Leibniz's Relational Space and Time as Superessentialist Properties In this paper, I argue that Leibniz's relational account of space and time can be divorced from some, if not all, of his metaphysical commitments. It initially seems as though it can be separated logically. This is clear, as Leibniz is able to argue without particular metaphysical appeals in his 'Correspondences' with Clarke. Indeed, he really only needs two particular metaphysical assumptions: the principle of sufficient reason and the identity of indiscernibles. He also implicitly relies on the principle of contradiction. The principle of sufficient reason states that nothing happens without a sufficient reason, a kind of form of 'ex nihilo nihil fit'. The identity of indiscernibles claims that if every predicate of object x is a predicate of object y, then x is identical to y. The principle of contradiction simply states that if A is true, then A cannot be equal to not A. Explanation-wise, a relational account of space and time is much harder to construct without appealing to something like Leibniz's monadology. This is pointed out in Geoffrey Sayre-McCord's 'Leibniz, Materialism, and the Relational Account of Space and Time'. I will attempt such a construction by utilizing bundle theory. There are two cases for this consideration, one seemingly stronger than the other one, but both seeming to not rely at all on Leibniz's monadology. Materialist explanations of a relational account of space and time seem altogether hopeless, as exemplified in the paper by Sayre-McCord. In Leibniz's 'Correspondences', Leibniz makes his case as to why space and time must be relational, as opposed to the absolute account given by Newtonians such as Clarke. Leibniz claims that time is an order of successions and that, likewise, space is an order of coexistences. Assuming that space is absolute, no point in space is distinct from any other - space is not divisible. Thus, God would have no good (or sufficient) reason to privilege one arrangement of objects from another, 'different' arrangement. For example, things could have been ordered in the contrary: things ordered east could have been ordered west, the entire universe could be ordered two feet to the left. There is no distinction that can be drawn between 'the ordering' and 'the contrary ordering'. Thus, there is no sufficient reason to inquire as to what the difference between the two arrangements may be. This clearly violates the principle of sufficient reason, and thus space cannot be absolute. Ad absurdism, space is relational. Also, via the identity of indiscernibles, it turns out that talking about 'this universe' and 'this universe with everything moved two feet to the left' is really just the same object called by a different name, as all of the predicates of 'this universe' are shared by 'this universe moved two feet to the left'. The argument runs likewise for time. Suppose time is absolute. Then God could have created the universe a year or millions of years older than he did. Then there is no reason for God not to do so, as the orders would have continued with precisely the same succession. Thus, instances are not separate from the things within them - the successive ordering. Therefore, time is not absolute, and so time is relational. He offers up another argument later on in the 'Correspondences' dealing with space and time as well. His argument for space is broken up into two cases. If space were finite, it would be extended without an object. But extended things without objects are merely properties, and thus space is relational. If space is infinite or absolute, it would have greater reality than the substances within it, and thus immutable and eternal. It would be, essentially, indiscernible from God. But nothing is God but God, and thus space must not be absolute. If time were not relational, then God could have created the universe at any point in time. Indeed, he could have created the universe two weeks earlier, a decade earlier, millions of years earlier, etc. Thus, God could have created the universe prior to any assignable time, and therefore the universe is eternal. Of course, this is prior to the 20th century conception of the Big Bang Theory or any of modern cosmology, and so he hazarded a guess that the universe was not eternal and indeed had a beginning, and so it could not be the case that time is absolute. In Sayre-McCord's paper, he argues that, even though Leibniz does not directly appeal to his monadology in proving that space and time are relational, he nevertheless requires it in order to give an adequate construction of what this relation may look like. He does this by examining Anthony Quinton's arguments in 'The Nature of Things' and demonstrating that the materialist has no ground to stand upon if space and time are taken to be relational. He points out throughout his paper that any nonmaterialist ontology can avoid the problems posed - that is to say, the only truly real things are immaterial. Thus, Leibniz's monadology, the idea that all things are made up of irreducible, mind-like substances that have perception and appetite, is a proper ontology for a relational account of space and time, but that Leibniz must have had this theory in the back of his mind while writing his letters with Clarke. Sayre-McCord quotes Leibniz: "the property is in the subject, but we never hear that a subject is in its property". Space and time are required to be constructed from things that are neither spatial nor temporal. But this is where the problem lies for the materialist - how exactly is one supposed to construct this spatio-temporal relationship. One could describe both of them at once; persisting space comes into existence because one happens to identify two momentary things as stages of a single enduring thing. However, the problem we run into is that there is no thing to do the taking of these observations yet - we are trying to construct the thing to begin with! Quinton offers up one of three possibilities for how this could be accomplished. First, we could consider oneself to be a spatial entity. However, this breaks down because it would be incredibly difficult to establish a framework to operate within due to the movement of our bodies. Also, creating such a framework would require more than one reference point to fix the positions of objects because we are operating in three dimensional space. The second is that we could consider the here-and-now. However, the here-and-now is momentary. It is unable to persist through time by its own nature. Finally, we could consider the objects of continuous observation. Quinton offers up three possible problems with this option: we could perhaps be mistaken that we have in fact performed an act of continuous observation, we are required to be able to classify and rectify misclassifications of objects through time, and we must be able to count candidates in each moment, even though counting would take time to perform. Because of all of these problems for the materialist's suggestions, it would seem impossible to classify space and time relationally without some sort of nonmaterial objects with which to relate them - space and time must be constructed from things that are neither spatial nor temporal. Leibniz does not need to appeal to monadology at all in order to argue for a relational account of space and time. He manages to construct a very strong argument simply appealing to the principle of sufficient reason and the identity of indiscernibles, which are two metaphysical claims that many would seemingly be very willing to accept. Indeed, Clarke accepts the principle of sufficient reason, and it is used against his position of absolute space by Leibniz. Leibniz then attempts to construct a worldview explaining this relational account through the use of indivisible, mind-like simple substances with perception and appetite. A rather extraordinary metaphysical claim to say the least. I would argue that appealing to monadology while still agreeing with Leibniz about space and time as relational is unnecessary. Instead, we can understand substances using bundle theory. There are two possible cases, one stronger and one weaker (comparatively). The stronger argument is that substances are no more than bundles of properties conceived as universals. The weaker, substances can be analyzed in terms of their properties conceived as universals. The weaker form merely leaves us open to considering the possibility that there is more to a substance than discoverable via its properties, although I find it weak enough to consider substance theory a strong contender to take its place - it seems like a willingness to accept the weaker version is a begrudging agreement to disregard substance theory. The argument claims that, if object x has a set of properties p1, p2, ...¦, pn, and these properties are bundled together within the object to give x all of the characteristics of which it is observed to have, then we have adequately described object x (either necessarily and sufficiently or merely sufficiently). For example, take object x to be an apple. It may be observed that this apple is red, relatively round, juicy, etc. The 'togetherness' of these properties are what make the apple what it is. How precisely these properties may be bundled together I am not sure - perhaps it is a particular combination of sub-atomic particles with certain charges, spins, arrangements, and so forth. This issue, however, fits slightly outside of the scope of this paper. Of course, we may perhaps run into an issue involving Leibniz's identity of indiscernibles. If, for example, these properties are transcendent, it would appear that it does not in particular matter where exactly these objects are situated. We could scatter apples across the universe, but as the apples would all share the same bundle of properties, they are in effect the same apple. However, if we were to accept a relational account of space, we could argue that, in fact, these are distinct appearances of the same bundle within the universe. That is to say, these substances have spatial properties. Likewise, we could perhaps run into an issue with regards to time. Say, for example, that we place an apple in our fridge, and we place another, similar apple on the windowsill. After a few days, the latter apple would be rather unappealing to most people, while the other remained crisp and fresh in the safety of our refrigerator. Whilst we are free of issues of space, the fact that the apples seemingly differ property wise over time is worrisome - do we maintain identity? If we were to consider, in addition to spatial properties, temporal properties, we likewise preserve a relational account of time, and it would see as though we are in the clear, so long as our properties are not considered as universals. As a result, we now have spatio-temporal properties as possibilities for to be in our bundles, and thus are able to maintain a relational account of space and time. Thus, the identity of indiscernibles does not hinder our progress. As space and time are now properties of objects, we avoid Max Black's criticism of the principle - as it turns out, the apples do not share all of the same properties, as they are located in different positions with respect to each other. Leibniz, as it seems, may not be too dissuaded from this view on the face of it, as both bundle theory and monadology are nonmaterialist ontological commitments, both avoiding all of the issues spelled out by Sayre-McCord. The explanation one gets is less metaphysically extravagant a strong indicator of a sound theory via Ockham's Razor. As has been demonstrated, the metaphysical commitments one is required to make in order to regard space and time as relational are not necessarily the same as Leibniz's. Monadology, while an interesting ontological perspective, is not a necessary condition. As the principle of sufficient reason and the identity of indiscernibles are preserved by immanent bundle theory, one is still allowed to make use of Leibniz's core arguments in his 'Correspondences' with Clarke for why space and time are relational, and as the use of bundle theory is not a materialistic view, we avoid all of the issues which Quinton has in his attempt at a construction of a relational view of space and time. ________________________________________________________________________________ Dilyn Corner (C) 2020-2022