PHILOSOPHICAL EGGS

The enlightenment philosopher and polymath G. W. Leibniz (1646-1716) was a master at articulating various general and fundamental principles and applying these principles to philosophical problems. Principles are statements of basic laws, truths, or rules from which other laws, truths, or rules are derived. In this post I want to (1) show how Leibniz’s principle of continuity requires that we accept the existence of what he refers to as mikron or imperceptible changes and (2) develop a suggestion he makes about how these changes relate to politics. I share these ideas because I think they can help us in our ongoing efforts to reduce the widespread polarization, demonization, and lack of civility around us.

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The principle of continuity asserts, as he puts it in his Discourse on Metaphysics (1686), that “nature never makes leaps” (see Discourse on Metaphysics and Other Essays, Hackett Publishing, p. 56). This “entails that one always passes from the small to the large and back again through what lies between, both in degrees and in parts, and that a motion never arises immediately from rest nor is it reduced to rest except through a lesser motion” (56). To think otherwise is “to know little of the immense subtlety of things, which always and everywhere involves an actual infinity” (57).

This principle has an impressive scope of application. For example, Leibniz claims it shows that atoms (in the literal meaning of indivisible objects) are unintelligible. He observes that when one thing collides with another and moves another, the movement can only take place continuously if each object has parts that are in turn made of parts, etc.  It is the movement of these parts, however subtle and unseen, that allows for the continuous and partially elastic movement that is experienced in the collision. If atoms exist then they have no parts and therefore their movement—whether acceleration or deceleration—would not occur in a gradual, continuous manner as their internal parts shift this way and that; rather, their movement would be an immediate leap from one state to another unconnected to any previous event. Indeed, the leap would be preceded by nothing which would violate another of Leibniz’s favorite principles, the principle of sufficient reason, which asserts that for every fact and true proposition there is a sufficient reason why it is thus and not otherwise (see his Monadology section 32). This would leave us with absurd motions with no explanation – something obviously devastating for science.

He also argues against the idea that a thing could become completely inactive. For then when it does act we would have an action that, rather than arising continuously, would be a discontinuous leap. Similarly, a soul with absolutely no thought at all is unintelligible. For then conscious thought would be a leap from non-thinking to thinking. So Leibniz postulates the existence of unconscious thought out of which conscious thought can continuously arise (Leibniz thereby made use of unconscious thought some 200 years before Freud). Leibniz also claims that “because of insensible variations, two individual things cannot be perfectly alike and must always differ in something over and above number” (57). Forms may seem to be the same but, upon closer inspection with a microscope, we will see that endless variations exist. Thus our knowledge that insensible perceptions exist “serves to explain why and how two souls of the same species, whether human or otherwise, never leave the hands of the creator perfectly alike, and why and how each of them always has its original relation to the point of view it will have in the universe” (58). Perhaps most interestingly, the principle of continuity, in ruling out gaps or any kind of void in the universe, implies that nothing exists in isolation and that every agent affects, and is affected by, everything else: “All things conspire” (sympnoia panta) as the ancient Greek Hippocrates asserted (Monadology section 61). In fact, Leibniz goes further and claims that “each simple substance has relations that express all the others, and consequently, that each simple substance is a perpetual, living mirror of the universe” (Monadology, section 56). Naturally, in all these examples we will not necessarily perceive the continuities that exist. But they must be there as imperceptible changes if our experience is to be rationally intelligible.

An image of a unique leaf under a microscope. As Leibniz says, “Never are two eggs, two leaves, or two blades of grass in a garden to be found exactly similar to each other.”

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Now the details of this principle and its applications are not always clear. Indeed, in his book The Philosophy of Leibniz: Metaphysics and Language (Oxford, 1986) Benson Mates points out that “As is only too obvious, none of these formulations and applications of the principle of Continuity is quite clear. Instead of having a good understanding of the principle and its consequences, and of seeing just how the consequences follow from it, we have to use, as an aid to interpretation, the fact that Leibniz thought such logical relationships obtained” (165; see chapter 9, section 3 for an analysis of the principle of continuity). But I think the above gives us enough understanding to see how the principle of continuity can be applied to politics. We can approach this application with the help of this interesting passage:

“If we thought in earnest that things we do not consciously perceive are not in the soul or in the body, we would fail in philosophy as in politics, by neglecting the mikron, imperceptible changes. But an abstraction is not an error, provided we know that what we are ignoring is really there. This is similar to what mathematicians do when they talk about the perfect lines they propose to us, uniform motions and other regular effects, although matter (that is, the mixture of the effects of the surrounding infinity) always provides some exception. We proceed in this way in order to distinguish various considerations and, as far as is possible, to reduce effects to their reasons, and foresee some of their consequences. For the more careful we are not to neglect any consideration we can subject to rules, the more closely practice corresponds to theory. But only the supreme reason, which nothing escapes, can distinctly understand the whole infinite, all the reasons, and all the consequences” (57).

Since we are in a world full of infinite gradations and continuous complexity, since we are in a world of imperceptible changes or mikron, we must be incredibly vigilant as we employ useful abstractions in our language, diagrams, models, ideas, etc. Simplifying things has a place as long as we are aware that we are simplifying. But when it comes to truly understanding the nature of things we must be acutely aware of how our simplifications, and indeed all our intellectual efforts, are bound misrepresent the infinite continuities of the world which only God’s supreme reason can fathom. And, as he says, we are bound to fail in politics.

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As we all know, we currently live in a highly politicized world permeated with differences that divide people and make them think they have little or nothing in common. Such thoughts lead people to sort themselves into like-minded and exclusive groups where they become more extreme versions of themselves and judge others as the extremists. Fascism is an extreme version of this group polarization dynamic insofar as it requires a strictly exclusive form of nationalism. It also requires a comprehensive negation of individuality. In her classic work The Origins of Totalitarianism (second edition, Harcourt Brace Jovanovich, 1968), Hannah Arendt observed that fascism seeks “Total domination, which strives to organize the infinite plurality and differentiations of human beings as if all of humanity were just one individual is possible only if each and every person can be reduced to a never-changing identity of reactions, so that each of these bundles of reaction can be exchanged at random for any other” (438). 

Nazi Nuremberg rally: so-called uniformity concealing the mikron which insures unique individuality and undermines dreams of exclusivity and superiority

But given the implications of the principle of continuity sketched above, we can see that this dehumanizing pathology of uniformity is doomed since no two people are the same and everyone’s perspective on the world matters. And exclusive nationalism and appeals to a master race discontinuous with others are doomed as well since the fact that “all things conspire” means humans are connected both genetically, psychologically, culturally, and, as far as Leibniz is concerned, spiritually. So, whether we are talking about fascism or less extreme forms of polarization, a world full of continuity and the mikron implies the uniqueness of every individual and “always provides some exception” to our inadequate labels and stereotypes. And its interconnections imply points of contact between all of us whether we realize it or not. These two insights can help us cultivate many things helpful to political action, namely, a sensitivity to context, a belief in unique individuals with unique perspectives, a suspicion of generalizations, and a realization that ongoing inquiry with others is crucial since we are all finite and fallible beings enmeshed in a world of infinite changes.

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Towards the end of his essay On the Ultimate Origination of Things (1697), Leibniz makes the optimistic claim that there is unbounded progress in the universe despite various temporary setbacks. This fits well with his Christianity and vision of a world governed by a God who created the best of all possible worlds. But he also thinks it follows from his principle of continuity as his concluding words show:

“And there is a ready answer to the objection that if this were so, then the world should have become Paradise long ago. Many substances have already attained great perfection. However, because of the infinite divisibility of the continuum, there are always parts asleep in the abyss of things, yet to be roused and yet to be advanced to greater and better things, advanced, in a word, to greater cultivation. Thus, progress never comes to an end” (48).

In a world of the mikron we can never say never since there is always the possibility that some new way, some new set of relationships, some new dynamics asleep in the abyss of things will awaken and make for a more beautiful world. However, Leibniz didn’t think our happiness is found in reaching a state of stable success. Rather, he thought, in accordance with the principle of continuity itself, that our happiness lies in the very activity of striving – continuously striving – for perfection. Perfection for Leibniz is an optimal combination of variety and order: as much diversity of life as possible with as few underlying laws as possible. This ideal certainly guides scientific inquiry (for example in the search for a theory of everything). But it should also guide those in politics to maximize as much human freedom as possible within the confines of a simple set of just laws. Societies guided by the law of continuity should strive to be more interconnected, diverse, and just rather than disconnected, homogenized, and unjust.

Of course, this is no easy task and it is all too easy to become cynical in the face of the world’s problems. But Leibniz’s principle of continuity offers us hope by reminding us that the causes for our cynicism, while real enough to us from our limited perspective, may be hiding ongoing advancements that will surprise us if we remain open and seek to cultivate them whenever possible. To think otherwise is, as we saw above, to know little “of the immense subtlety of things, which always and everywhere involves an actual infinity” (57).

A page from Leibniz’s notes on calculus which he invented (independently of Newton) and which mathematically expresses his principle of continuity. Nicholas Rescher, in his essay “Leibniz and the Concept of a System,” points out how it also expresses Leibniz’s new vision of a system based on his vision of perfection: “For him, the ideal model of a cognitive system was provided not by the geometry of the ancient Greeks but by the physics of seventeenth century Europe. In his view, the calculus was not just a convenient mechanism for solving mathematical problems, it provided a new model of rational systematization, for implementing that “principle of determination in nature which must be sought by maxima and minima.” Such an instrument provides, as Leibniz saw it, a tool for discerning, amidst an infinite variety of diverse phenomena, those operative principles (e.g., Snell’s law in optics) through which the desiderata of rational economy are instituted in the nature of things. With the Euclidian axiomatization we have a finite basis of elements (axioms and definitions) from which these are extracted by finite deductive processes. With the calculus-and especially the calculus of variations-we are put in a position of being able to survey an infinite range of alternatives and to discern amidst a literally endless variety of possibilities those particular determinatives indicated by the principles of rational economy. Here, with this system-oriented resort to the mechanism of the calculus, we once again see at work the thought of Leibniz a Renaissance-inspired busting of the classical bonds.” See his book On Leibniz (University of Pittsburgh Press, 2003), p. 115.

For my other posts on Leibniz, go here.