Is the Difference Between a Fact and Its Constituents a Brute Difference?

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. 

Comments

[Steven]

Hi Bill,

Thanks for the post. I am sympathetic to the argument, and in fact I think that if is sound, it would prove to be one of the most important arguments of your book, for reasons I will cover at the end of this comment; but one thing is unclear to me.

I suppose you are arguing against a "groundless" theory of facts (GT) as follows. The GT states (a) There is no ontological ground of the unity of a fact's constituents, and because the GT-ist by hypothesis grants the difference between a fact and the sum of its constituents, he accepts (3). But somehow, some way, the GT-ist must accept (2), which contradicts (3); so GT is false.

I am not clear on why the GT-ist must accept (2). Is there an attempt to infer (2) from (a)?

It is true that the unity of the fact will not be "discoverable" by analyzing the fact, for familiar Bradleyan reasons. It won't be interior to the fact. And we won't discover it by external means such as sense perception. This is all just a consequence of the unity being brute!

But does this show that (a) entails (2)? The GT-ist could, it seems to me, simply say: Yes, the unity of a fact is incapable of discovery by analysis, nor is it empirically detectable. When you analyse a fact, all you get are constituents, not them unified. But nonetheless, the fact is something more than those constituents, and nothing accounts for this "something more."

My problem, therefore, is understanding the inference from (a) to (2).

Or, are you not trying to infer (2) from (a), but rather are trying to argue that the only way to have reason to reject (2) is if we admit of an ontological ground for the unity of a fact's constituents? Again, I would have to say it isn't clear to me why this is so!

I admit that I have framed the discussion in a different way than you did in your post, and this is perhaps the cause of the lack of understanding on my part.

- - -

I said above that this argument would prove to be quite important if sound. Note the following interesting consequence of this discussion, apropos to something else we were discussing Friday. You and I both believe that if we admit a ground of unity of facts (or more broadly, of ontological constituents of concrete particulars), we must admit an external unifier who is God. You and I think that there is a tight logical relation between fact or constituent ontology and theism, if we admit there is a ground of unity. But the problem for us is that it is not clear there must be a ground of unity, as much as the belief that there is a ground seems eminently plausible to us. One could remain a fact ontologist or a constituent ontologist and an atheist, if there need not be a ground of unity. But if there does have to be a ground, as your above argument attempts to show, then the constituent ontologist cannot also be an atheist. And if someone is an atheist, therefore, they must be a non-constituent ontologist.

But I remember you argue non-constituent ontology is incoherent. Then it follows that atheism is incoherent, pace our good friend Peter Lupu. Would you, if we manage to get the above argument cleared up (at least to my mind!), mind going over some of your arguments against non-constituent ontology?

[Bill Vallicella]

Steven,

Thanks for the prompt response. You ask why the GT-ist must accept (2), i.e., 'A fact is its constituents taken collectively.' Well, because when we analyze a fact all we find are its constituents. It's like King Milinda and his chariot. The Buddhist monk Nagasena demanded of the good king that he show the monk the chariot, when all the monk could find were wheels and hubs, etc.

What I am saying is that we and the GT-ist have good reason to accept (3) but also good reason to accept (2) -- despite their being logical contradictories.

I don't know what you mean by '(a).'

You make a good point: if the unity of a fact's constituents is a brute unity, then of course there will nothing internal to the fact that accounts for the unity.

Again, what does your '(a)' refer to? My 'a' is a logically proper name of an individual. It does not denote a proposition. One cannot infer anything from an individual.

So I'll stop here. I can't proceed until you tell me what '(a)' refers to.

[Steven]

Sorry, Bill, I should have been more clear. (a) is:

The GT states (a) There is no ontological ground of the unity of a fact's constituents...,

(a) is: There is no ontological ground of the unity of a fact's constituents.

[Bill Vallicella]

Oh, I thought you were referring to an 'a' in my post. You are asking whether I am inferring
2. A fact is its constituents taken collectively
from
a. There is no ontological ground of the unity of a fact's constituents.

No I am not. And it wouldn't follow. For one could hold that there is a unifier and it is a constituent of the fact.

My point is that we have as good reason to accept (2) as to accept (3) despite their being logical contradictories. I take it you accept (3). But don't you feel at least some inclination to accept (2)?

More later.

[Steven]

Okay, but now I'm having a hard time understanding what the argument against (a), i.e., the groundless theory is!

You're not, as you say, inferring the false (2) from (a). As you say, this inference wouldn't follow: "For one could hold that there is a unifier and it is a constituent of the fact." [But I think that's mistaken; after all, if the unifier was a constituent of the fact, there would then be an ontological ground of unity, and hence (a) would be false.]

But if you're not inferring (2) from (a), I don't understand how any of this is an argument against the GT-ist. After all, what have you said that a GT-ist couldn't say? Why couldn't the GT-ist say: "Ah, yes, there is more to a fact than its constituents: it is the constituents unified. But nothing accounts for or grounds this unity."

Are you trying to argue that the only way we can reject (2) is if we accept that there be a ground of unity, and hence (a) is false?

My problem is understanding the connection of the whole argument to (a), the groundless theory.

[Bill Vallicella]

Steven,

You didn't answer my question: Do you or do you not feel inclined to accept (2)? My point is that both (2) and (3) are reasonably accepted. Do you agree? If not, my argument will leave you cold.

How do you know that (2) is false?

Answer these questions and then we can proceed.

[Steven]

In response to your questions:

I think I must not be getting something, because I don't find myself at all compelled to accept (2). You're right, you don't find the unity of the fact just upon reflection of its constituent parts, but that hardly seems to me to be reason to accept that a fact is just the parts together; you don't find the unity of a chariot by reflecting upon its various parts, but if you know what a chariot is, you know it is not just a bunch of parts taken in collection.

Or, if that is some kind of reason to accept (2), it is only prima facie reason to believe (2); for upon further reflection one will find defeaters for (2). So belief in (2) may be reasonable, but only prima facie. Upon further reflection, it can easily be seen (2) is false.

I know (2) is false because there is clearly a difference between a mereological sum of some fact's constituents and the fact itself: the unity of the fact being what the difference is.

[Bill Vallicella]

Thanks for the nice, clean, direct response. You say you know that the following is false: a fact F = F's constituents. Let F be the relational fact Rab, e.g., Al's loving Betty. Then an instance of what you claim know is that Rab is not identical to R + a + b. (X + y is the mereological sum of x and y.) But some philosophers accept Extensionality of Composition, the principle according to which, if x and y are composed of the same things, then x = y. Now Rab and (R + a + b) are composed of the same things, hence fact and sum are identical.

This is not plausible as it stands, but is more plausible if you add the thesis of the Relata-Specificity of Relations: a relation is relata-specific iff it is in its nature to relate specific relata. If R in our example is relata-specific, then, as soon as it exists, it relates a and b. Consequently, R could not have existed and failed to relate a and b.

An objection has been made to my view along theses lines in "Relata-Specific Relations: A Response to Vallicella," Dialectica 62, 4 (December 2008) p. 509-524

So if one combines Extensionality of Composition with Relata-Specificity of Relations, then there is an argument for (2), and this would undermine your claim to know that (2) is false.

[Steven]

I have a few objections to such a view.

1. The argument from Extensionality of Composition conjoined with Relata-Specific Relations to (2) is invalid. Even if R could not exist and fail to relate a & b does not show there is no difference between the mereological sum R + a + b, and the fact Rab. Rab is still a structured entity, the mereological sum is not.

2. If R could not exist and fail to relate a + b, then Rab exists just as necessarily or contingently as R does. But an abstract critter like R would exist necessarily if at all, whereas Rab obtains contingently. Hence there must be a distinction between R's existing and R's obtaining, or relating, and thus there is room for Bradley-style worries about R operating as a unifier of a fact's constituents, even if R could only operate upon a & b.

3. A single ball is round, a certain weight, a certain color. But upon heating it, it loses the roundness and perhaps its weight while keeping its color. Heat it some more, then it loses its color as well. If relations are determined by their nature to relate the relata they do, then there must have been, in a single ball, 3 relations: one to relate the particular and some particular color, some particular weight, and some particular shape. This is uneconomical, given that that the ball has many more properties than just those three; we'd need who-knows-how-many relations to exist for any one of the particulars that exist in the actual world, not to mention that there are lots of particulars in the actual world. Positing a single relation which is a universal, i.e. not determined by its nature to relate any particular relata, is more economical.

4. There are a number of relations which appear to me to not be relata-specific in the above way suggested.

I exemplify whiteness, and so did my grandfather and Socrates (let's say). If numerically the same relation relates all of us to our whiteness, then this means no one else besides the persons that actually exemplified whiteness could have exemplified whiteness. But there are possible white persons.

Another example. If God exists, then everything stands in the relation "being created by" to God. But because of the relata-specificity of this relation, nothing else besides what God actually created could have been created by God. But this is contrary to divine omnipotence.