This piece is also published by Miskatonian.
Baron Gottfried Wilhelm von Leibniz (1646-1716) was a remarkable man. During his life, he made seminal contributions to a wide variety of fields of study, including mathematics, physics, technology, philosophy, theology, philology, politics, library science, and others. Alongside Sir Isaac Newton, he is credited with the invention of calculus, in addition to statistics and binary arithmetic, the latter of which is the foundation of computer science. Leibniz was also a committed man of Christian faith; he saw the East-West Schism (1054 ᴀ.ᴅ.) as a great tragedy, and hoped his own life's work might contribute to the reunification of Christendom.
Since the beginning of this year, I have been reading a volume called Basic Writings, which includes Leibniz’s texts Monadology, Discourse on Metaphysics, and a series of letters exchanged between himself and the distinguished French Catholic priest and theologian Antoine Arnauld which discuss the contents of the Discourse on Metaphysics. These texts deal with the most fundamental questions of metaphysics: the nature of being, knowledge, substance, cause, and other such concepts.
The introduction to my edition was written by Paul Janet (1823-1899), a French philosopher and writer. Janet writes with sharp clarity and provides helpful background knowledge for the reader of Leibniz's texts, including a thorough exploration of the Peripatetics' theory of substantial forms. This theory was dominant during the first half of the seventeenth century, during which time René Descartes lived and worked.
According to Janet, the Peripatetics proposed that “in each kind of substance [there is] a special entity which constitute[s] the reality and the specific difference of that substance independently of the relation of its parts” (Leibniz VII). Janet continues on to say that “the theory of substantial or accidental forms introduced errors which stood in the way of any clear investigation of real causes” (Leibniz IX).
Descartes disagreed with the Peripatetics, proposing that, instead, there are “only two kinds of things or substances in nature, namely, extended substances and thinking substances, or bodies and spirits; that, in bodies, everything is reducible to extension with its modifications of form, divisibility, rest and motion, while in the soul everything is reducible to thinking with its various modes of pleasure, pain, affirmation, reason, will, etc.” Janet tells us that Descartes “reduced all nature to a vast mechanism, outside of which there is nothing but the soul which manifests itself in existence and its independence through the consciousness of its thinking.” Janet tells us that this proposal is the most important revolution in modern philosophy (Leibniz VII).
When I first read this passage, I found it fairly intelligible, except for the term “extension.” After doing some preliminary search-engine reading, I discovered that Descartes defines “extension” to mean “the property of existing in more than one dimension;” we might also think of this concept as “spatial occupation.” As I continued on, I discovered the relevance of this discussion: while Leibniz “affirmed that everything in nature could be explained mechanically,” he strongly disagreed with Descartes’ awarding extension the privileged position as the defining characteristic of material substance (Leibniz XI). Leibniz said, no, force takes precedence.
Janet provides the following five bullet points explaining Leibniz’s contention:
Bodies cannot be essentially passive, because when “a body in motion comes into contact with one at rest, it loses some of its velocity and its direction is modified.” Thus, “higher conceptions must therefore be added to extension, namely, the conceptions of substance, action and force” (Leibniz XII).
Extension is not sufficient to explain changes which take place in bodies, particularly displacements in space or motion. The space occupied by a body must be treated as a subsidiary characteristic to some deeper quality (Leibniz XIII).
Extension cannot be substance, because “there must be a subject which is extended, that is, a substance to which continuity appertains.” Extension presupposes substance (Leibniz XIII).
Unity is a necessary characteristic of substance, because a compound is never a substance. If one took two stones and soldered them together, the nature of these two stones will not be changed; they are still two separate stones. Thus, “it must be admitted that [substantial reality] is reducible to simple and consequently unextended elements” (Leibniz XIV).
The essence of every substance is in force because “a being only exists in so far as it acts.” A being in an absolutely passive state would be a “pure nothing,” as it would have no characteristics or attributes. Being is rooted in activity (Leibniz XIV).
Janet’s writing served as an outstanding prolegomenon and it prepared me quite thoroughly for the conversations taking place in the book itself. Once I finished reading this introduction, a thought occurred to me: what if I had not read this? In what state would I be, attempting to sift through this dense volume of philosophy, had this great gift of disambiguation not been bestowed upon me? Thus, we reach the thesis of this essay.
When you begin reading a new book, carefully read the introduction, the editor’s note, the prologue – read all of the sequentially appropriate preliminary material. You may uncover gems of comprehension as I did, and even if you don’t, it is worth it to make the effort.
Artwork for Simultan by Roland Kayn (1977)
Leibniz, Gottfried Wilhelm. Basic Writings. The Open Court Publishing Company, 1968.
Leibniz seems to variously anticipate both relativity and modern field theories, though translating from his language to modern theory is difficult enough that it's hard to infer how well the correspondence works. The "extension" idea seems very much like what we would call "volume" today, as the property of an object (which he'd distinguish from any property of empty space).
Volume is mostly a function of quantum statistics rather than what we'd call "force" in the intro-physics sense, though I think statistical interactions would fall under the larger umbrella that Leibniz means in his use of the word force. Electrons define volume (and photons do not) because of fermionic statistics, not because of "mass" -- massless fermions would define a volume in a way that massive bosons could not. That seems like an essential vindication of relational views of spatial extension.