simply not the same as that of ancient mathematics.

As modern mathematics grew and developed, the emphasis shifted from Euclidian deduction to the now customary methods of symbolization and formalization we all learned in school. Formal logic also later underwent a similar change. In an Aristotelian syllogism, the truth of the premises was thought to actually cause the truth of the conclusion. By contrast, in modern symbolic logic, the relationships within valid argument forms are entirely formal. Those formal systems unfold according to internally consistent rules, but the relationships are not regarded as causal.

The significance of these changes is not restricted to abstruse philosophical debates in epistemology. They have become embodied in the success of the modern sciences over Aristotelian physics. For instance, Bacon complains in the New Organon that the lack of new “inventions” offers proof enough of the deficiency of the Aristotelian system. Our age of course teems with new inventions. There is no question that if the standard of scientific progress is the production of technology and the power it offers to make us “lords and masters of nature” (Descartes), then modern systems are unquestionably superior. One of the essential keys to this superiority has been the development of the new mathematical “models” we use to manipulate and control nature in continually unprecedented ways. While the ancients could stack the massive Pyramids through sheer determination and the medievals could fashion the stunning elegance of Chartres through unparalleled craftsmanship, only the moderns could bind the entire planet (and beyond) into what is essentially a single interconnected electro-mechanical system.

It is less immediately clear, however, that this new technical mastery in fact resulted a new “ethics.” In the Meditations, Descartes acknowledges that while mankind is far inferior to God in intellect, “strictly in itself, God’s will does not seem any greater than mine.” The will, taken in itself, is boundless: this is fundamental to the modern understanding of knowledge as power. “To be ‘modern’ in the most exacting and exalting sense,” writes Lachterman, “is to be carried along this trajectory from mathematical construction (in its precise technical sense) to self-deification. The mind is not nature’s mirror; it is nature’s generative or creative source.” Inevitably, the dominance of the will over the intellect not only inverts the traditional priority of speculative over practical reason, but also produces in us a fundamentally new comportment to the world; that is, a new ethics.

In the earlier philosophical tradition, ethics was primarily concerned with the development of a particular kind of character rather than a way of evaluating the moral permissibility of an action. We retain some of this in our directly borrowed term ethos, which even in English signifies a way things are done within a particular cultural context. The root sense of ethos is tied to what is customary or ordinary in a particular place or culture. To be “ethical” is to be the sort of person (i.e. to have the sort of character) that is characteristic of a place or culture. This reflects the fact that the way we live in some particular time and place is deeply formative of who we are and what we become. What is “normal” in the conditions of our daily lives determines the kind of people we are. Of course, as those conditions change, we are changed along with them, whether we are directly conscious of this or not.

The new ethics of modernity has taken hold by transforming the conditions of our normal lives. This modern ethos underwrites, or even demands, the exponential growth of technology into an ever-accelerating feedback loop, unfolding according to its own internal logic and lack of constraints. Lachterman’s original notion of an “ethics of geometry” embodied in early modern philosophy has become democratized through the explosion of technology in our lives. The “way of being” that was inaugurated with the rise of early modern mathematics has now become now the default way of life of contemporary mankind.

Modeling Reality

We moderns now live in a world of “models”: climate models, economic models, digital models of all sorts. In the past, this kind of thinking was much more restricted simply owing to the sheer intellectual complexity involved; in the 17th century it required the genius of a Descartes to think in these terms. However, today’s technology allows the externalization of most of the intellectual heavy lifting. The construction of digital models, complete with sophisticated physics engines, is now literally child’s play.

This is how the early modern mode of philosophy has become democratized in our age. It is no longer the exclusive purview of those with the intellectual capacity to reconceive the world in mathematical terms. Instead, we are nearly all required to participate in it, even if we do not really understand what actually goes into the models or how they are constructed. The complexity becomes hidden from us by being incorporated into the tools we use on a daily basis, and especially by being presupposed by the default modes of explanation offered by nearly everyone around us. As we grow habituated to this mode of life, we become transformed by it, and now unconsciously comport ourselves more to representations that fit our models and less to the realities to which the models putatively correspond.

This is why we can be said to be living a new “ethics.” Without thinking much about it, we become what we are habituated to be through the intellectual tools that nearly everyone uses to frame almost all of our discussions. Political, cultural, even artistic explanations are framed in these terms, so much so that they become the only currency for explanation available to us. It has simply become the way we speak and think; it is our “normal”; it is common sense.  

It is precisely this kind of distancing between model and reality that enables us to even take seriously, much less believe, a “woke” claim like someone is actually a “woman in a man’s body.” As we become more and more accustomed to living in a world of models, we eventually see ourselves and our own bodies as part of our own self-generated abstractions. This ethos also explains why “intellectuals” were originally more readily drawn into thinking this way than “normal” people. People who work with their hands are much more intimately familiar with the straightforward intransigence of material reality to the human will. Wood, steel, and stone will ultimately yield, but only after a great deal of effort and a deep understanding of their proper natures. Master craftsmen become so only because they accustom themselves to the intrinsic properties of their materials and tools.

In our age, however, the intellectuals have truly become the vanguard of the proletariat, not in the Leninist conception by leading the working class to their supposed liberation in Socialism, but in that ways of thinking that once primarily characterized the intellectuals have now become universal. As more and more “normal” people do jobs that primarily involve the manipulation of intellectual and mathematical models, instead of the literal imposition of form on matter, the “proletariat” itself becomes intellectualized. The Marxist proletariat putatively arose from the alienation of labor from meaningful work. Traditional skilled craftsmen were replaced by “wage slaves” doing low-skill labor within industrialized economies. We have largely exported much of that alienation overseas, but in the daily lives of our new economies we now find ourselves facing a new and deeper alienation from human nature itself.

We are in the midst of political and cultural controversies over issues that would have seemed practically unthinkable just a scant few years ago. The plausibility structures of our lives have been radically transformed in ways that would have beggared belief even for the early modern philosophers. Seeing how the ethics of modernity has opened the door to our present woke debates, however, suggests that our contemporary controversies around gender and sex are mere precursors to even more radical changes to come. If something like “transgenderism” can go from Bedlam to the Whitehouse in just a couple of decades, it is not difficult to imagine what “transgressive” innovations are next, from engineered children with three or more genetic “parents” to the possibility of chimeras (human-animal genetic hybrids) and other posthuman and transhuman nightmares.

The ethics of modernity is truly a Faustian bargain. We have traded knowledge and power for a deep alienation from Nature. I noted earlier Descartes’ claim that the human will is as unlimited as God’s. If that is true then nothing must hold it back, not even death itself. This is the true meaning of the modern project: the quest for immortality was built into it from the beginning. Descartes himself alludes to the possibility, and it’s the driving force behind the radical experiments in contemporary transhumanism. Of course, that pursuit is actually the supreme alienation from human nature. It is a flight from the fact of human finitude and contingency. It is, indeed, man’s ultimate non serviam to Nature and Nature’s God.

Today’s woke convulsions are only the most recent expression of the unfolding of the modern ethos. The ethics of modernity reigns supreme in our age and there is no obvious path to return to sanity. However, as has been aptly observed: what cannot go on forever will not go on forever. Despite everything, the true limits are what they have always been: the contours of a human nature (and an objective reality as a whole) entirely apart from our wills. However, until we can rebuild and recover cultures that embody the perennial and truly multicultural understanding of what it means to be human, I fear we will continue headlong down the path of madness we now seem determined to tread.

The American Mind presents a range of perspectives. Views are writers’ own and do not necessarily represent those of The Claremont Institute.

The American Mind is a publication of the Claremont Institute, a non-profit 501(c)(3) organization, dedicated to restoring the principles of the American Founding to their rightful, preeminent authority in our national life. Interested in supporting our work? Gifts to the Claremont Institute are tax-deductible.

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