The Structure of Experience: A Hegelian Reading of Leibniz’s Mill

In §17 of The Monadology, there is an elegant, notorious, and, to my dismay, all too often misunderstood, gedankenexperiment—Leibniz’s Mill:

“It must be confessed, however, that Perception, and that which depends upon it, are inexplicable by mechanical causes, that is to say, by figures and motions. Supposing that there were a machine whose structure produced thought, sensation, and perception, we could conceive of it as increased in size with the same proportions until one was able to enter into its interior, as he would into a mill. Now, on going into it he would find only pieces working upon one another, but never would he find anything to explain Perception. It is accordingly in the simple substance, and not in the composite nor in a machine that the Perception is to be sought. Furthermore, there is nothing besides perceptions and their changes to be found in the simple substance. And it is in these alone that all the internal activities of the simple substances can consist.” (Leibniz, The Monadology, §17)

To better understand Leibniz’s Mill, let’s consult the previous sections of The Monadology where Leibniz emphasizes the fact that the “self-differentiated” structure of Experience (i.e., “perception”) is a “multiplicity-in-unity”—it is “internally-differentiated.”

“Now besides this principle of change there must also be in the Monad a manifoldness which changes. This manifoldness constitutes, so to speak, the specific nature and the variety of the simple substances….This manifoldness must involve multiplicity in the unity or in that which is simple….The passing condition which involves and represents a multiplicity in the unity, or in the simple substance, is nothing else than what is called Perception….We, ourselves, experience a multiplicity in a simple substance, when we find that the most trifling thought of which we are conscious involves a variety in the object.” (Leibniz, The Monadology, §12-§16)

Before continuing, it is necessary to sketch the nature of Experience and Matter. Now, there is an important likeness between Experience and Matter: both are “self-differentiated.” However, there are distinctive characteristics peculiar to Experience and Matter’s respective “self-differentiations.” Experience must be conceived as a particular unity-of-the-manifold. Indeed, as F.H. Bradley once put it, Experience is “a unity of the manifold in which the externality of the manifold has utterly ceased.” Experience is exhaustively self-differentiated “into-itself” (i.e.., “Partes intra partes”), whereas Matter is exhaustively self-differentiated “out-of-itself” (i.e.., “Partes extra partes”). Hegel elegantly presents a concise illustration of this in his Introduction to the Philosophy of History and Philosophy of Mind:

“The nature of Spirit [i.e., Experience] may be understood by a glance at its direct opposite—Matter. As the essence of Matter is Gravity, so, on the other hand, we may affirm that the substance, the essence of Spirit is Freedom….Matter possesses gravity in virtue of its tendency toward a central point. It is essentially composite; consisting of parts that exclude each other. It seeks its Unity; and therefore exhibits itself as self-destructive, as verging toward its opposite [an indivisible point]. If it could attain this, it would be Matter no longer, it would have perished. It strives after the realization of its Idea; for in Unity it exists ideally. Spirit, on the contrary, may be defined as that which has its center in itself. It has not a unity outside itself, but has already found it; it exists in and with itself. Matter has its essence out of itself; Spirit is self-contained existence….This self-contained existence of Spirit is none other than self-consciousness—consciousness of one’s own being. Two things must be distinguished in consciousness; first, the fact that I know; secondly, what I know. In self-consciousness these are merged in one; for Spirit knows itself. It involves an appreciation of its own nature, as also an energy enabling it to realize itself; to make itself actually that which it is potentially.” (Hegel, Introduction to the Philosophy of History, 18) 

“The substance of mind is freedom, i.e., the absence of dependence on an Other, the relating of self to self. Mind...attains actuality not by fleeing from the Other but by overcoming it. Mind can step out of its abstract, self-existent universality, out of its simple self-relation, can posit within itself a determinate, actual difference, something other than the simple, “I,” and hence a negative; and this relation to the Other is, for mind, not merely possible but necessary, because it is through the Other and by the triumph over it, that mind...returns to itself out of its otherness...[and comes to be] the self-differentiating universal which in its difference is at home with itself and for itself. The Other...therefore also belongs to the nature of mind....In the Other, therefore, mind manifests only itself, its own nature; but this consists in self-manifestation. The manifestation of itself to itself is therefore itself the content of mind and not, as it were, only a form externally added to the content; consequently mind, by its manifestation, does not manifest a content different from its form, but manifests its form which expresses the entire content of mind, namely, its self-manifestation. In mind, therefore, form and content are identical with each other….[Mind] as such only is, in so far as it manifests itself to itself.” (Hegel, The Philosophy of Mind, §382-§383) 

“Accordingly, the peculiar quality of mind is rather to be the true infinite, that is, the infinite which does not one-sidedly stand over against the finite but contains the finite within itself as a moment. It is, therefore, meaningless to say: There are finite minds. Mind quâ mind is not finite, it has finitude within itself, but only as a finitude which is to be, and has been, reduced to a moment….[It] is therefore only in mind that we find…true infinitude. The very fact that we know a limitation is evidence that we are beyond it, evidence of our freedom from limitation. Natural objects are finite simply because their limitation does not exist for the objects themselves, but only for us who compare them with one another. We make ourselves finite by receiving an Other into our consciousness; but in the very fact of our knowing this Other we have transcended this limitation. Only he who does not know is limited, for he does not know his limitation; whereas he who knows the limitation knows it, not as a limitation of his knowing, but as something known, as something belonging to his knowledge; only the unknown would be a limitation of knowledge, whereas the known limitation, on the contrary, is not; therefore to know one’s limitation means to know of one’s unlimitedness. But when we pronounce mind to be unlimited, truly infinite, this does not mean that mind is free from any limitation whatsoever; on the contrary, we must recognize that mind must determine itself and so make itself finite, limit itself….Finitude, truly comprehended, is as we have said, contained in infinitude, limitation in the unlimited. Mind is, therefore, as well infinite as finite, and neither merely the one nor merely the other; in making itself finite it remains infinite, for it reduces the finitude within it to a mere moment….Only momentarily can mind seem to be fixed in a finite content; by its ideality it is raised above it, and it knows that the limitation is not a permanent one. It therefore transcends it…frees itself absolutely from the limitation, from its Other, and so attains to absolute being-for-self, makes itself truly infinite.” (Hegel, The Philosophy of Mind, §386)

Echoing Hegel, the British Idealist philosopher Edward Caird writes:

“We must, indeed, think of [Experience] as having life in itself and therefore as differentiating itself from itself; but this differentiation is held within the limit of its unity, it is a separation of movements which are separated only as they are united.” (Caird, Metaphysic, 434)

And again, we find a similar theme in Giovanni Gentile’s work:

“But by [the inwardness of consciousness] we do not mean to point to a specific part of space outside of which there would be another part....The [inwardness of consciousness] is nothing but the negation of the [outwardness that is characteristic of space]; but it is not the negation of the specific difference by which, for instance, the space outside a circle is distinguished from the space inside it. [On the contrary, the inwardness of consciousness is precisely the fact that, our consciousness of the insidedness and outsidedness of a given space] is the negation also of the proximate genus within a given space which may indifferently be called inside or outside, depending on whether the observer places himself inside or outside the circumference. Since in space all things are mutually external, everything can be reduced to a sum of parts or points alongside one another; there is nothing but the multiplicity of elements, every one of which is outside all the others. The externality, which is negated [through our being conscious of it], is not a relative but an absolute externality; and that which negates it is not a relative but an absolute inwardness. Within this absolute inwardness, which is characteristic of [our consciousness]…everything [of which we are conscious] becomes internal, that is to say everything which, from a spatial point of view, seemed outside us, intrinsically external by the multiplicity of its elements alongside one another.” (Gentile, The Philosophy of Art, 56-57)

Whereas Experience “has its center in itself,” Matter, by contrast, has its center “out of itself.” For, Matter is exhausted by the reciprocal exclusion and repulsion of its composite parts. All parts of Matter exemplify nothing other than flatness, out-spreadedness, and side-by-sidedness. Matter is never at home with itself; indeed, Matter is neither “transparent-to-itself,” nor does it return “into-itself” or “into-its-parts.” Matter is “opaque-to-itself.” Indeed, Matter is “simple” in all of its dimensions: the entirety of its character is determined by what lies “outside” it. 

Gyrating patterns of physical particles are, therefore, in toto, pervaded by a self-othering “side-by-sidedness.” Indeed, these events quâ “material happenings” (i.e., processes that “outspread” and “diffuse” themselves across an extended, spatio-temporal manifold) are what they are only insofar as their “unfoldings” are repulsions “out-of-themselves”—no one of these “repulsions” either being, or having, a “moment of return” (i.e., a differentiation or phase wherein there is an “overreaching,” “including,” or “enveloping” of the distinction between “itself” and its “other” within “itself”). For any such “material happening”—regardless of its peculiar kind or character—there is neither an “interpenetration,” nor a “mutual-inclusion,” of its manifold differentiations or phases; on the contrary, we only find its differentiations or phases “withdrawing-towards-Others” (i.e., “passing-out-of-themselves” at the expense of their own self-identity). However, these “Others”—the “beyonds” towards which the differentiations or phases of a “material happening” seek to “withdraw”—are themselves repulsions “out-of-themselves”—prolonging the monotony ad infinitum. 

The only spatial “representation” that might help us illustrate (pictorially) the “Partes intra partes” character of Experience would be a torus undergoing “hyperspace rotation” (i.e., rotating in a poloidal direction). Such a torus would be simultaneously “rotating-out-of-itself” and “rotating-into-itself, “moving-away-from-itself” and “moving-into-itself,” and “diffusing-itself-out-of-itself” and “infusing-itself-into-itself.” It is important to note that it is impossible for a physical object to undergo “hyperspace rotation” in a three-dimensional space without tearing itself apart. Here is an animation that I found which just so happens to represent what I have in mind:

Now, in order to grasp how the nature of Experience is analogous to a torus engaging in “hyperspace rotation,” we ought to replace the “spatial language” used in our illustration with expressions that best represent different modes of “differentiation.” Thus, we should understand Experience in its “Unity” as having been represented by the torus as a whole. Now, as mentioned above, Experience is exhaustively self-differentiated. We should understand Experience’s “exhaustive self-differentiation” (or Experience in its “Manyness”) as having been represented by the torus “rotating-out-of-itself.” However, Experience is not a mere “Many;” on the contrary, it is also a “One.” Thus, Experience is not merely “exhaustively self-differentiated,” rather Experience is exhaustively self-differentiated to, through, and for, itself (i.e., A manner or mode of differentiation that is a “differentiation-into-self”). We should understand Experience’s “exhaustive self-differentiation to, through, and for, itself” as having been represented by the torus “rotating-into-itself.”

We are thus able to see how Experience transcends, includes, and manifests itself as a Unity of Oneness and Manyness. Indeed, Experience simultaneously transcends and includes within itself, and expresses itself as, both Subject and Object. For, Subjectivity is Experience-in-its-Manyness “flowing” or “converging” into Experience-in-its-Unity. Objectivity is Experience-in-its-Unity “diffusing” or “differentiating-itself-out-of-itself” through Manyness. By “differentiating-itself-out-of-itself,” Experience manifests itself as Objectivity. In doing so, Experience’s manifold “differentiations-out-of-self” (i.e., Experience-in-its-Objectivity) flow or converge “inward” to, through, and for Experience-in-its-Subjectivity (i.e., the Subject). H.H. Joachim beautifully captures this “toroidal” character of Experience in the following illustration:

“[In self-consciousness] “I” am for myself a centre from which radiate, or a focus in which converge, certain rays of immediate consciousness….For all my experiences…are “immediately for me,” are “appropriations” of my inward spirituality: and thus considered they are rays streaming from, and converging into, the centre or focus which is myself….If “I” am a centre, my centrality is also its own circumference: and if I am a “focus,” the “focus” is one with the rays which it focuses.” (Joachim, Some Preliminary Considerations on Self-Identity, 53)

With that being said, I’ll conclude this brief essay by presenting my own adaptation of Leibniz’s Mill:

If we were to take infinitely many coplanar geometrical figures of various determinable shapes and sizes, and have them expand, contract, and move about for an infinite time, we can rest assured that no transformation, redistribution, pattern, or collision of said figures will ever yield a new figure with “cubical content”—a figure that not only exhibits a new dimension, but also envelops those aforementioned plane geometrical figures. Indeed, all qualitative changes and transformations in those figures—and patterns thereof—will always be determinate manifestations of a generic character—or determinable—that had hitherto manifested itself in another determinate form. If, after an infinite time, a change in the arrangement of those coplanar geometrical figures resulted in the manifestation of a new figure exhibiting “cubical content” and enveloping those aforementioned coplanar geometrical figures that gave rise to it, then said manifestation would be the manifestation of a new determinable that was itself “inclusive of” the former determinable, without itself being “included under it” as a determinate manifestation of said determinable. Such an incoherent and disparate breach of continuity is paralleled in the idea that—at some point in time—Experience was “birthed” by transformations and redistributions in Matter.

Leibniz’s Mill is a powerful and compelling illustration of the fact that qualitative changes and alterations in the structure and arrangement of material objects (e.g., transformations such as dilations, expansions, translations, rotations, reflections, etc.) cannot account for what would be the manifestation of a new determinable (hitherto unmanifested) that (i) exhibits an “internally-differentiated” structure (i.e., Or, to use Hegel’s words, is such that it “is distinguished within itself and returns from this difference into unity with itself”), and (ii) is “inclusive of” the material objects that are alleged to have given rise to it. This new determinable would be none other than Experience.