Pure Undifferentiated Substances?

Recently I was confronted, in the midst of a discussion about Transubstantiation, with the idea that a commitment to substance realism seems to entail a commitment to the reality or possibility of a pure undifferentiated substance. I responded in the standard Leibnizian way, that even while no substance can be imagined or conceived of without at least one of it’s properties, so also no property can be coherently imagined without being conceived of as inhering a property-bearing thing (properties are always in principle ‘of’ something). There are no substances without properties, and there are no properties without substances. I explained that, on my view, it isn’t logically possible that there be a substance without any properties (a pure undifferentiated substance) precisely because there is no logically possible world in which such a substance is exemplified, and there is no such world because in all logically possible worlds constituent substances are all at least related to each other (relations are properties); if substances weren’t related to each other then they technically wouldn’t be part of the same world-ensemble.

However, since my argument implicitly accepted that substances don’t have any particular property of necessity [bracket out entirely, for the moment, properties like contingent existence or being identical with oneself, since these aren’t necessarily differentiating properties anyways], let’s imagine now a logically possible world in which there is only one substance which exists, and it is without any properties other than relations – obviously it doesn’t have relations either. It has no differentiating properties. Let’s express this possibility as: there is a logically possible world in which there is one pure undifferentiated substance. So, somebody may formulate the following argument against substance realism:

  1. There is no logically possible world in which is exemplified a pure undifferentiated substance.
  2. If Substance Realism is correct then there is a logically possible world in which only one substance exists, without any properties or relations.
  3. If there is a logically possible world in which only one substance exist, without any properties or relations, then there is a logically possible world in which is exemplified a pure undifferentiated substance.
  4. Therefore, Substance Realism is incorrect.

The substance realist will want to go after the second premise. How can this be done though? A Substance does not have any differentiating property of necessity, or so it seems (how could it, for if it were necessary then every substance would have it, and how could that be a differentiating property?). However, maybe there is a way. Suppose we accept the arguments for substance realism, and also accept arguments against the possibility of any pure undifferentiated substance. In every logically possible world a substance would need to have at least one differentiating property. Suppose that there is a necessary being of the sort posited by theism, then we could say that even in a logically possible world in which there existed only one substance, that substance would of necessity bear a relation to God. The following argument is only somewhat enthymematic, but that’s ok, since I’m just giving the argument a general outline.

  1. Substance Realism is correct (substances do exist, and there is no logically possible world in which there is not at least one substance).
  2. There is no logically possible world in which is exemplified a pure undifferentiated substance.
  3. If there is no logically possible world in which is exemplified a pure undifferentiated substance, then all substances necessarily have at least one differentiating property.
  4. Substances necessarily have a property either by their own necessity or else by the necessity of something else.
  5. Substances cannot have any differentiating property of their own necessity.
  6. Substances must have any differentiating property by the necessity of something else.
  7. The ‘necessity of something else’ must be a relation (either contingent or necessary).
  8. The ‘necessity of something else’ cannot be a contingent relation.
  9. The ‘necessity of something else’ must be a necessary relation (a relation which obtains in all logically possible worlds).
  10. If there is a necessary relation, then there is a necessary being (a being which exists in all logically possible worlds).
  11. Therefore, there exists a necessary being.

This argument may be a bit tighter than it looks. The most controversial part is just the underlying assumption of substance realism. However, if one grants substance realism (and thus recognizes that there is no logically possible world with any properties and without at least one substance), and presumably grants that there is no ‘empty world‘, (which would be a ‘pure undifferentiated’ world, which is unintelligible), then it’s hard to locate a disagreement anywhere else along the path. At best one can just dislocate the necessary being concluded to and the God of theism. I suppose that the person who believes that the empty world is logically possible could say that a pure undifferentiated substance is possible, but that seems unreasonable, or at least less reasonable than the conclusion of the argument (substance realism & theism). Of course, most people who believe in an empty world do so to avoid believing in a necessary being like God in the first place, so the argument may not move them.

Here’s a simpler rough sketch of the argument:

  1. Substance Realism is correct (substances do exist, and there is no logically possible world in which there is not at least one substance).
  2. There is no logically possible world in which is exemplified a pure undifferentiated substance.
  3. If there is a logically possible world where only one substance exists and God does not exist, then there is a logically possible world in which is exemplified a pure undifferentiated substance.
  4. Therefore, there is no logically possible world where only one substance exists and God does not exist.
  5. There is a logically possible world in which only one substance exists.
  6. Therefore, there is no logically possible world in which at least one substance exists and God does not exist.
  7. If God exists in one logically possible world then he exists in all logically possible worlds.
  8. Therefore, there is no logically possible world where God does not exist.

There is a serious residual problem which this argument poses to me, however. Clearly, if substance realism is correct and also entails that no logically possible world does not contain at least one substance, then strictly speaking there is no logically possible world in which God exists and nothing contingent exists (since God is not a substance). To say that there is a logically possible world where God failed to create, however, is incumbent upon me, it seems, by faith, since faith commits me to the proposition that God freely chose to create. That says nothing about how I should construe logically possible worlds I suppose, but if one postulates some proposal which cannot be captured in and expressed by logically possible world semantics then I’m inclined to think they aren’t being intelligible. However, maybe I could modify substance realism to commit one to the following: “In any logically possible world where at least one contingent state of affairs obtains, there exists at least one substance.” God can still be regarded as a being exemplified in one and all logically possible worlds.

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About tylerjourneaux

I am an aspiring Catholic theologian and philosopher, and I have a keen interest in apologetics. I am creating this blog both in order to practice and improve my writing and memory retention as I publish my thoughts, and in order to give evidence of my ability to understand and communicate thoughts on topics pertinent to Theology, Philosophy, philosophical theology, Catholic (Christian) Apologetics, philosophy of religion and textual criticism.
This entry was posted in Apologetics, Metaphysics, Natural Theology, Philosophical Theology, Philosophy, Philosophy of Religion and tagged , , , . Bookmark the permalink.

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