Gottfried Wilhelm Leibniz, one of the most influential European philosophers, had different views on the concept of space than many of the other philosophers during that era, such as Newton. Leibniz held a view that mostly contrasted with Newton, and also Francesco Patrizi since Patrizi was influential to Newton himself. In a series of conversational papers between Leibniz and Samuel Clarke, Leibniz argued against Newtonian philosophy, and Clarke was in defense of Newtonian philosophy. In the five papers that Leibniz and Clarke had exchanged, Leibniz explained his own philosophy of space and opposed the Newtonian idea of absolute space. Leibniz posits that space is merely the relation of one body to another, which will not exist as a substance, and there is no absolute space when the body is removed (Leibniz, third paper). By “space is the relation of one body to another”, Leibniz specifically means that space is how “far” one thing is to another, for example, a rock is pointed one millimeters away from the ground, and at the same time the support is also ten meters from a tree. The change in distance and position of the bodies will result in the change of space between bodies, in other words, space is dependent on bodies. Further, it could be reached that space did not exist first in the world. As Leibniz described in his fifth paper to Clarke, Leibnizian space is similar to an abstract form of the branches of a “family tree”, which connected bodies like siblings (Leibniz, fifth paper). For Leibniz, space as “branches of the family tree” will exist only after the bodies (family members) have been presented. This is distinctively different from the fundamental concept of Patrizi, who posits that space is fixed and the primary thing that existed after God. Nevertheless, Patrizi’s description of space is much similar to Newtonian space, which existed like a container that enclosed the world within.
Leibniz countered the idea of absolute space by Newton and early philosophers like Patrizi, mainly because the existence of absolute space is inconsistent with the Principle of Sufficient Reason (Leibniz, third paper). The Principle of Sufficient Reason could be explained as there will always be a reason or a cause for anything to be itself. If there is no sufficient reason on any aspect of absolute space, then it would be proved not to be a real substance. Leibniz, using the Principle of Sufficient Reason, asked for the reason of God, who created this world particularly, to choose this world with this space over another world with a different kind of space (Leibniz, third paper). Before this inquiry, Leibniz set that space is always consistent, that no particular difference should exist between a point of space and another point of space (Leibniz, third paper). To infer from the two points, Leibniz believed that there should be no absolute space as there is no sufficient reason for God to choose to form this particular world over another. According to the Principle of Sufficient Reason, God must choose this space for some reason. If the space is indistinguishable itself, then any absolute space of the world should have no differences. If there are no fundamental differences between spaces, then for what reason could God choose to create this particular space and world? Leibniz answered that then the existence of absolute space should be undermined as it is inconsistent with the Principle of Sufficient Reason.
Leibniz also refused the existence of empty space, or vacuum, which is conflicting with Patrizi’s theory on the vacuum and universal space. Though not directly refuting Patrizi’s empty space theory, Leibniz confronted a similar theory placed by Newton, in which Newton held that bodies and matters were only filling a small portion of our universe, and where bodies and matters did not occupy is the empty space (Patrizi held the same opinion with Newton on this point.) Leibniz believed that God created the world in the best possible solution, and the world should be created obeying the Principle of Plenitude: the more bodies existed in the world, the more God could exercise his wisdom and power upon them (Leibniz, second paper). Therefore God should be creating bodies as much as possible to make sure the most power could be exercised in the world. Then Leibniz concluded that there should not be empty spaces without bodies filling them up because God needed to exercise the power. In contrast, Patrizi used several examples he drew from real life to argue that the existence of empty space should be noticeable. Patrizi argued that both tiny empty spaces and larger empty spaces existed within bodies and outside bodies, and this argument could be proven by the property of reluctance of sharing space of bodies. But on the other hand, Leibniz also admits that bodies obtained some degrees of reluctance to share space with one another in his New Essays on Human Understanding.
In his fifth paper to Clarke, Leibniz also stated that the outer space that “covered the world within” should be counted as imaginary (Leibniz, fifth paper). The reason that Leibniz undermined the concept of outer space was that outer space could simply be counted as empty space, and empty space should not exist because it conflicted with God and the Principle of Plenitude. The outer space, which was called Locus (external space) by Patrizi, was believed to exist as an infinite and fixed substance that the world was placed in. Since Patrizi believed in the existence of a vacuum, and a vacuum should not be equally considered as the external space (in fact, vacuum existed prior to the external space), Leibniz was completely opposing the view of Patrizi. But it should be noted that Leibniz and Patrizi have diverged on the fundamental concept of space from the beginning, that Leibniz held space as the relation between bodies, while Patrizi counted space as the primary substance of the universe.
Though the two philosophers essentially had distinct and contradicting views, Leibniz and Patrizi agreed on one aspect of space. Leibniz did not refuse the possibility of space being infinite, as he also had stated that space could be infinitely divisible (Leibniz, fifth paper). Patrizi also held that universal space is infinite on the side of not bounding the world. But overall, Patrizi’s space theory is much closer to the Newtonian explanation, which Leibniz argued against. The two separate theories on space were diverse in the content, yet they were both convincing in their own ways.
Clarke, Samuel, Gottfried Wilhelm Leibniz, Isaac Newton, and H. G. Alexander. The Leibniz-Clarke Correspondence : Together with Extracts from Newton’s Principia and Opticks Manchester: Manchester University Press, 1976.