Note to Steven Nemes: Tell me if you find this totally clear, and if not, point out what is unclear. Tell me whether you accept my overall argument.
The day before yesterday in conversation Steven Nemes presented a challenge I am not sure I can meet. I have maintained (in my book, in published articles, and in these pages) that the difference between a fact and its constituents cannot be a brute difference and must therefore have a ground or explanation. But what exactly is my reasoning?
Consider a simple atomic fact of the form, a's being F. This fact has two primary constituents, the individual a, and the monadic property F-ness, which a possesses contingently. But surely there is more to the fact than these two primary constituents, and for at least two reasons. I'll mention just one, which I consider decisive: the constituents can exist without the fact existing. The individual and the property could each exist without the former exemplifying the second. This is so even if we assume that there are no propertyless individuals and no unexemplified properties. Consider a world W which includes the facts Ga and Fb. In W, a is propertied and F-ness is exemplified; hence there is no bar to saying that both exist in W. But Fa does not exist in W. So a fact is more than its primary constituents because they can exist without it existing.
A fact is not its constituents, but those constituents unified in a particular way. Now if you try to secure fact-unity by introducing one or more secondary constituents such an exemplification relation, then you will ignite Bradley's regress. For if the constituents include a, F-ness, and EX, then you still have the problem of their unity since the three can exist without constituting a fact.
So I take it as established that a fact is more than its constituents and therefore different from its constituents. A fact is different from any one of its constituents, and also from all of them taken collectively, as a mereological sum, say. The question is: What is the ontological ground of the difference? What is it that makes them different? That they are different is plain. I want to know what makes them different. It won't do to say that one is a fact while the other is not since that simply underscores that they are different. I'm on the hunt for a difference-maker.
To feel the force of the question consider what makes two different sets different. If S1 and S2 are different sets, then it is reasonable to ask what makes them different, and one would presumably not accept the answer that they are just different, that the difference is a brute difference. Let S1 be my singleton and S2 the set consisting of me and Nemes. It would not do to say that they are just different. We need a difference-maker. In this case it is easy to specify: Nemes. He is what makes S1 different from S2. Both sets contain me, but only one contains him. Generalizing, we can say that for sets at least,
DM. No difference without a difference-maker.
So I could argue that the difference between a fact and (the sum of) its constituents cannot be a brute difference because (i) there is no difference without a difference-maker and (ii) facts, sets, and sums, being complexes, are relevantly similar. (I needn't hold that the numerical difference of two simples needs a difference-maker.) But why accept (DM) in full generality as applying to all types of wholes and parts? Perhaps the principle, while applying to sets, does not apply to facts and their constituents. How do I answer the person who argues that the difference is brute, a factum brutum, and that therefore (DM), taken in full generality, is false? As we say in the trade, one man's modus ponens is another's modus tollens.
Can I show that there is a logical contradiction in maintaining that facts and their constituents just differ? That was my strategy in the book on existence. The strategy is to argue that without an external ground of unity -- an external unifer -- one lands in a contradiction, or rather cannot avoid a contradiction. That the unifier, if there is one, must be external as opposed to internal is established by showing that otherwise a vicious infinite regress ensues of the Bradley-type. I cover this ground in my book and in articles in mind-numbing detail; I cannot go over it again here. But I will refer the reader to my 2010 Dialectica article which discusses a fascinating proposal according to which unity is constituted by an internal infinite, but nonvicious, regress. But for now I assume that the unifier, if there is one, must be external. If there is one, then the difference between a fact and its constituents cannot be brute. But why must there be a unifier?
Consider this aporetic triad:
1. Facts exist.
2. A fact is its constituents taken collectively.
3. A fact is not its constituents taken collectively.
What I want to argue is that facts exist, but that they are contradictory structures in the absence of an external unifier that removes the contradiction. Since Nemes agrees with me about (1), I assume it for present purposes. (The justification is via the truth-maker argument).
Note that (2) and (3) are logical contradictories, and yet each exerts a strong claim on our acceptance. I have already argued for (3). But (2) is also exceedingly plausible. For if you analyze a fact, what will you uncover? Its constituents and nothing besides. The unity of the constituents whereby it is a fact as opposed to a nonfact like a mereological sum eludes analysis. The unity cannot be isolated or located within the fact. For to locate it within the fact you would have to find it as one of the constituents. And that you cannot do.
Note also that unity is not perceivable or in any way empirically detectable. Consider a simple Bergmann-style or 'Iowa' example, a red round spot. The redness and the roundness are perceivable, and the spot is perceivable. But the spot's being red and round is not perceivable. The existence of a fact is the unity of its constituents. So what I am claiming is equivalent to claiming that existence is not perceivable, which seems right: existence is not an empirical feature like redness and roundness.
So when we consider a fact by itself, there seems to be nothing more to it than its constituents.
Each limb of the triad has a strong claim on our acceptance, but they cannot all be true as formulated. The contradiction can be removed if we ascend to a higher point of view and posit an external unifier. What does that mean?
Well, suppose there is a unifier U external to the fact and thus not identifiable with one or more of its primary or secondary constituents. Suppose U brings together the constituents in the fact-making way. U would then be the sought-for ground of the fact's unity. The difference between a fact and its constituents could then be explained by saying that the difference is due to U's 'activity': U operates on the constituents to produce the fact. Our original triad can then be replaced by the following all of whose limbs can be true:
1. Facts exist
2*. A fact, considered analytically, is its constituents taken collectively.
3. A fact is not its constituents taken collectively.
This triad is consistent. The limbs can all be true. And I think we have excellent reason to say that each IS true. The truthmaker argument vouches for (1). (2*) looks to be true by definition. The argumentation I gave for (3) above strikes me as well-night irresistible.
But if you accept the limbs of the modified triad, then you must accept that there is something external to facts which functions as their unifier. Difficult questions about what U is and about whether U is unique and the same for all facts remain; but that U exists is 'fallout' from the modified triad. For if each limb is true, then a fact's being more than its constituents can be accounted for only by appeal to an external unifier.
But how exactly does this show that the difference between a fact and its constituents is not a brute difference? The move from the original to the modified triad is motivated by the laudable desire to avoid contradiction. So my argument boils down to this: If the difference is brute, then we get a logical contradiction. So the difference is not brute.
But it all depends on whether or not there are facts. If facts can be reasonably denied, then my reasoning to a unifer can be reasonably rejected. But that's a whole other can of worms: the truthmaker argument.
Analytically considered, a fact is just its constituents. But holistically considered it is not. Unity eludes analysis, and yet without unities there would be nothing to analyze! Analytic understanding operates under the aegis of two distinctions: whole/part, and complex/simple. Analysis generates insight by reducing wholes to their parts, and complex parts to simpler and simpler parts, and possibly right down to ultimate simples (assuming that complexity does not extend 'all the way down.') But analysis is a onesided epistemic procedure. For again, without unities there would be nothing to analyze. To understand the being-unified of a unity therefore requires that we ascend to a point of view external to the unity under analysis.