Leibniz’s Origin of the Idea of Space
Leibniz’s theory provides premises to demonstrate the existence of space. In his first assumption, he asserts that the presence of anything, irrespective of its form, has a reason. Notably, this assumption gives a variant of the concept of sufficient reason, which asserts that all existing things have a cause or explanation for their being (Arthur, 2022). A rejection of this concept contradicts the entire premise upon which science is based since objects would not spontaneously appear without a cause. In addition, it is acceptable that the generated logical conclusions be supported by adequate evidence. Therefore, it would seem arbitrary to dispute the concept of sufficient reason but to embrace it again to challenge its notion (Leibniz & Clarke, 2000). Consequently, all conclusions reached are always supported by logic.
The spatial extension belongs to the realm of occurrences, although monads are not located in space; they represent one another with spatiotemporal features. Along with coexisting monads, a depiction of a monad in the real world of representational monads is a genuine precondition of the monad. A monad perceives the universe of events as if it were the focal point of this view. The monads and their essential traits and properties generate space. Leibniz reasoned that following the idea of perfection and its counterpart, the theory of preset harmony, that space is a relation intrinsic to cross-sectional contexts (Leibniz & Clarke, 2000). In the perspectives of monads, for instance, the mutual accord is such that any view of a particular unit corresponds perfectly to the viewpoint of any other unit.
The third premise — that the cosmos exists — is so self-evident that any argument against it would be ludicrous. The fourth premise argues that the existence of the cosmos can be explained, and to oppose this would need a specific circumstance. It would be absurd to believe that the cosmos is the sole object without explaining its existence and that it spontaneously generated itself. It would raise the question of how nothing could collide with nothing to create everything. Subatomic particles originate from nothing; a challenge to this premise would be posed. Again, this demonstrates a complete misunderstanding of science and its concepts (Leibniz & Clarke, 2000). Subatomic particles are logical outcomes of energy fluctuations in the vacuum. Therefore, if humans say the universe was created like subatomic particles, people would not need substantial knowledge to deduce that it originated from energy. Consequently, it means that the space must have originated from something that could have also evolved from another thing that was requisite in and of it — a chain that would end in an essential being.
Leibniz presented two similar claims in the principle of indiscernible. Below is this research’s illustration of space as per Leibniz’s theory. Imagine two objectives, such as tennis balls tied to a pendulum, identical to Earth, except that all matter is moved and repositioned in absolute space, with no change to the interaction between the two tennis balls. If the space is Euclidean, there are no discernible distinctions between the two locations of the two objects moving in a circular motion. Again, consider two tennis balls tied to a pendulum, identical to the Earth, except that each ball’s absolute velocity fluctuates and varies by a constant set amount as it rotates, with no change in the interaction between the objects. In this example, the difference between the two speeds is constant; hence, no noticeable changes are recorded. For instance, the two circulating objects cannot be differentiated — if there were unlimited space, the particles’ movements would be entirely different; consequently, the concept of absolute space contradicts the notion of indiscernibility. Therefore, the indiscernible principle is founded on sufficient reason, as explained in the example of tennis balls.
However, Newton’s theory of space is opposed to Leibniz’s concept. He rejects the assumption that space is an absolute thing or existence (De Risi, 2020). According to him, the concept of simultaneous existence via absolute space is illogical, as it would make space in which universal objects exist a simple illusion and not an ideal being (Leibniz & Clarke, 2000). The premise of absolute space would imply that it exists in portions. The premise is problematic, however, since God, who has been established as the necessary entity underlying the existence of the cosmos, cannot have parts. Primarily, it would imply that he mysteriously controls events, which would again undercut his omnipresence. As such, Leibniz’s arguments, in contrast, are relational, and they are founded on a variety of moral precepts. Two self-evident principles exist at the level of categorical imperatives: the principle of perfection and the concept of identity.
Du Châtelet’s Discussion of the Idea of Space
Du Châtelet remarks that there is a debate among philosophers on the nature of space, with some saying that it is empty while others believe that it contains meaning. In certain circumstances, the nature of bodies is up to speculation. There is a common belief that significant quantities of space exist between matters in the cosmos, illustrating the disorganized nature of the universe’s structure. According to Du Châtelet, space and time are anchored on genuine relationships between different components and are not just abstractions of shared perceptions by all fundamental aspects (Du Châtelet, 2017). The current research contests these claims: according to Du Châtelet, space, like extension, is a mental construct that is a muddled depiction of the relationships between innocuous.
In Chapter 5, Du Châtelet makes this dichotomy juxtaposition between the concept of space as an impartial substance on the one hand and the representation of actual bodies in space on the other. As such, those who intended to apply to actual space — the demonstrations that they had deduced regarding imaginary space could not help but get lost in a labyrinth of errors from which there was no escape (Du Châtelet, 2017). The imaginary universe is the view of space as material humans create for themselves while contemplating extended entities in the abstract that people may contemplate in isolation. On the other hand, absolute space is where individuals depict actual beings whose existence relies on these bodies.
According to this interpretation, part of the essence of space is its structural likeness to this mind-independent order; hence, the strong reading is not essence idealist. On the other hand, according to the weak interpretation, space and extension are both created by erroneous human impressions of discrete innocuous as unified wholes. As it has been shown, Du Châtelet is a fundamental extension idealist. On a weak interpretation, she is also an essence idealist about the spatial nature of human representations, which are both a phenomenon and an appearance.
The core claim of Du Châtelet’s explanation of extension is the fundamental reality that people mistake multiplicities for extended unities. It is a fundamental truth that people express multiplicities as unities via extension and that it is a logical absurdity that humans represent multiplicities as unities through extension. Consider that other methods exist to express a plurality as a unit. For instance, inside a hierarchical organization, one may depict separate persons as having a variety of positions, including principal and manager. The notion of organization then unites these diverse people; hence, Du Châtelet does not support this allegation.
In establishing the space argument, Du Châtelet asserts that space is relative. Specifically, it makes no sense for humans to see themselves in two separate forms, and things cannot exist in two distinct states (Du Châtelet, 2017). If humans are to view things in two distinct ways, it must be due to the universe’s variety and unity. Specifically, this is consistent with Leibniz’s concept of extension. She believes that while humans view things differently, they all belong to the same cosmos. The notion that the cosmos is both varied and a unified whole inspires the notion of extension. The soul, an abstract entity with multiple capacities, cannot be seen as an extension; otherwise, it may seem as if people suppose the traits and modes of the body to be distinct from the body itself. Therefore, Du Châtelet agrees with Leibniz’s argument on space concerning a relative extension.
Du Châtelet’s Space as Similar to Newton’s Conception
Du Châtelet accepts Newtonian absolute space as a distinct substance. As such, Du Châtelet agrees with Leibniz that space is an idea, not a substance (Du Châtelet, 2017). However, it is necessary to differentiate between two accounts of space as a substance. The first describes what space is, while the second describes how humans acquire the concept of space. Du Châtelet equates the two questions because, in her opinion, there is nothing substantial about space beyond an individual’s conception of it. Du Châtelet explains that humans arrive at the concept of homogeneous extension by abstracting the internal determinations of the diverse and united simples people mistake for bodies.
While Newton’s theory alludes to the fact that gravity is responsible for determining the shape and movement of objects in space, he does not attempt to explain gravity itself. While acknowledging that many relationships have no observable consequences, Newton demonstrated that the absolute acceleration of a rotating physical object is itself observable (Wood, 2019). To illustrate the forces generated by circular patterns, he conducted two mental studies: the rotational forces on the water’s surface in a spinning bucket and the tension of a string connecting two realms spinning about their center of mass (Wood, 2019). Following these depictions, linear accelerations generate noticeable forces.
Newton likened the absolute displacements and forces to absolute space, a quantizing system that does not change. Therefore, Newtonian scientific knowledge regarded the distinctions between states of rest, homogeneous motion, and accelerated motion to be absolute. This principle is what Du Châtelet refers to as the “order of coexisting things” (Du Châtelet, 2017). This is how Du Châtelet derives the essential properties of absolute space, including its uniformity, infinity, and immutability. Therefore, I agree about her claim that humans think of space as Newtonian since her arguments are founded on the concept of extension, the same way as Newtonian.
References
Arthur, R.T.W. (2022). Leibniz on time, space, and relativity. Oxford University Press.
De Risi, V. (2020). Leibniz and the structure of sciences: Modern perspectives on the history of logic, mathematics, epistemology. Springer.
Du Châtelet, É. (2017). On space. In K. Brading (Ed.), Foundations of physics, 1740 (pp. 77-93). University of Notre Dame.
Leibniz, G, W., & Clarke, S. (2000). Leibniz and Clarke: Correspondence. Hackett Publishing.
Wood, A. (2019). Sir Isaac Newton. Rosen Publishing.