In Part I of this series I provided a preliminary description of the problem that exercises Orilia and me and a partial list of assumptions we share. One of these assumptions is that there are truth-making facts. We also both appreciate that Bradley's Regress ('the Regress') threatens the existence of facts. Why should this be so? Well, the existence of a fact is the unity of its constitutents: when they are unified in the peculiar fact-constituting manner, then the fact exists. But this unity needs an explanation, which cannot be empirical-causal, but must be ontological. The existence of facts cannot be taken as a brute ontological fact. But when we cast about for an explanation, we bang into the Regress. Let me now try to clarify this a bit further. We distinguish between an internal Regress and an external Regress, and in both cases we must investigate whether it is vicious or benign.
1. The Internal Regress and Whether it is Vicious
We can think of the Regress as arising either within facts, or outside of and between them. We thus distinguish between an internal Regress and an external Regress. A clear example of an external regress is the truth-regress. Let 'T' abbreviate 'It is true that ___.' 'Tp,' then, is to be read as 'It is true that p.' Now if p is any proposition, then surely p entails Tp. This is obviously iterable: Tp entails TTp which entails TTTp and so on ad infinitum. This infinite regress (progress?) is both infinite and non-vicious. It is non-vicious because, if the truth of p needs an ontological explanation, it will be in terms of a non-proposition, a truth-making fact or perhaps some other non-proposition, and not in terms of the next propositional member of the infinite series commencing wth p. Each member of the infinite series, if true, is true not because the next member of the series is true; the first member (assuming it is contingent) is true because of the way the world is and each succeeding member is true because it is entailed by the preceding member. (The 'because' in the preceding sentence is the 'because' of ontological explanation.) The members of the infinite series commencing with Tp play no explanatory role as regards the truth of p. If p is necessary, then presumably it needs no explanation. And even if it did need an explanation, it could not be in terms of the next member of the infinite series.
As far as I can see, nothing hinges on whether, following Bernhard Bolzano and Georg Cantor, one accepts actual infinities or instead rejects them in favor of the traditional notion that all infinities are potential. Fortunately, we needn't take a position on this question for present purposes.
The truth-regress, then, is a clear example of an infinite regress which is both non-vicious and external. It is external in that the regress does not subsist within p, Tp, TTp, or any member of the series; it subsists between the members, and is thus external to the members. Thus p entails Tp which is numerically distinct from p, Tp entails TTp which is numerically distinct from Tp, and so on. Due to the regress, an infinite complexity arises, but it is not an infinite complexity within a proposition, but an infinite complexity of propositions each of which is finitely complex.
Now consider the fact of a's being F. Although this fact has a and F-ness as constituents, it is not identical to its constituents. For the constituents can exist even if the fact does not. This is a possible scenario: there are facts Ga and Fb but no fact Fa. Since Ga exists, a exists, and since Fb exists, F-ness exists. So a and F-ness exist but Fa does not. Therefore Fa is not identical to its constituents. The existence of Fa is not 'automatic' given the existence of a and F-ness. How then do we explain the existence of Fa? One way is by attempting to uncover a further constituent in Fa that connects a and F-ness. We could call this the Internalist Approach to the problem of the unity of a fact. To quote from Orilia (p. 227):
What makes Fa an entity that exists over and above F and a is the presence in Fa of the dyadic exemplification [relation], E2, which connects F and a so that Fa = E2Fa.
The Internalist Approach begets an infinite regress within each fact. Let 'En' denote an exemplification relation of adicity n. Thus E2 is the dyadic exemplification relation. On the Internalist approach Fa = . . . E4E3E2Fa. That is, the fact of a's being F is infinitely complex in that it numbers among its constituents not only a and F-ness, but an infinity (actual or possible) of exemplification relations, dyadic, triadic, tetradic, and so on.
But is this a problem? Suppose there are actual infinities as Bolzano and Cantor maintained. Then, on the Internalist Approach to the problem of the unity of a fact, there is an actual infinity of constituents within each fact. And it might be thought that since this is an actual infinity, there is no exemplification relation that remains unconnected to the other constituents: at each stage of the regress the E in question unites all the preceding constituents, and since there is an actual infinity of Es, no E remains as an 'ununited uniter' or 'ununified unifier.' The problem with this, however, as Orilia clearly sees, is that the Internalist Approach implies than no constituent of Fa is really attributive. Let me explain.
If the fact Fa had just two constituents, F-ness and a, then F-ness would be the attributive constituent and a would be the subject or the 'argument' of the attribution. But of course there must be more to Fa than a and F-ness: there must also be that which connects them. Let the connector be the dyadic exemplification relation E2. The presence of dyadic exemplification in the fact has the effect of demoting F-ness from attributive role to argument role: F-ness and a are then the two arguments of dyadic exemplification. Triadic exemplification, in turn, demotes F-ness and dyadic exemplification to argument roles. And so on ad infinitum with the result that no constituent of Fa is really attributive. This is because every exemplification relation of adicity n gets demoted by an exemplification relation of adicity n + 1. And since no exemplification relation is really attributive, there is nothing internal to the infinitely complex fact to tie together all of its constituents. What we must conclude is that the Internalist Approach to the problem of the unity of a fact begets an infinite regress that is vicious. And so on the Internalist Approach we get no ontological explanation of the unity of a fact.
So far, Orilia and I are in broad agreement. We agree that: there are truth-makers; truth-makers are facts; facts are complexes possessing ontological parts; facts are (partially if not wholly) analyzable into these parts or constituents; there is a problem about the unity of a fact; the problem arises because a fact is more than its constituents and so cannot be identified with the list, set, sum, or collection of its constituents; the unity of a fact needs an explanation; this explanation cannot be empirical-causal, but must be ontological; ontological explanations are part of the tradition of philosophy; ontological explanations are 'kosher'; the unity of a fact cannot be an ontologically 'brute fact'; the truth-regress is external but benign; the Internalist Approach to the explanation of fact-unity issues in an infinite regress that is fact-internal and vicious and so cannot explain fact-unity; if there is to be an explanation of fact-unity, then an Externalist Approach must be explored.
I now turn to our disagreement.
2. The External Regress and Whether it is Vicious
Orilia proposes an Externalist Approach to the explanation of the unity (existence) of a fact along the following lines:
What makes Fa an entity that exists over and above F and a is the state of affairs E2Fa, understood as different from Fa, in that E2 is taken to be the really attributive constituent of the former, whereas F is taken to be the really attributive constituent of the latter. (p. 229)
As I formulate it, the problem is that we need a unifier of Fa's constituents. This unifier cannot be internal to the fact on pain of a vicious Bradleyan regress. So it cannot be a further constituent such as an exemplification relation. On this point Orilia and I are in agreement. And we agree that it won't do to say that the fact unifies itself if this means that it is in no need of a unifier. It follows, then, that the unifier must be external to the fact. For Orilia, the unifier of Fa is not an additional constituent but an additional fact, or rather an infinite series of additional facts. Thus the unifier of Fa is not a special unifying constituent internal to Fa, but a fact numerically distinct from Fa, namely, the fact E2Fa. But what makes this latter fact exist over and above its constituents? What is its unifier? On Orilia's view this is the fact E3E2Fa. As Orilia well appreciates, his proposal, which he calls "fact infinitism," gives rise to an external Bradleyan regress. But this regress, he maintains, is benign. The regress subsists between, not within, facts starting with Fa as the first member of the regress. Each member finds its ontological explanation in the next member. If we assume that there is an actual infinity of members, then each member has an explanation. And it does seem that Orilia needs the assumption of actual infinity. For if the regress were potentially infinite, then we could not say that each member has an explanation: the last member arrived at would go unexplained. But the assumption of actual infinity is readily granted.
I now explain why I do not accept Orilia's fact infinitism.
Glancing back at the last quotation, we note that the really attributive constituent of Fa is F-ness, and that the really attributive constituent of E2Fa is E2. Now to say that F-ness is attributive in Fa is to say that F-ness succeeds in connecting itself to, or unifying itself with, the argument constituent in Fa, namely, a. Simply put, F-ness's being attributive implies that F-ness is the unifier of Fa's constituents. But if so, then we have our ontological explanation of the unity of Fa, and can stop right here without explanatory recourse to the external infinite regress. Recall that the problem was to explain the difference between a + F-ness, on the one hand, and a's being F, on the other given that the constituents can exist without the fact existing. The problem was to explain was makes Fa an entity that exists over and above its constituents. Now the problem is solved if F-ness is really attributive. For then F-ness is both a unified constituent of Fa and the the unifying constituent of Fa: F-ness both occurs in Fa as an argument or subject and as a unifer. To put it metaphorically: F-ness is one of the items glued to a to form Fa, but also the glue. If so, the external Bradleyan regress has no explanatory significance whatsoever, any more than the truth-regress has explanatory significance when it comes to ontologically explaining the truth of contingent proposition p. We simply do not need the external Bradleyan regress for explanatory purposes if F-ness in Fa is a genuinely attributive constituent. For then F-ness is not merelya constituent of Fa, but a unifying constituent of it. It plays a dual role: it functions both as a proper ontological part of the fact, and as that which secures the unity of the fact's ontological parts thereby explaining why the fact is a non-supervenient entity over and above its constituents.
There is a tension in Orilia's treatment of the problem. On the one hand, he offers an ontological explanation of fact-unity and refuses to consider the existence of facts as ontologically brute. But the explanation he gives presupposes that facts are, after all, ontologically brute. For if he takes F-ness in Fa to be genuinely attributive, then the problem of fact-unity is solved as soon as it is posed: it is just a brute ontological given that a and F-ness are so related as to form a fact.
In sum, I agree with Orilia that the external Bradleyan regress is not vicious, but I disagree with him in that I hold that it has no explanatory role to play. I conclude that Orilia has not succeeded in explaining how facts are possible.