Two Spheres

For any ontological category, it is preferable to have a principle of individuation that will make it possible to distinguish entities within it.  However, discovering exactly what it is that makes one substance diverse from another can be a difficult task; this is particularly true when the substances in question are exactly alike (share the same internal properties).

Imagine a universe in which the only things that exist are two spheres.  These spheres are exactly the same in their internal properties.  The question that must be answered is this: “What is it that makes these spheres different?”  Or, in other words, what is the principle of individuation for these two objects?  I will examine the merits of the following four theories.

  1. They are individuated by space and time.
  2. They are individuated by the matter of which they are composed.
  3. They are individuated by their properties.
  4. Individuation is a brute fact.

1. Individuation by Space and Time
One possible theory is that the two spheres could be individuated by space and time.  Thus, Sphere A is distinct from Sphere B because A and B occupy different places at the same time.  This theory may seem very plausible at first glance; it is quite obvious that the two spheres are not in the same place at the same time, so it seems that this must indeed be what dinstinguishes them.  However, after closer examination, we find that this theory brings some heavy baggage along with it: namely, this theory presupposes the Absolute Theory of space. 

The Asbsolute Theory of Space, championed by Sir Isaac Newton, asserts that space is a container that holds the objects that exist within it.  Therefore, space is not dependent upon objects and would exist regardless of whether anything else did.  Modern physics, however, has powerfully discredited this theory of space and it is no longer espoused by many scientists or philosophers.  Furthermore, we are sitll left with the question, “What would the principle of individuation for each place be?”

One may ask, then, why it is not possible to use the competing theory of space (the Relational Theory) instead of the Absolute Theory in formulating a principle of individuation for the spheres?  The Relational Theory, famously held by Gottfried Wilhelm Leibniz, asserts that space is dependent upon objects.  In other words, what we refer to as space is merely the realtion between objects and their observers within the universe.  The Relational Theory of space will not accomodate a place-centered principle of individuation, however, due to the fact any appeal to “place” within the relational framework will lead to a circle of interedependence of places and objects since space exists in relation to objects.  Thus a principle of individuation based upon space and time does not appear to be plausible.

2. Individuation by Matter
Another principle that could be used two differentiate between the two spheres is that of matter: so that A is distinct from B because A and B are composed of different matter.  This theory assumes the priority of understanding substance as “stuff” (formless matter) over the priority of understanding substance in a counting sense (individual substances).

Aristotle (and consequently, Aquinas) held that matter is prior to individual substances and that one could individuate substances by the matter of which they were composed.  In other words, an individual substance is matter that has form imposed upon it.  Thus it seems that Aristotle’s principle of individuation relied heavily upon the forma indentity of a substance.

Leibniz, on the other hand, asserted that individual substances are prior to stuff.  Indeed, he believed “stuff” to be composed of individual substances which he referred to as ‘monads’.  Although Leibniz’s monads lead to an idealistic understanding of reality, the basic principle (if there are complexes, then there must be simples) holds true.  In the view of modern science, these simple substances would not be monads, but the basic particles which exist on the atomic level.  Thus, individual objects seem to have more priority than formless matter.

Furthermore, the principle of individuation given above involves circular reasoning.  If we individuate the two spheres, A and B, by the matter that they contain, what then is the principle of individuation for the matter itself?  One may reply that we can individuate the matter by the form imposed upon it, but this leads us back, once again, to the two spheres.  How do we individuate the forms?  By the matter which composes them.  On and on we go.

3. Individuation by Properties
A third (and quite promising) possible principle of individuation for the two spheres is individuation by the properties which the spheres possess.  The reason that this theory is more feasible than the previous two is that it appeals to an ontological category outside of the concrete category.  Whenever a theory attempts to individuate an entity on the basis of something within the same category as that entity, it leads to serious problems (usually a vicious circle).  This theory of individuation is based upon an inverse understanding of the Indiscernability of Identicals known as the Diversity of the Dissimilar:

Necessarily, for any A and B, and for any property, P, if A possesses P and B does not possess P (or vice versa), then A and B are not identical.

All that is necessary, then, to individuate the two spheres is to demonstrate that they do not actually share all of their properties.

Leibniz actually proposed that it was impossible for any two substances to have the exact same properties.  He believed that any similar objects would differ at some point even if that point were so miniscule as to escape observation.  However, Leibniz’s reasoning behind this was pure theological speculation.  He asserted that God would never create any two substances with the exact same properties because there would be no reason to do this and that doing so would contradict God’s good and reasonable nature.  Again, pure speculation.

Duns Scotus disagreed with Leibniz.  Scotus proposed that substances could be identical in every general property, but that each individual substance possessed a nongeneral property that was unique to that substance.  He called this special property a haecceity or “thisness” (from the Latin pronoun for “this”).  Thus Sphere A is distinct from Sphere B, because A possesses the property of ‘A-ness’ and B does not (and vice versa).  While the idea of haecceities may seem almost too convenient for the problem at hand, there does seem to be strong evidence for their existence when one considers the concept of self-recognition.  How is it that we are able to simply know that we are indeed ourselves?  What is it that we appeal to when we do such?  It appears that I am appealing to the property of “Josh-ness” when I consciously recognize myself.  Thus the principle of individuation based upon abstract properties seems much more viable than the theories we have looked at thus far.

4. Individuation as a Brute Fact
A fourth, and final, response that can ve offered to the problem of explaining the diversity of the two spheres is that individuation, itself, is a brute fact that has no explanation.  It seems that the nominalist would be forced to accept this fourth proposal since any appeal to individuation that he would make would be within the same ontological category (concrete) and would lead to circular reasoning.  Brute facts, however, are not welcome within the theories of most philosophers, since a good system of metaphysics will seek to explain as much as possible.  Therefore, after reviewing the four theories given above, it is the property-based principle of individuation that seems to be the most promising explanation to the problem of the two spheres.