Last Thursday, Steven N. and I had a very enjoyable three-hour conversation with ASU philosophy emeritus Ted Guleserian on Tempe's Mill Avenue. We covered a lot of ground, but the most focused part of the discussion concerned the subject matter of this post. If I understood Guleserian correctly, he was questioning whether there is any such problem as the problem of the unity of a fact. I maintained that there is such a problem and that it is distinct from the problem of order.

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The problem of order arises for relational facts and relational propositions in which there is a relation R that is either asymmetrical or nonsymmetrical. If dyadic R is asymmetrical, and x stands in R to y, then it follows that y does not stand in R to x. For example, *greater than* and *taller than* are asymmetrical relations. If I am taller than you, then you are not taller than me. If dyadic R is nonsymmetrical, and x stands in R to y, then it does not follow, though it may be the case, that y stands in R to x. For example, *loves* and *hates* are nonsymmetrical relations. If I love you, it does not follow that you love me, nor does it follow that you do not love me. But if I weigh the same as you, then you weigh the same as me: 'weigh the same as' picks out a symmetrical relation.

Well, suppose R is either asymmetrical or nonsymmetrical. Then the relational facts *Rab* and *Rba* will be distinct. For example, *Al's loving Bill*, and *Bill's loving Al* are distinct facts. A fact is a complex. Now the following principle seems well-nigh self-evident:

P. If two complexes, K1 and K2, differ numerically, then there exists

a constituent C such that C is an element of K1 but not of K2, or vice

versa.

In other words, if two complexes differ, then they differ in a constituent. 'Complex' is intended quite broadly. Mathematical sets are complexes and it is clear that they satisfy the principle. There cannot be two sets that have all the same members. Ditto for mereological sums.

Now if *Rab* and *Rba* are distinct, then, by principle (P), they must differ in a constituent. But they seem to have all the same constituents. Both consist of *a*, *b*, and *R*, and if you think there must also be a triadic nexus of exemplification present in the fact, then that item too is common to both. And if you think there is a benign infinite regress of exemplification nexuses in the fact, then those items too are common to both. Since both facts have all the same constituents, what is the ontological ground of the numerical difference of the two facts? What makes them different? The question is not whether they differ; it is obvious that they do. The question concerns the *ground* of their difference. What explains their difference? Of course, I am not asking for an explanation in terms of empirical causes. Consider {1, 2} and {1, 2, 3}. What is the ontological ground of the difference of these two sets? It would be a poor answer to say that they just differ, that their difference is a *factum brutum*. The thing to say is that they differ in virtue of one set's having a member the other doesn't have. When I say that 3 makes the difference between the two sets I am obviously not giving a causal explanation. I am specifying a factor in reality that 'makes' the two entities numerically different.

So what, if anything, is the ontological ground of the difference between *aRb* and *bRa* when R is either asymmetrical or nonsymmetrical? This, I take it, the problem of order, or, in the jargon of Gustav Bergmann, the problem of providing an 'assay' of order. It may be that no assay is possible. It may be that the difference is a brute difference. But that cannot be assumed at the outset.

It seems to me that the problem of unity is different although related. What is the difference between the fact *aRb* and the set or sum of its constituents? If *a* contingently stands in R to *b*, then it is possible that *a*, R, and *b* all exist without forming a relational fact. So what is the difference between *aRb* and {*a*, R, *b*}? Here we have two complexes that share all their constituents, but they are clearly different complexes: one is a fact while the other is not. What is the ground of fact-unity, that peculiar form of unity found in facts but not it other types of complex?

Suppose you deny that they share all constituents. Suppose you maintain that the fact includes a triadic exemplification nexus that is not present in the set. I will then re-formulate the problem as follows. What is the difference between *aRb* and {a, R, NEX, }?

The problem of order is different from the problem of unity. The latter is the problem of accounting for the peculiar unity of those complexes that attract such properties as truth, falsity, and obtaining. For some of these complexes, no problem of order arises. For example, a monadic fact of the form, *a's being F*, precisely because it is nonrelational does not give rise to any problem of order. Since the problem of unity can arise in cases where the problem of order does not arise, the two problems are distinct.

The unity problem is the more fundamental of the two. The question as to the ground of the difference of a fact and the mere collection of its consituents is more fundamental than the question as to the ground of the difference between two already constituted facts which appear to share all their constituents.

Related: Is the Difference Between a Fact and its Constituents a Brute Difference?

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