Vallicella on Orilia on Bradley’s Regress

1.  Some of us posit states of affairs (STOAs) as truth-makers of (some) contingent truths.  Bradley’s regress, however, poses a threat to the existence of STOAs.  Suppose individual a stands in relation R to individual b.  Suppose further that R is an external relation such as next to  and that R is a universal (as opposed to a relation-instance, or relational trope).  The STOA Rab  is a complex consisting of three constituents in which one of the constituents, R, connects the other two.  Since each of the constituents can exist without the others, the Bradleyan question arises as to what connects R to a and to b.  It seems a further relation is needed, namely, a triadic instantiation relation.  Thus is engendered the STOA I(3)Rab, where ‘I(3)’ denotes the triadic instantiation relation.  (In the monadic case, where a instantiates F-ness, we have I(2)Fa.)  But if a triadic instantiation relation is needed to connect R, a, and b, then (given that I(3) is both external to its relata and a universal) it would appear that a tetradic instantiation relation is needed to connect I(3), R, a, and b.  And so on ad infinitum.  Of course, not every infinite regress is vicious.  The Bradleyan idea, however, is that this regress is vicious, and threatens the existence (in ultimate reality) of both external relations and STOAs.  (Since a relation that does not relate anything is arguably no relation at all, it seems clear that external universal relations and STOAs stand and fall together.)

2. There are several responses to the Bradleyan threat.  A nearly exhaustive catalog and critique of them is provided in my A Paradigm Theory of Existence, ch. 7.  One of D. M. Armstrong’s proposals — his main proposal — is that STOAs are a special type of complex: a STOA is a complex that holds its constituents together.  Thus there is no need for instantiation relations to secure this togetherness.  More generally, there is no need for anything internal to a STOA — whether an instantiation relation or an ordinary relation or a Bergmannian nexus — to secure the togetherness of the STOA’s constituents.  If Armstrong is right, the regress cannot begin.  Orilia favors a different approach, which he calls “fact infinitism,” an “unjustly neglected alternative” according to which  “the infinity of distinct relations and facts . . .” is unproblematic or non-vicious.  At this point we may insert a minor criticism.  Something like the alternative Orilia calls “unjustly neglected” is proposed by Richard Gaskin in “Bradley’s Regress, the Copula and the Unity of the Proposition,” The Philosophical Quarterly (April 1995), pp. 161-180.  Nevertheless, Orilia’s contribution is substantially different and contains several new insights.                

3. The general problem before us is that of the unity of a complex.  If we take ‘complex’ broadly enough, we should be able to agree that some complexes are such that their existence follows immediately from the existence of their members or constituents.  I have in mind sets and the sums or fusions of unrestricted mereology.  But I mention those types of complex only to set them aside.  The unity problem begins in full earnest with complexes whose constituents are only contingently united.  Since the unity of the constituents of a complex c is equivalent (and perhaps identical) to c’s existence, we may refer to these complexes as contingent complexes.  Prima facie, four types of contingent complexes should be distinguished: (A) ordinary physical complexes, whether natural or artificial; (B) truth-makers, which I am here assuming (on the basis of arguments in my PTE) are STOAs; (C) truth-bearers, whether these are contents of judgments, declarative sentences uttered assertively, or whatever; and (D) unities of consciousness/self-consciousness, whether synchronic or diachronic.  

4. Ad (A).  If a tree stump and a board exist, it does not follow that a primitive table T consisting of a board B on top of a tree stump S exists.  There is a difference between the set {B, S} and T just as there is a difference between the sum (B + S) and T.  In response to some Orilian pressure emanating from p. 11 of his article, however, I can make the point without assuming the existence of sets and sums.  Clearly, there is a difference between B and S taken collectively and T.  T is not identical to B; T is not identical to S; T is not identical to B and S taken (in thought) together; and of course T is not identical to something wholly distinct from B and S, the atman of the table, if you will.  The problem here is essentially that of the Chariot in Milinda’s dialogue with Nagasena.  (Click on my Buddhism link to read about chariots and how far they can take us into the land of anatta / anatman.)         

What then is T?  T is the unity of its parts, their connectedness.  This unity is not nothing, but it is also not something.  It is not nothing, because it is what makes the difference between B + S and T.  But it is not something that can be found by analysis of  T. Unless we are willing to embrace the contradiction of saying that the unity of T’s constituents is both something and nothing, we must find a way to remove this (apparent) contradiction.  As I see it, this is the correct statement of the problem of the unity of a complex.

Thus I am saying that there is something unintelligible about contingent complexes.  T is more than B + S, and so is not identical to B + S.  Yet T is identical to B + S since there is nothing in T to distinguish T from B + S.  The same goes for STOAs.  A STOA is not identical to its constituents, since it is their unity; yet it is identical to them, since there is nothing in it to distinguish it from them.  Orilia does not accept that there is any (apparent) contradiction here.  To him, it is obvious that there is no contradiction, and that the situation is “perfectly intelligible.”  To my claim that a’s being F is identical to a + F-ness (because there is nothing to distinguish the STOA from its constituents), Orilia’s response is that the difference “consists in the fact that we have three entities in the one case,  Fx, F and x, and only two in the other one, namely F and x.”  (p. 11)

This simply begs the question against me.  I am saying that there is a problem about admitting into our ontology such contingent complexes as STOAs.  The problem is that they appear to be self-contradictory structures in that a STOA is distinct from its constituents, but without there being anything that distinguishes a STOA from its constituents.  To respond to this by saying that a STOA consists of three entities while its constituents (taken collectively) consist of only two is equivalent to saying that what distinguishes a STOA from its constituents is the STOA itself.  But Orilia has no right to assume that there any STOAs unless he can explain how Fa, which is composed of F-ness and a, is more than F-ness and a.  He has already admitted, on p. 1 of his paper, that STOAs are “theoretical entities” whose existence can be denied if their postulation leads to a contradiction.  In short, if I argue that STOAs cannot exist because they are self-contradictory, but Orilia presupposes that they do exist and so cannot be self-contradictory, then Orilia begs the question against me, and we have a stand-off.

But not only does Orilia beg the question against me, it appears that his suggestion leads to the untenable  result that a STOA is wholly distinct from its constituents. It is clear that F-ness and a are wholly distinct from each other in that neither is a proper or improper part of the other.  But a’s being F cannot be wholly distinct from its constituents, since it is composed of them.  Orilia, however,  must hold that STOAs are wholly distinct from their constituents.  For if what distinguishes a STOA from its constituents is the STOA itself, then

a) The STOA = that which unifies its constituents (the unifier).  But,

b) The STOA = a + F-ness + unifier.  This implies that

c) The STOA = a + F-ness + the STOA.  (From a, b) But,

d) The unifier (= the STOA) cannot be a proper constituent of the STOA. Therefore,

e) The STOA is wholly distinct from its own proper constituents.

Suppose a big fish swallows two smaller  fishes. How many fish do we have? We have three fish.  So in this case, the difference between the big fish with two fish-constituents and the two fish-constituents is the difference between three fish and two fish.  But a STOA does not contain its constituents in the way the big fish contains the two smaller fishes.  Now compare a wall constructed from 1000 stones with a stone vault containing 1000 stones.  In the second case, there are clearly 1001 stone objects.  But in the first case, it is not clear that there are 1001 stone objects.  The stone wall is obviously not wholly distinct from its stone constituents, whether taken distributively (one by one) or collectively.  The stone wall is also not wholly identical to its constituents.  The truth seems to be that the wall is partially identical to and partially different from its constituents.  The partial difference is due to the stacking or arrangement of the stones.  The arrangement – which also accounts for why the wall is a wall rather than a heap – is obviously not a further constituent of the wall, nor is it the wall itself.  The arrangement is real, but cannot be found in or at the wall; hence, if we restrict ourselves to the wall, we get a contradiction: the arrangement is both real and unreal.

On p. 11, Orilia gives the example of a bicycle with n parts. He says that when the bicycle is unassembled, there are n objects.  But when it is assembled, there are n + 1 objects.  But this strikes me as mistaken.  Suppose I start counting the bicycle’s proper parts and arrive at the number n.  I cannot add the bicycle itself to the arithmetical sum for the simple reason that the bicycle is not a proper part of itself.  It is at most an improper part of itself.  The bicycle is just the proper parts assembled; it is not a further proper part, which, when added to the ‘canonical’ proper parts, results in the bicycle.  Orilia is treating the bicycle as if it were wholly external to its proper parts.  Furthermore, if I could count the bicycle as a proper part, why could I not count the front tire-cum-tube as a proper part of the bicycle? The list of proper parts would then look like this: tire, tube, tire-cum-tube, tire-cum-tube-cum-rim, etc.

As for my idea that the unifier of a contingent complex must be external to it, Orilia has this to say: “to appeal to an assembler to describe the difference [between the unassembled and assembled bicycle] is to illicitly move from the ontological level to the level of causal explanation.” (p. 11) But since I have refuted Orilia’s suggestion that the difference is that between n objects on the one hand, and n + 1 objects on the other, we need some explanation of the real difference between an unassembled bicycle – which of course is not a bicycle stricto sensu – and the same bicycle assembled.  We cannot invoke the connectedness of the parts,  if this is taken to be a further part, nor can we invoke the connectedness if this is taken to be the bicycle itself.  We must think of the connectedness as the effect of a cause.  In this way we remove the contradiction of saying that the connectedness is both something and nothing.  It is something in that it derives from a cause.  It is nothing in that it is no independent entity in or at the bicycle.

There is the wider question of causal/ontological level-confusion.  It is not obvious that there cannot be a causal explanation of an ontological difference.  John Searle holds, with some plausibility, that brain events cause mental events despite the fact that the two sorts of events differ ontologically, i.e., in their mode of existence.  I believe he speaks of a 3^rd person and a 1^st person mode of existence. (See his The Mystery of Consciousness, 1997) But this is a large issue that cannot be adequately addressed on this occasion.

5.  Ad (B)  The (apparent) contradiction therefore remains in force on Orilia’s approach.  The contradiction, once more, is that the unity of a complex is not nothing, but it is also not something either isolable in experience – it cannot be empirically detected – or discoverable by analysis.  Before we consider how Orilia removes it, if he does remove it, let’s ‘up the ante’ as they say by noting that a STOA is not just any old complex, the unity of whose constituents is contingent, but a complex the unity of whose constituents equips it to function as a truth-maker.  The unity of a bicycle’s parts gives those parts ‘bicycle-functionality,’ a property not possessed by the parts taken distributively – one by one – or collectively (as a mere collection or sum).  But the unity of a bicycle’s parts does not in any obvious sense confer upon the bicycle the property of being a truth-maker.  So STOAs possess a peculiar type of unity.  For one thing, the unity of a STOA such as a’s being F is not a symmetrical togetherness like we find in T: S is together with B iff B is together with A.  It is rather the asymmetrical togetherness of instantiation or exemplification: if a instantiates F-ness, then F-ness does not instantiate a.  Since STOAs possess a type of unity not found in ordinary physical complexes, we should not expect that a solution to the unity problem for the latter will also solve the unity problem for the former.

6.  It appears that Orilia understands the problem of the unity of a complex differently than I do.  As he puts it, “The question is, given that a generic complex c is assumed to exist, why is it true that c exists. . .?”  He goes on to say that the answer should provide a “unification proposition” P that asserts that the constituents of c are unified.  Hence, the explanation of why it is true that c exists should be of the form, “it is true that c exists in virtue of P’s being true.” (p. 5) One of the positive features of Orilia’s paper is that, unlike many philosophers, he carefully explains the ‘in virtue of’ relation, marking it off  from the entailment relation.  Whereas entailment is reflexive in that every proposition entails itself, ‘in virtue of’ is irreflexive: no proposition is true in virtue of itself.  A minor criticism: Orilia use ‘anti-reflexive’ when the standard term is ‘irreflexive.’  A more serious problem, however, is that Orilia appears to confuse asymmetry with anti-symmetry. (Of course, it may be that he is simply unfamiliar with the standard English term.)   ‘In virtue of’ is asymmetric in that, if P is true in virtue of Q’s being true, then it is not the case that Q is true in virtue of P’s being true.  To say that ‘in virtue of’ is anti-symmetric, however, would be to say that if  P’s being true is true in virtue of Q’s being true, and Q’s being true is true in virtue of P’s being true, then P = Q.  Asymmetry and anti-symmetry are distinct properties.

7.  These technical quibbles aside, I have two main philosophical criticisms.  First of all, if the problem is to account for the unity of a STOA, it is not clear how bringing propositions into the picture can help.  For a proposition is itself a contingent unity of constituents.  (Of course, much depends on how exactly propositions are conceived, and Orilia does not say anything about this in the paper in question.) Note that, for Orilia, the relata of the ‘in virtue of’ relation are propositions.  Thus the explanandum proposition c exists is said to be true in virtue of the “unification proposition” P asserting that the constituents of c are unified.  But this assumes that the unity of propositions is unproblematic.  It seems to me, however, that the proposition that a is F is just as problematic as the STOA a’s being F.  The proposition is problematic because it apparently both is and is not its constituents.  It is not identical to its constituents because it is their unity, a unity that is not nothing.  It is identical to its constituents because there is nothing in the proposition that could be called its unity.  A proposition is obviously not a list, set, or sum of its constituents.  It is a peculiar unity of constituents that equips the proposition to serve as a truth-bearer.  But this unity cannot be identified with any constituent of it, not even a special constituent posited to play a unifying role. Thus there is an apparent contradiction that needs to be removed.  We are in the same predicament we were in with STOAs: they are apparently self-contradictory structures.  Invoking them to explain STOAs, if not a case of obscurum per obscurios, seems to be a case of explaining the obscure in terms of the equally obscure.

8.  More fundamentally, however, Orilia simply helps himself to the existence of contingent complexes when he writes, “given that a generic complex c is assumed to exist . . .” (p. 5) This cannot be legitimate, since the precise problem bequeathed to us by Mr. Bradley is to explain how it is possible that there be any contingent complexes in the first place.  In effect, Bradley’s message is that a STOA cannot exist in ultimate reality because it involves a contradiction.  If Orilia simply assumes that there are STOAs in ultimate reality, then he begs the question against Bradley and me.  Since Orilia admits, on p. 1, that STOAs are “theoretical entities,” he cannot take the existence of STOAs to be obvious or ‘datanic.’ In plain English, it is not a datum, a given, that there are STOAs.

Now if A accuses B of begging the question, it is often the case that B, with equal right, can accuse A of begging the question.  We then enter the dreaded circle of mutual question-begging.  Thus if I say to Orilia, “You beg the question against me by simply assuming that STOAs are non-contradictory,” he can reply, “But you beg the question against me by assuming that STOAs are contradictory.”  It seems to me, however, that this reply is not effective, since I have argued in painful and mind-numbing detail for the contradiction in question.

9. Now for some comments on Orilia’s reconstruction of Bradley’s regress.  On p. 9, we read: “For any c, if c is a complex, then the proposition that c exists initiates an infinite vicious regress.”  This is true at most for contingent complexes.  Sets and sums do not ignite a regress.  But this is a minor quibble.  My real problem is Orilia’s claim on p. 9 that  “…that a complex c exists is true in virtue of a proposition E!(Ux1 … xn) ….”   For example, the proposition P that a’s being F exists is true in virtue of the truth of the proposition P* that a’s exemplifying of  F-ness exists, which in turn is true in virtue of the truth of the proposition P** that a, F-ness, and dyadic exemplification’s exemplification of triadic exemplification exists, ad infinitum.  I simply deny this.   P is true in virtue of the existence of  a’s being F, not in virtue of the truth of

P*.  It appears that Orilia has it precisely backwards: it is the STOA, which is not a proposition (though it is proposition-like as Armstrong points out), that makes P true. Thus P is true in virtue of the STOA’s existence and not in virtue of P*’s truth.  Part of the problem here is that Orilia defines ‘in virtue of’ as a relation on propositions.  But truth-making is not a relation between propositions, but between something extra- or sub-propositional and a proposition.  Another part of the problem is that Orilia – as I said above – just helps himself to the existence of STOAs, when their existence is precisely what is in question.  He therefore shifts the problem to the level of propositions when it is at the level of STOAs.  In other words, the vicious regress occurs within the STOA, not among propositions.

On p. 10, Orilia makes a perceptive observation.  He says that his “fact infinitism” “…is compatible with the main conclusion that Vallicella (2000, etc.) reaches after his thorough investigation of states of affairs, namely, that the ‘unifier’ of a state of affairs, as he puts it, is external to the state of affairs in question, i.e., is neither a constituent of it, nor the state of affairs itself.”  This is correct: we both hold that the unifier of a STOA’s constituents must be external to it.  Orilia’s idea seems to be that the unifier of a given STOA is another higher-order STOA, and so on ad infinitum.  Orilia’s idea could perhaps be interpreted as follows: the unifier of a STOA’s constituents is the entire actually infinite sequence of propositions beginning with the first “unification proposition” P, and proceeding to P*, P**, etc.  This seems close to R. Gaskin’s view that “Bradley’s regress is the metaphysical ground of the unity of the proposition.” (p. 176)  If so, Bradley’s regress would be positively virtuous and not merely benign.

But I detect a confusion in Orilia between STOAs and propositions.  Or does he identify the two?  He uses ‘state’ and ‘proposition’ – two different terms – and this suggests a distinction.  Is it the proposition that Fa exists that is the unifier of Fa’s constituents?  This seems to be Orilia’s idea especially from p. 5.  But I find this notion incoherent.  The proposition that Fa exists merely REFLECTS or RECORDS the unity of Fa’s constituents, it does not GROUND that unity.  The unifier is an ontological ground of unity; it is not a mere proposition that states that the constituents of a STOA form a unity.  To be honest, I cannot understand how a proposition could function as the unifier of a STOA’s constituents.  Suppose I have two boards and some glue.  The proposition that the boards are glued together does not bring it about that they are glued together.  And if the boards are glued together, then the proposition that states this is true because the boards are glued together, and not vice versa..  The ground of the difference between the glued and the unglued boards cannot be either the glue – since a dab of glue can exist without gluing anything – or the glued boards, for reasons I have already belabored.

To help clarify my critique of Orilia, let us distinguish among vicious, benign, and virtuous regresses.  We already know what a vicious regress is.  Here is a benign regress: p; it is true that p; it is true that it is true that p, and so on ad infinitum.  This is benign because p’s truth is not explained by the truth of ‘It is true that p,’; rather, p’s truth is explained by p’s truth-maker, which is something extra-propositional, namely, a STOA.  Note that, in the benign truth regress,  there is a sense in which the members beyond p are merely ‘along for the ride’ and ‘do no real work.’  A positively virtuous regress, therefore, is one in which all the members of the infinite sequence ‘do real work.’    Suppose that every state of the universe is caused by an earlier state, and that there is no first state.  It follows that every state is caused.  This may be an example of a virtuous regress.  So it looks like Orilia’s “fact infinitism” amounts to the embracing of such a virtuous regress, a regress that is positively necessary to secure the unity of a STOA’s constituents.

On p. 10, Orilia states that “Vallicella neglects infinitism….”  I believe this is false.  In my PTE, pp. 209-211, I discuss and refute a position that derives from McTaggart which is essentially that of fact infinitism.

10.  On p. 13, Orilia discusses the question of tropes and how they may or may not provide a solution to the Bradley problem about unity.  Here I would refer Orilia to my forthcoming paper, “Bradley’s Regress and Relation-Instances.” He  should also consult Anna-Sofia Maurin’s discussion of Bradley in her bizarrely titled book, If Tropes (Kluwer, 2002), pp. 134-163.

11.  To conclude these comments, I cannot see that Orilia has successfully defended the ‘brute fact’ view according to which it is the STOA itself that holds its constituents together.  And I cannot see what his fact infinitism comes to, inasmuch as it appears to rest on a confusion of STOAs and propositions, and thus a confusion of the benign truth regress with some kind of virtuous STOA regress.  To the extent that I understand fact infinitism, I have already refuted it in my discussion of McTaggart in PTE.  But Orilia’s paper is a preliminary draft, and it may be that I will come to understand his view when he explains it more clearly.  His paper is needlessly technical – given his desire for complete generality at every step – and needs to be better organized.  That being said, there is much excellent material here about the ‘in virtue of’ relation and the various types of regress.  I thank Orilia for giving me the opportunity to study his paper and learn from it.  I look forward to future exchanges with him.