The Structure of Experience and the Beauty of Leibniz’s Mill

“[Leibniz’s Mill] is an instance of the phenomenological fallacy—the idea that if minds are brains, the brain would have to have the properties perceived.” (Digital Gnosis)

Unfortunately, this is a mistake. Leibniz, for all his faults and shortcomings, did not fall prey to the “phenomenological fallacy” when he penned §17 of The Monadology. To understand why he did not commit this fallacy—if it even is a “fallacy”—it would be helpful to go into what the “phenomenological fallacy” actually is. One commits the “phenomenological fallacy if they attribute the characteristics of an Experience’s “content” to the Experience itself. (e.g., Supposing that the “sensation of redness” is what is “red” or the “perception of blueness” is what is “blue”). The “phenomenological fallacy” was introduced by U.T. Place as a “cheap and easy” way of discrediting conceptions of Experience other than his own.

“The “phenomenological fallacy” is the mistake of supposing that when the subject describes his experience, when he describes how things look, sound, smell, taste, or feel to him, he is describing the literal properties of objects and events on a peculiar sort of internal cinema or television screen, usually referred to in the modern psychological literature as the “phenomenal field”. If we assume, for example, that when a subject reports a green after-image he is asserting the occurrence inside himself of an object which is literally green, it is clear that we have on our hands an entity for which there is no place in the world of physics….The phenomenological fallacy…depends on the mistaken assumption that because our ability to describe things in our environment depends on our consciousness of them, our descriptions of things are primarily descriptions of our conscious experience and only secondarily, indirectly and inferentially descriptions of the objects and events in our environments.” (Place, Is Consciousness a Brain Process?, 49) 

Now, let’s move on to the question of Leibniz’s Mill itself. If we turn to §17 of The Monadology, we are greeted with the following eloquent passage:

“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:

“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)

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 [inward] we do not mean to point to a specific part of space outside of which there would be another part….The inward is nothing but the negation of the outward; 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; rather it 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 [in our consciousness 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 thought…everything 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. Even space reveals itself as the form of a certain level of experience. This form is proper to the spirit and intrinsic in it: hence the possibility of [our being conscious of] not only our bodies and all their organs, but everything that surrounds our bodies, from the nearest to the most remote, everything in heaven or in earth, real or imaginary. Everything is inward, where the foundation of everything lies. If that foundation is denied, all will inevitably collapse.“ (Gentile, The Philosophy of Art, 56-57)

Whereas Experience “has its center in itself,” Matter 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.

Far from being an instance of the “phenomenological fallacy,” Leibniz’s Mill is an illustration of the fact that qualitative changes and alterations in the structure and arrangement of material objects (e.g., changes consisting in transformations such as dilations, expansions, translations, rotations, reflections, etc.) cannot account for what would be the manifestation of a new determinable (hitherto unmanifested) that (1) exhibits an “internally-differentiated” structure, and (2) is “inclusive of” the material objects that are alleged to have given rise to it. This new determinable would be none other than Experience.