Mereology and Divine Simplicity

Hold on to your horses people, what is about to follow is a pretty technical discussion of a philosophical concept. At first you might say, “why the heck are you blogging about this?” Trust me. Follow along and it will make sense in the end.

Mereology – Study of Parts

In Parts, Peter Simon shows that in classical Mereology it is not possible that there be a universe with exactly four parts.  In order to understand why this is so, we must first understand what is meant by the technical term “Universe” which is denoted in Mereology by ‘U’.  After we understand what a “Universe” is we can use the notion of a sum in order to see why there cannot be a universe with exactly four parts in classical Mereology.

A universe is the unique individual of which all individuals are parts.  In this system of logic, the universe is not the thing occupied by individuals, it is simply the individuals considered as one individual.  If there were no individuals there would not be a universe.  As soon as individuals are introduced, there is a universe.

The notion of a sum in Mereology  is merely the idea that when there are two individuals (for example x and y) there is an individual which contains both individuals.  As Simon puts it: the mereological sum of two individuals x and y is defined as that individual which something overlaps if and only if it overlaps at least one of x and y.

Now that we have seen that it is individuals which make up a universe, and that two individuals added together are considered another individual we can move on to answer the challenge posed at the beginning of this blog.  Consider a universe with 1 individual.  How many individuals are there in this universe? 1.  Now consider a universe with two individuals, x and y, how many individuals are there in this universe? There is x, y, and according to the logic of summation xy is a third individual; there are 3 individuals.  Now consider a universe with the individuals x,y,z.  How many individuals are there? There are 7 individuals: x, y, z, xy, xz, yz, xyz.   Now consider a universe with w, x, y, z.  In this universe there are 15 individuals: w, x, y, z, wx, wy, wz, xy, xz, yz, wxy, wyz, wyz, xyz, wxyz.  By working this out we see that in any universe if there are c atoms, where c is any counting number then there are exactly (2 to the power of c) -1 individuals.  Thus there can never be a universe with 4 individuals.  There can be a universe with as little as 1 individual, 3 individuals, 7 individuals but never any less 7 but more than 3.

Why This Matters….

So why am I discussing “parts?” Because of Divine Simplicity. Throw away divine simplicity (the notion that lacking spatial and temporal parts, God is free of matter/form composition, potency/act composition, and existence/essence composition, that there is also no real distinction between God as subject of his attributes and his attributes. That God is thus in a sense identical to each of his attributes, which implies that each attribute is identical to every other one) and you bring mereology into the discussion of the Trinity. Without Divine Simplicity you get 7 individuals…. As I explained above in universe with the individuals x,y,z. There are 7 individuals: x, y, z, xy, xz, yz, xyz. Lets change the letters to F(ather), S(on), H(oly Spirit). Now you get F, S, H, FS, FH, SH, FHS. If these U’s have real ontological weight then we really have run into a HUGE mess. All because we threw away the notion of divine simplicity.

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