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.

My Adaptation of the “Mary’s Room” Argument Against Physicalism

Mary lives in a room that is purely black and white—there are no achromatic gradients or shades of grey in the room whatsoever. While she is in the room, Mary learns all of the “physical” facts about light and color vision (i.e., All that neuroscience and physics have to say about light and color vision and the relationships between different colors). For example, while Mary is in her room, she learns that the color red is identical to light wavelengths of 625nm to 700nm, the color blue is identical to light wavelengths of 450nm to 485nm, the color green is identical to light wavelengths of 500nm to 565nm, and the color yellow is identical to light wavelengths of 565nm to 590nm. Mary also has memorized the sequence of colors in order of shortest-to-longest wavelengths.

One day Mary leaves the room (which, as we must keep in mind, was purely black and white without any kind of shading or achromatic gradient mediating between the black and white). Mary is then escorted to a table where a couple of fellow scientists are waiting for her. On the surface of the table lies an assortment of colored tiles (which are not in any particular order or arrangement; they are simply “scattered” and “mixed up”). There is one red tile, one blue tile, one green tile, and one yellow tile. Mary (who had learned all of the “physical” facts about light and color vision; indeed, she has even memorized the light wavelengths of red, blue, green, and yellow) is told—on the spot—the following: “Mary, you are in the presence of four colored tiles. Arrange the colored tiles in the order of shortest-to-longest wavelengths.”

It’s clear that Mary would be stumped.

Another scientist interrupts the silence and says, “Mary, with your left hand, pick up the red tile, or the tile whose color is identical to wavelengths of 625nm to 700nm; and, with your right hand, pick up the green tile, or the tile whose color is identical to the wavelengths of 500nm to 565nm.”

It is pretty clear that (i) Mary would not know which four tiles to pick up with her left hand and (ii) Mary would not know which of the four tiles to pick up with her right hand.

Despite her exhaustive knowledge of all the “physical” facts about light and color vision, Mary would not know which of the four colored tiles presented to her was the red tile and which of the four tiles was the green tile.

After a few moments without any answer from Mary, one of the scientists places the red tile in Mary’s left hand and says, “This is red.” The other scientist then places the green tile in Mary’s right hand and says, “This is green.” Upon hearing these statements, Mary learns new facts about light and color vision; namely that there are drastic qualitative differences and similarities between red and green—e.g., they have different sensory characteristics; one is “softer” than the other; one is “warmer” than the other; one is more “vibrant” than the other; and one is less “harsh” and more “mellow” than the other. One of the scientists then picks up the yellow tile and tells Mary, “This is yellow.” Upon hearing this statement, Mary, again, learns another new fact about light and color vision; namely the fact that yellow is more “vibrant” than green—which is “mellower”—and that the qualitative character of yellow is lighter and less “imposing” than red.

Now, suppose, on the other hand, the situation was altered. Suppose that immediately after Mary left her room, one of the scientists placed the red tile in Mary’s left hand and said, “This is green;” and the other scientist placed the green tile in Mary’s right hand and said “This is red.” Clearly, if Mary learned all the “physical” facts about light and color vision, she would immediately respond by saying “You both are wrong. The green tile is in my right hand, and the red tile is in my left.” However, it’s obvious that upon leaving her room, Mary would have no idea that she was being told falsehoods about the colors of the tiles—indeed (after being told that the red tile in her left and was green, and the green tile in her right hand was red) she would think that the red tile was green and the green tile was red. However, red and green have different wavelengths—and Mary would have known this upon her release.

If Mary knew all there is to know about light and color vision, then Mary should have been able to identify the colors of the tiles and arrange them in sequence of shortest-to-longest wavelengths upon her release, without hesitation. And yet, she couldn’t. Thus, since Mary knew all of the “physical” facts about light and color vision before leaving her room (i.e., All that neuroscience and physics have to say about light and color vision and the relationships between different colors), it follows that not all facts are “physical” facts.

Fragmentary Notes §46—§47

§46

Objects “appear” and manifest themselves perspectivally; however, an Object’s various “appearance-patterns” do not themselves “appear” or manifest themselves perspectivally, rather they are the “appearings” of the Object. Fleeting and transitory, an “appearance-pattern” is ideal—it is essentially incomplete and fragmentary. It passes beyond itself and strives for completion and stability in what lies beyond itself.

§47

In referring to myself as “I”, I consciously determine myself as a being of which I am conscious; I posit myself as knowing, and knowing myself as such—thus, I establish myself as an identity of Subject and Object. As Object, I am enveloped within my own knowledge; as Subject, I am the enveloping.