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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.


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Dilyn Corner (C) 2020-2022