To advance physics, a young field at Immanuel Kant’s time, the nature of space and matter was a crucial question that requires discoveries through the marriage of metaphysics and geometry. He worries that the endless arguments in these fields about physics will stifle its growth. He wants to contribute to ending their debate about space and monads (S&M). And in Physical Monadology, he sets a specific objective to prove S&M coexistence and provide insights on how monads, assuming they exist, should behave in accordance to natural phenomena.
There are two problems that fostered a widespread misconception among Kant’s contemporaries—the coexistence between S&M is a delusion. First (1) is that metaphysics denies the infinite divisibility of space (Kant 51), while geometry asserts the opposite. This is a dead end where metaphysicians and geometricians supposedly diverge that requires interdisciplinary reconciliations. Second (2) is the belief that even if one grants space infinite divisibility, to divide space that contains monads is to divide the indivisible, so S&M coexistence is absurd. (2) is also the final obstacle to proving S&M coexistence.
As the discussion of (2) progresses from (1), Kant will settle (1) to upgrade the status of the premise about spatial infinite divisibility in (2) from having been granted to proven. Solidifying this premise opens the window for potential soundness in an argument that subverts (2) and strongly supports the coexistence of S&M. His general strategy to do so runs in two stages: 1. Present polished definitions of S&M and settle the debate on spatial divisibility through geometry; 2. Illustrate the division of space and highlight its distinctiveness in function and effect from the division of substance, revealing the misguiding thought process that’s caused the false conclusion in (2).
He defines monads as what exist absolutely and independently without parts. They are indestructible, impenetrable and unique individuals whose three characteristics are summarized into the word “simplicity.” All bodies deconstructed to their most basic parts are monads, which forbid any further decomposition. On the other hand, space is where bodies fill, by nature free of substantiality, and infinitely divisible.
He implements the simple geometric technique to prove his controversial supposition that space is infinitely divisible. Imagine two vertical lines, L1 and L2 are set in the same order between two infinitely long parallel horizontal lines, P1 (top) and P2 (bottom), forming four points of intersection, A, B, C and D. A, B, C, and D create a rectangle with its lengths resting on P1 and P2. Take point A as the top-left vertex and point B the top right, C the bottom left corner, and D the bottom right of the rectangle. As a result, AC=L1 is the left width, BD=L2 the right width, AB the left length, and CD the right length. At an infinitely acute angle, draw a diagonal line from point A that crosses and divides BD to reach any point E on L2. AE will infinitely approach but never coincide with A.
How does this show that space is infinitely divisible? As Kant has prescribed, the process of continuously dividing matter ultimately ends and produces monads. The above demonstration yields the opposite result. Regardless of how small the scale of division, some space will always be leftover available for division; continuous division for space is endless, or infinite. Thus, this geometric demonstration, probably ironic to his contemporaries, establishes a metaphysical claim that space is infinitely divisible and effectively debunks the myth of the absolute incompatibility between geometry and metaphysics. It also reveals that space and body differ in their makeup and function. The body at least is composed of something substantial, namely monads, whereas space has no substantial components. Body moves decompose and restructure, while space only contains bodies. They are quintessentially distinct.
Newton’s response to spatial divisibility in De Gravitatione is a possible objection to Kant. Newton suggests that if one acknowledges the immobility of space, this property also applies to its parts. The character of space immobility “is best exemplified by duration” of time (Janiak 39). Parts of time are individuated and non-interchangeable. Otherwise, one arrives at the funny situation where today can interchange with tomorrow or yesterday, so today, tomorrow and yesterday become equivalent to each other. Each part of space, similarly, must remain unique and stay where they are to not confuse the order of the physical universe. If two objects were occupying different positions that are interchangeable, how were they considered situated in different positions in the first place? Effectively, they would be in the same position. A Newtonian fanatic may question Kant, “Then what’s the purpose of even trying to conduct a thought experiment on dividing space? Isn’t it obvious that one can’t divide it into parts?”
If one thinks twice, Newton’s idea isn’t an objection. Kant is actually carrying Newton’s perspective into his deeper inquiry about spatial division. Immobility of space and its parts don’t imply their indivisibility. It’s how one divides space that makes a difference. Newton states that one cannot physically cut space into pieces, like tomatoes, and move them around. Granting this perspective, Kant’s geometric thought experiment deliberately attempts a more sophisticated spatial division, unlike cutting tomatoes. The smaller the area of the resulting divided space by Kant, the more specific its position is. It’s similar to dividing a whole book in one’s mind into sections, paragraphs, or to the very end, characters. The content of the book is intact, but the mind’s references to what’s on the page can vary in specificity. The spatial division sets itself apart from book content referential division by its capacity to withstand infinite divisions and generate infinitely specific references to positions within space itself. Thus, the fact that both philosophers are in agreement wins me over to their side.
Because Kant has proved the infinite divisibility of space and its consequences, he can work with this premise as established rather than granted to address (2) and demonstrate S&M coexistence. He emphasizes that the disciplinary incompatibility is no father of the problematic and oversimplified conclusion in (2). Instead, it’s an unquestioned bias that roots in one’s lack of rigorous intellectual investigation into the nature and subtle mechanisms of S&M. Kant cannot permit the unjustified to continue stagnating the progress of physics.
He then proposes that although a monad fills space, dividing the space where substance occupies “is not the separation of things” from which creates a new component of independent existence (56). Rather, space “displays a certain plurality of quantity in an external relation.” He never clarifies what this external relation is, but he clearly views space as similar to an immaterial canvas displaying objects’ relations in the physical world.
In other words, space is at least the effect of a property, possibly out of many, that manifests itself as a domain that contains substance. Only dividing the immaterial “canvas” produces more physical relations and complexities in its presentation of them. This addition/change of relations within the immaterial “canvas” doesn’t apply to physical objects and monads in space, but only affects the portrayal of their physical relations, not their inherent motion, density, or shape. It follows that when monads are within a space that is being divided, they don’t lose their simplicity or become smaller pieces because the effect of spatial division isn’t applicable to their substantial form but the presentation of their physical relations to other things.
Henceforth Kant declares that the coexistence between S&M is justifiable and compatible with geometry and metaphysics. To answer the question about how Kant reconciles geometry and metaphysics on S&M, I think his effort is not reconciliation between conflicting disciplines. It’s reassessing the validity of philosophical biases. A more direct judgment from Kant will express that it’s not the impossibility of interdisciplinary knowledge or practice, but under-analyzed opinions among some philosophers and unnecessary disciplinary rivalries, that became popular and distorted into S&M incompatibility. Kant worries not about the awkwardness of implementing interdisciplinary thinking. He accomplishes what many considered “impossible.” He just combines existing methods and understanding from both disciplines. It’s a direct approach that disregards individual biases and creatively and meticulously wields whatever intellectual tools one needs from various disciplines to advance human understandings of reality. Consequently, geometry and metaphysics have worked together just fine for Kant. He intends to preach that the study of reality necessitates attention to detail, thorough and specific questions about our world, consistent awareness of our subjectivity, and careful and open-minded selections from diverse methodologies, to discover the truth.
After dealing with S&M coexistence, Kant cruises on to fill the intellectual gap on monads and explores their primary qualities (motion, size and shape), based on what he has already established. Where monads are placed doesn’t define their position; it’s their relations to external things because monads hold no plurality of substances. This is because each monad is independent and always pushing and pulling each other. A monad constantly moves in a sphere of activity, driven by the monad’s central inherent repulsive and attractive forces that interact with those of other monads. Because of their simplicity and inherent and interactive forces, more than one monad cannot occupy the same position. As they exercise their forces persistently, they always move away or towards each other’s center.
In addition, the power of the attractive force is inversely proportional to the external object’s distance from the center of a monad, whereas the closer something approaches the center of the monad, the extent of the repulsive force becomes greater and approaches infinity.
Why are attraction and repulsion necessary for monads? They need both forces to achieve complex motion to interact with external objects and form new matter. With only one of the two, either monads all run away from each other and never form any compound, or become the one and only united matter in our universe.
Furthermore, Kant believes monads share the same size but not the extent of their forces. They have the same size because the intensity of their attractive forces depends on the distance from external things, following the same physical law discovered by Newton (1r2). In the contrary, their varying force intensities are based on the observation that non-simple material objects can have an equal volume but vary in their densities and inertia, which Kant identifies as the sum of monads’ forces in the object.
I don’t agree monads are indivisible in every way. I grant the definition that monads are indivisible substantially and the same in size. Kant’s proposition that monads must differ in their inherent forces is open to interpretation though. Are these differences in forces present since day one? Monads may lose and absorb other monads’ forces through their never-ending and sometimes intense interactions (let’s say a supernova). Maybe they do experience these changes in intensities of their inherent forces, so it’s possible to divide their forces. Although people today still have no clue about how far we can divide matter, it’s unreasonable to conclude monads are indivisible in every aspect of their behaviors. Considering the intricacy of the inner workings of our universe, one shouldn’t assume any less behavioral complexity of monads than that reflected by Kant’s conjectures.
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