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 gravely mistaken. 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 grasp 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. In the case of the green after-image there is no green object in the subject’s environment corresponding to the description that he gives. Nor is there anything green in his brain….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. It is assumed that because we recognize things in our environment by their look, sound, smell, taste and feel, we begin by describing their phenomenal properties, i.e., the properties of the looks, sounds, smells, tastes, and feels which they produce in us, and infer their real properties from their phenomenal properties. In fact, the reverse is the case. We begin by learning to recognize the real properties of things in our environment….Indeed, it is only after we have learnt to describe the things in our environment that we can learn to describe our consciousness of them.” (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, it would be helpful to consult the previous sections of The Monadology where Leibniz emphasizes the fact that the structure of perception (or Experience) 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)

I have taken the liberty of developing 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 a single plane of indefinite extent for 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 Experience.