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.
Let me say first of all that I enjoyed very much the admirably clear description of the issue and of our shared assumptions provided by Vallicella, as well as his nice summary of my paper. And let me also say that Vallicella’s writings on Bradley’s regress aroused again my interest on this topic after I had written on it many years before and I did not think there was any need to go back to it. The paper in Meinong Studies under scrutiny here has a 2004 unpublished ancestor. The email correspondence with Vallicella and the previous discussion on his site certainly helped me to derive from it the Meinong Studies paper.
Having said this, let me explain why I disagree with Vallicella’s present criticism. I would like to use an analogy to illustrate where I think he is wrong. Consider a stupid physical object made just of two lego parts, say a red one r and a green one g plugged on top of r. Call this object gr. What makes gr one object, as opposed to two disconnected items, is, we may say, the fact that g is plugged on top of r. Moreover, we may add, this fact makes gr an object such that its part g has the “superior” role and r the “inferior” role. Without this fact, g and r could not have these roles in gr, for they would not have been parts of an object or would have been parts of a different object. For example, had r been plugged on top of g, we would have had another object, which we could call rg, instead of gr, an object with g as filling the inferior role and g the superior role. Still, we do no want to say that the relation *plugged on top*, or the state of affairs *g is plugged on top of r*, are additional parts of gr. Similarly, it seems to me that we can say (at least for present purposes) that Fa has only the constituents F and a and that they make up a complex Fa because there is the additional state of affairs E2Fa. F could not have the attributive role in Fa without the additional state of affairs E2Fa. And thus it is wrong to say that F “succeeds in connecting itself” to a so as to give rise to the complex Fa. F cannot succeeds by itself. There is the need of a relation (namely, E2) and a state of affairs involving that relation. And, depending on the relation, the kind of complex that is generated changes.
For example, if we admit sets in our ontology, we may view the set {F, a} as made up of the same constituents F and a, but brought about by a different state of affairs, namely, say, *F and a constitute-one-set*, a state of affairs involving the relation *constitute-one-set* as attributive constituent. In my terminology, the set {F, a} is an object that supervenes on its constituents, i.e. an object that must exist if its constituents F and a exist. In contrast, the state of affairs Fa does not supervene on F and a (on the assumption that F is a contingent property of a). (I believe that Vallicella would call Fa simply contingent rather than supervening on its constituents, as I propose). In the paper of mine under discussion here I confined myself to entities, more specifically state of affairs, that supervene on their constituents. But it seems to me that the problem of explaining how a complex that supervenes on their constituents is brought about arises just as it arises for complexes that do not supervene (see note 7 of my paper). And it is not enough to say that the former are brought about because of the necessity of their being around, given that the constituents are around. For we may want to admit that different complexes supervene on the same constituents.
For instance, if we admit unrestricted mereological sums in addition to sets, we should say that both the set {F, a} and the mereological sum F+a supervene on F and a. But these two objects differ because, we may say, they depend for their existence on two different states of affairs. The former depends on the above mentioned *F and a constitute-one-set*, and the latter on something like *F and a constitute-a-mereological-sum*.
(A terminological remark for clarity’s sake: I have simply written “F” in many cases in which Vallicella would have written F-ness.)
Hence, it seems to me that we can and must appeal to E2Fa to explain why Fa is around (and is the kind of complex it is), but by the same token we must appeal to E3E2Fa, etc. And by contemplating, so to speak, the whole sequence (which Vallicella admits not to be vicious) we can have an ontological explanation of the existence of Fa.
Posted by: Francesco Orilia | Sunday, November 16, 2008 at 01:01 AM
Francesco,
Thanks for your detailed reply and for writing such a stimulating and interesting paper. You write, "Similarly, it seems to me that we can say . . . that Fa has only the constituents F and a and that they make up a complex Fa because there is the additional state of affairs E2Fa. F could not have the attributive role in Fa without the additional state of affairs E2Fa. And thus it is wrong to say that F “succeeds in connecting itself” to a so as to give rise to the complex Fa. F cannot succeed by itself. There is the need of a relation (namely, E2) and a state of affairs involving that relation."
But let's compare this with what you said in your paper: "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)
Your official theory is that there are two numerically distinct facts Fa and E2Fa. In Fa, F-ness is really attributive, while in E2Fa, E2 (dyadic exemplification) is really attributive, which of course implies that in E2Fa F-ness is not really attributive but plays the role of an 'argument.' (We can drop 'really.') Now if F-ness is attributive in Fa, then how can it be that "F cannot succeed by itself" in connecting F-ness and a, as you say in your comment above? It is not clear to me how the following propositions can all be true:
1. F-ness is attributive in Fa, and is thus not a mere argument.
2. Fa and E2Fa are distinct facts.
3. What makes F-ness attributive in Fa is the distinct fact E2Fa in which F-ness is not attributive, but plays an argument role.
Given (2), F-ness in Fa has no need of E2Fa to make it attributive.
Posted by: Bill Vallicella | Sunday, November 16, 2008 at 01:01 PM
Dear Bill,
Dear Francesco,
I apologize for interrupting your interesting discussion.
Perhaps it would be helpful to explicate and generalize your take(s) on viciousness. I think both of you would agree that it has to do with explanation and explanatory failures (e.g. Bill wrote: "on the Internalist Approach we get no ontological explanation of the unity of a fact").
But how exactly? Up to now I failed to see a general and intelligible criterion in terms of explanation on which the, what you call, Internal Regress turns out vicious.
Many thanks
& see you soon,
Jan Willem
Posted by: Jan Willem | Sunday, November 16, 2008 at 02:36 PM
Jan Willem,
Welcome to the discussion. You raise an excellent point: unless we have a clear criterion of viciousness, we won't be able to determine with confidence whether a given regress is vicious or not. It seems clear that viciousness has to do with explanatory failure, more precisely, ontological (as opposed to causal) explanatory failure. The idea of ontological explanation also needs clarifying.
Are you suggesting that you do not find the internal Bradleyan regress vicious?
What would you propose as a general criterion of viciousness?
I wonder if Francesco has a general criterion in mind.
Posted by: Bill Vallicella | Sunday, November 16, 2008 at 06:35 PM
Dear Bill,
I tried the following. Please let me now if you find certain steps implausible or superfluous.
Here's an instance of B's regress for the relevant abbreviations:
(T) aRb
(IP) In virtue of what does R relate a, b?
(IR) In virtue of EX1 which unifies R with a and b.
(IP-sim1) In virtue of what does EX1 relate a, b, R?
(IR-sim1) In virtue of EX2 which unifies EX1 with a, b, R.
(IP-sim2) In virtue of what does EX2 relate a, b, R, EX1?
(IR-sim2) In virtue of EX3 which unifies EX2 with a, b, R, EX1.
And so on to infinity.
The argument in five steps (1)-(5):
1. Any response involves a new problem, and any problem has its response: IP, IR, IR involves IP-similar, IR-similar, to infinity.
2. The solution to IP (wholly or partly) depends upon all the solutions to an infinity of IP-similars: IR because [IR-sim1 & IR-sim2 & IR-sim3 & IR-sim4 & etc.]
3. IP isn’t solved until all IP-similars are solved.
4. There will arrive no point at which all IP-similars are solved.
5. Hence, IR can’t solve IP. (1-4)
If this works, then we proved the explanatory failure of the theory (IR) that generates B's regress. Besides, the criterion of viciousness would be (2): A regress is vicious iff the solution to IP (wholly or partly) depends upon all the solutions to an infinity of IP-similars.
However, I have a hard time accepting the argument for mainly two worries:
(i) What exactly is explanatory dependence? What do we know about this relation?
(ii) Step (4) is ambiguous and disputable. What's meant by "point"? If it's a point in time, then one may deny its importance.
So, as long as there are open questions like these (and perhaps others), I think we can't dismiss the theory which has an infinity of binding relations EXs per complex. Or course, one may be unhappy with so many strange ontological posits, but in that case one doesn't reject the theory for its explanatory failure.
Posted by: Jan Willem | Monday, November 17, 2008 at 02:23 AM
Jan writes, "I think we can't dismiss the theory which has an infinity of binding relations EXs per complex. Or course, one may be unhappy with so many strange ontological posits, but in that case one doesn't reject the theory for its explanatory failure."
Suppose that each fact or complex contains an actual infinity of exemplification relations. I have no problem with this idea. And you are right that such a wild proliferation of entities does not amount to explanatory failure. But Orilia's point, which I endorse, is that in a fact containing an actual infinity of exemplification relations, none of these relations is attributive: each plays only the role of an argument. Let the fact be Rab. If triadic exemplification is introduced to tie together a, R, and b, then the result is EXRab in which R has been demoted from attributive status to argument status. Metaphorically, R is no longer the glue that connects a to b, it is just one more item that needs gluing. At the next step EX*EXRab, EX is demoted to mere argument status. And so on ad infinitum. Now if there is an actual infinity of exemplification relations in each fact, then all of them get demoted to argument status so that none of them is attributive. An attributive exemplification relation would be an 'undemoted demoter.' But there cannot be an undemoted demoter in a fact that is infinitely complex. And since there is no undemoted demoter, there is no constituent in the fact that serves to unify all the fact's constituents.
So it sems to me that the Internalist Approach to fact-unity fails for this reason, and not because of the proliferation to infinity of fact constituents.
Posted by: Bill Vallicella | Monday, November 17, 2008 at 06:34 PM
You write: "Let the fact be Rab. If triadic exemplification is introduced to tie together a, R, and b, then the result is EXRab in which R has been demoted from attributive status to argument status. Metaphorically, R is no longer the glue that connects a to b, it is just one more item that needs gluing. At the next step EX*EXRab, EX is demoted to mere argument status. And so on ad infinitum."
The point in case of infinite regresses, I think, is that one may put the very same chain in a negative and positive way:
- Each relation gets "demoted" by the next VS each relation relates in virtue of the next.
- Each problem (e.g. the unity of aRb) gets shifted to the next (the unity of EX1aRb) VS each problem has its solution.
So, I'm not sure we can say a regress is vicious by choosing the negative description. Perhaps the step to the "actual infinite" will do the trick, but then we'll need the details. (I'm sorry if you think this is getting boring, but I'd really love to hear more.)
Posted by: Jan Willem | Tuesday, November 18, 2008 at 12:34 AM
Jan Willem,
I appreciate your comments and I look forward to meeting you. Boring? Not at all. Quite the contrary: permanently fascinating to someone of my cast of mind.
You are making a very good point which deserves a thoughtful response. Agreeing with Francesco, I said that each EX relation is demoted by the next from attributive status to argument status. Thus, in . . . EX**EX*EXRab, EX demotes R, EX* demotes EX, EX** demotes EX* and so on through an actually infinite series of demotions, with the result that no exemplification relation is an 'undemoted demoter,' which implies that all the constituents of the fact are ununified or 'unglued.' My conclusion was that the internal Bradley regress is vicious: no decent expanation has been provided of the unity of the fact. Your point is that it is equally plausible to view each exemplification relation as a genuine 'relating relation' (Russell used this phrase in his debate with Bradley) in virtue of the next exemplification relation. On this way of looking at it, the internal regress is not vicious since every exemplification relation is attributive in virtue of the next.
But even if both ways of looking at the situation, the negative and the positive, are equally valid (and I am not quite convinced that they are), it seems a different problem arises. For now, at every stage of the regress what we have is an ex. relation which is both attributive and non-attributive (or 'argumentative') -- and that is a contradiction which 'condemns' (as Bradley might have said) the fact to nonentity.
It seems you cannot deny that my negative way of looking at the situation has merit. Now supposing that your positive way of looking at it also has merit, equal merit, then that would seem to suggest that each ex. relation harbors a contradiction. For each is both rendered attributive by the next relation AND demoted from attributive status by the next relation. So again I get the result that I and Bradley want, namely, facts cannot be 'independent reals': they need a unifier but that unifier cannot be a constituent or constituents.
As for actual infinity, wouldn't you say that your view that there is no internal vicious regress logically requires the existence of actual infinities? Isn't it worse for you if infinity is potential?
Posted by: Bill Vallicella | Tuesday, November 18, 2008 at 01:17 PM
Dear all
this is just a brief note to say that I have not yet replied because I have been busy working on, guess what?,my draft for the Bradley conference in Geneva,as I am trying to meet the Novemeber 20 deadline decided by the organizers. But I shall try to reserve a niche for this nice debate today or tomorrow.
Francesco
Posted by: Francesco Orilia | Tuesday, November 18, 2008 at 10:55 PM
"For now, at every stage of the regress what we have is an ex. relation which is both attributive and non-attributive (or 'argumentative') -- and that is a contradiction which 'condemns' (as Bradley might have said) the fact to nonentity."
This is a very interesting and surprising suggestion!
I've to pack for Geneva, but I hope to return to this and your new post on regresses soon.
Posted by: Jan Willem | Wednesday, November 19, 2008 at 07:53 AM
Francesco,
I look forward to your further comments when you find time to make them. Did they give us a deadline? Well, then I should send something in too!
Jan Willem,
You are headed for Geneva already? I would very much like your comments on the newer regress posts.
Posted by: Bill Vallicella | Wednesday, November 19, 2008 at 03:58 PM
Dear Bill and Jan:
Let me first deal with Bill’s worry about my approach and then move to the points raised by Jan and commented on by Bill.
Bill says:
“Your official theory is that there are two numerically distinct facts Fa and E2Fa. In Fa, F-ness is really attributive, while in E2Fa, E2 (dyadic exemplification) is really attributive, which of course implies that in E2Fa F-ness is not really attributive but plays the role of an 'argument.' (We can drop 'really.') Now if F-ness is attributive in Fa, then how can it be that "F cannot succeed by itself" in connecting F-ness and a, as you say in your comment above? It is not clear to me how the following propositions can all be true:
1. F-ness is attributive in Fa, and is thus not a mere argument.
2. Fa and E2Fa are distinct facts.
3. What makes F-ness attributive in Fa is the distinct fact E2Fa in which F-ness is not attributive, but plays an argument role.
Given (2), F-ness in Fa has no need of E2Fa to make it attributive.”
The point, as I see it, is this. F is attributive in Fa because it is related to a in a certain way, namely by exemplification. Were it not related to a in any way it could not be a constituent of a complex together with a. Were it related to a in another way, rather than by exemplification, we could not say that it would have an attributive role with respect to a. Suppose, for illustration, that there is a fact such as *F is more abstract than a*. Then F and a are related but not in a way that gives F the attributive role with respect to a. Thus, F by itself, i.e., without being related to a, and being related by exemplification, cannot have the attributive role. So we need 1 and 3. Moreover we must accept 2, otherwise we get the internalist Bradley regress, which seems to me vicious for the reasons I have explained in my paper and that Bill has endorsed in his reply to Jan. But, more precisely, I do not want to say that Fa and E2Fa must be different just because otherwise we get the internalist regress. Independently of that, it seems to me that that is the right thing to say by reasoning analogically (for what is worth) by way of comparing Fa to the lego object gr made of the two pieces g and r. The object gr (rather than rg) exists because g is on top of r. But the relation being on top is not a part of gr. Its parts are just g and r. Rather, being on top is a constituent of the state of affairs *g is on top of r*. Similarly E2 is not a constituent of Fa and thus Fa is distinct from E2Ra. The issue of course is whether even in this case we get a vicious regress and thus we come to one of the points raised by Jan Willem who says:
“Perhaps it would be helpful to explicate and generalize your take(s) on viciousness.”
And Bill replies:
“You raise an excellent point: unless we have a clear criterion of viciousness, we won't be able to determine with confidence whether a given regress is vicious or not. It seems clear that viciousness has to do with explanatory failure, more precisely, ontological (as opposed to causal) explanatory failure. The idea of ontological explanation also needs clarifying.
...
I wonder if Francesco has a general criterion in mind.”
Here I am. True, the point is crucial. Without a criterion for viciousness we don’t get much progress. My view is that in order to claim that a regress is vicious one must show that it contradicts some background assumptions that is very difficult or impossible to give up. Thus, one could say, more precisely, that in the first place we have viciousness relative to these assumptions, but then we must see whether the assumptions are really worth keeping before declaring the regress vicious in absolute terms. The internalist regress contradicts the thesis that one constituent of a fact should have the attributive role (be the relating relation): as Bill has explained very well each tentative candidate for that role cannot really be the filler of the role and thus none is. In this case I cannot see how the thesis in question could be dropped. The externalist regress contradicts the thesis that an explanatory chain cannot go ad infinitum without reaching a bottom line (or, relatedly, that a dependency chain cannot go ad infinitum without reaching a bottom line). In this case it seems to me that we can drop the assumption after all, or so I tried to argue in my paper. The issue of course is intertwined with the question, what should we expect from an explanation (an ontological one in particular)?. An explanation should increase our understanding of the matter, and in the case of the externalist regress coming to see that there can be an infinite dependency chain can perhaps be viewed as providing such an increase.
Let me further explain by taking advantage of this further interesting point by Jan Willem:
“The point in case of infinite regresses, I think, is that one may put the very same chain in a negative and positive way:
- Each relation gets "demoted" by the next VS each relation relates in virtue of the next.
- Each problem (e.g. the unity of aRb) gets shifted to the next (the unity of EX1aRb) VS each problem has its solution.
So, I'm not sure we can say a regress is vicious by choosing the negative description”
Here I think Jan is considering both the internalist and the externalist regress. I basically agree with the reply provided by Bill on the internalist one. Let me just add that I have hard time in figuring out what it means to say that in a state of affairs more than one relation plays the relating role. But to say that each relation relates in virtue of the next means that an infinity of relations play this role (in one state of affairs). My bedrock thesis here, which I cannot see how to drop, is that ONE relation or property plays the attributive (relating) role in a state of affairs. Thus, I am forced to choose the “negative way” of looking at the regress. As regards the externalist regress, I think I can make sense of “each problem has its solution” (by the next step in the regress) and thus I choose the “positive way” of looking at the regress (thereby dropping the background assumption that an explanatory chain cannot go on indefinitely).
Well, hope this helps. As for myself, it was quite interesting to look at the issue for your angles.
Posted by: Francesco Orilia | Thursday, November 20, 2008 at 02:15 PM
Francesco,
Let me focus in this comment on your analogical argument for the thesis that 'Fa' and 'E2Fa' pick out distinct facts (as opposed to the thesis that 'E2Fa' is a more faithful representation of the same fact that 'Fa' is a less faithful representation of.)
You mention a lego object gr consisting of two pieces, g and r, with g on top of r. This is distinct from the object rg. You say that the relation being on top of is not a part of gr. This relation is a part of the fact of g's being on top of r. Similarly, E2 (dyadic exemplification) is not a part of Fa, but it is a part of E2Fa. Therefore, Fa and E2Fa are distinct.
A very interesting argument, but I don't find it convincing since it raises some thorny questions. First of all, is it really obvious that being on top of is not a part of gr? Note that gr is distinct from the set {g, r} and from the mereological sum g + r. To put it more simply, gr is distinct from its parts taken collectively. This is because g and r can exist without gr existing. For gr to exist, g must BE on top of r. So gr is more than its parts g and r. Arguably, this 'more' is the relation, which must be a part of gr. If you deny this, then how would you explain the obvious difference between gr and g + r?
Second, are you suggesting that gr is a nonfact? You seem committed to this because you distinguish gr from the fact of g's being on top of r. But surely (or rather arguably) g is a fact, the atomic fact of a thin particular's exemplifying of a conjunctive universal (or a conjunction of universals). And the same goes for r. It too is an atomic fact. This makes gr a molecular or complex fact, not a nonfact.
Therefore, I deny that gr is distinct from the fact of g's being on top of r. The two are the same. Similarly, I deny that Fa is distinct from E2Fa. They are the same fact; it is just that 'E2Fa' is a more faithful representation of the complexity of the fact.
Finally, if gr exists, then g and r are unified by the relation on top of. Why is there any need for the state of affairs or fact of g's being on top of r to play a role in unifying them? Similarly, if F is really attributive in Fa, then E2Fa is simply irrelevant to F and a's forming a unity.
Thanks for your comments, and I look forward to further discussions.
Posted by: Bill Vallicella | Thursday, November 20, 2008 at 06:58 PM
Dear Bill,
sorry for taking so long in answering but here I am trying to address your objections. Of course we all agree that an argument by analogy is very far from being conclusive, but let us pursue the idea to see where it leads us.
Certainly gr is more than its parts g and r. My suggestion is that we sharply distinguish between the physical parts g and r, which we can touch and manipulate, and their being related by the relation *on top of*. For this relatedness arises once we arrange g and r in a certain order and it is not one more thing that we arrange together with g and r. Thus we distinguish gr and rg not by a difference in constituents, for they have the same ones. Let us leave aside here Armstrong’s distinction between a thin and thick state of affairs. As I see it, gr is just an object. The fact that it has properties and is involved in relations does not make it a state of affairs, whether thick or thin: the fact that there cannot be objects without there being states of affairs (for the objects instantiate properties) does not imply that the objects are states of affairs.
Let us now pursue the analogy. Just as gr and rg do not differ in parts, similarly the fact *g is on top of r* and the sets and sums {g, r, being on top} and g+r+being on top do not differ in constituents (assuming for the sake of the argument that there are such things). For all three of them we have the constituents, g, r, being on top. How do they differ then? By something external to them: for the fact this something external is the further fact (roughly) *being on top is exemplified by g and r (in that order)*, for the set it is the fact *g, r and being on top constitute a 3-membered set* (or something like that), etc.
You can imagine that we can go on and on by applying the externalist Bradley’s regress. It seems to me that this is just in the nature of relatedness. Whether this exhausts all we want to say in explaining complexity and relatedness is another issue. I am inclined to say yes and I assume you want to say no. I think it has to do with what one takes to be ontological explanations (and there can be different kinds with different degrees of success) and with whether or not we think that everything must ultimately rest on a layer of necessity. Thus one may say that the infinite chain Fa, E1Fa, E2E1Fa, ... stands on its own, with each non-initial member explaining the unity of the previous one, or one may say the whole chain is still in need of explanation, because it might have failed to exist. And perhaps here you might want to invoke your transcendental subject. Jan Willem’s attempt to provide criteria for viciousness might help. I plan to look at what he is proposing with more attention. But perhaps we can look at these criteria to assign degrees of explanatory value and not necessarily to banish a certain explanatory attempt as no explanation at all.
Posted by: Francesco Orilia | Tuesday, November 25, 2008 at 01:37 AM
Francesco,
Thanks for the helpful comments. You write, "the fact that there cannot be objects without there being states of affairs (for the objects instantiate properties) does not imply that the objects are states of affairs." I agree. 'Objects are states of affairs' does not logically follow from 'There cannot be objects without there being states of affairs.' But if q does not follow from p, q might nonetheless be true for other reasons. I suppose I am under the influence of Gustav Bergmann and Armstrong who think of thick particulars as states of affairs having thin particulars and universals as constituents. This is a large topic that we don't have the time to address now. But I suspect it has something, and perhaps a lot, to do with why we are disagreeing.
I will have to hear more about your theory of states of affairs. Are they abstract objects? Does Tom's being tired have Tom himself, all 200 lbs of him, as a constituent? Or does this state of affairs have some abstract representative of Tom as a constituent? If yes, how does a state of affairs differ from a Fregean proposition?
Further, if states of affairs are abstract, how could they be truth-makers?
As I see it, Bradley's regress arises and has its sense within the context of the ancient problem of the unity of a complex which can be traced back at least as far as Theaetetus 202e-205e. Among complexes are not just propositions and states of affairs but also physical things like the lump of sugar Bradley discusses in Appearance and Reality, ch 2. It seems clear that Bradley is thinking of the properties of the sugar lump as constituents of it, and of the lump itself as either a concrete fact or a concrete bundle. His regress arises within such physical things.
You seem to hold that, although physical things have physical parts, there is no sense in which their properties are parts of them. Is that right? If yes, then we differ in our approach to ontology. I am a constituent ontologist.
Posted by: Bill Vallicella | Tuesday, November 25, 2008 at 11:38 AM
Hi Bill,
some quick answers for the time being.Later on I'll see if I can do better.
I think states of affairs are concrete,at least concrete enough to be truthmakers and be causes and effects. But I also think that the sense in which properties are constituents of them is very different from the sense in which parts of physical objects can be said to be constituents of objects. That properties are constituents of states of affairs has to to with their being instantiated by an object. and then the question is, how close is instantiation to a part/whole relation? It seems rather close from the point of view of the bundle theory, which I used to hold, but now I don't want to be committed to it. It seems to me that for the sake of discussing Bradley's regress we can leave the issue open
Francesco
Posted by: Francesco Orilia | Friday, November 28, 2008 at 08:16 AM
Francesco,
You ask, "how close is instantiation to a part/whole relation?" And then you say, "for the sake of discussing Bradley's regress we can leave the issue open." I am not so sure. If Bradley's regress arises within the context of the problem of the unity of a complex -- and it does so arise as one can see from App and Reality -- then understanding the nature of the regress would seem crucially to depend on how close instantiation is to a part/whole relation. In particular,it seems to affect the relevance of your distinction between an internal and an external regress. I'll have to think about this some more.
Posted by: Bill Vallicella | Friday, November 28, 2008 at 09:06 AM
Bill,
think of it this way. suppose you are a bundle theorist. Then if you say that x is F you mean that there are propertties G1,..., Gn and a compresence relation C such that C(F, G1), C(F, G2), etc. But then you can ask: by virtue of what do we have,e.g., C(F,G1)? And the regress starts, if you appeal to E3(C, F, G1), etc.. On the other hand, if you are a substratist you may want to say that x is F does not involve any compresence but the instantiation of F by an irreducible particular. And then you may start the regress by bringing E2(F,x),etc. to the fore.
I had in mind something like this. In both cases, the regresses can be understood internally or externally, it seems to me.
But you are certainly right in saying that all this needs further thought. We can gain a better picture by reconstrunting how Bradley's regress would go from the point of view of different ontological conceptions. From what I recall your paper on trope theory and BR can be thought inter alia as contributing to this picture and I am looking forward to reading the version that has now been posted in the conference site.
Francesco
Posted by: Francesco Orilia | Saturday, November 29, 2008 at 11:56 PM
Francesco,
That's only a link on the conference site to my paper; you will find the paper on this weblog if you scroll up. Scroll up a bit further and you will find an addendum on the 'adicity' of compresence. I will be very interested in whether you think my criticisms of Maurin hold water.
Common to the bundle approach and the fact approach is the notion that ordinary particulars (thick particulars) are wholes of ontological parts. Thus on both approaches property-possession is brought into close proximity to a part/whole relation. Let A be a thick particular, and a the thin particular 'in' A. We want to understand A's possession of some property F-ness (F-ness might be a universal or it might be a trope, but for now let's think of it as a universal). On the fact approach, A is F in virtue of a's instantiating F-ness. Thus instantiation is a relation internal to the thick particular A: it does not connect A to something external to it. F-ness is an immanent universal in a two-fold sense: it cannot exist uninstantiated, and it is a constituent of thick particular A. So both a and F-ness are proper parts of A, and the problem of the unity of complex A arises. A is not a mere aggregate: it is a complex whose existence is not entailed by the existence of its parts. What then unifies A? The instantiation relation is supposed to do the job: it connects each property to a thin particular, the same thin particular, and in so doing connects them to each other. But I fail to see how any constituent or any series of constituents (even if actually infnite) of a fact or a bundle can do the job of unification.
We can say that instantiation within a fact plays the same unifying role as compresence plays within a bundle. (Of course there are several differences, e.g., instantiation is asymmetrical while compresence is symmetrical, etc.) In both cases, then, we have a whole of ontological parts; we face the problem of unity; and we need a unifier.
And although I agree with you that we can and must distinguish between an internal and an external regress, and that the external regress is benign, I deny that the external regress can do the job of unification.
In a nutshell, our disagreement may be this: You are assuming what I am questioning, namely, that there are facts. Taking facts to be actual, you infer that they are possible, and see the philosophical task as defusing theose arguments that cast doubt on their possibility. Like Bradley, I argue the other way: facts are unintelligible, not possible, hence not actual and 'independent reals.'
This of course requires more clarification! Thanks again for your stimulating comments.
Posted by: Bill Vallicella | Sunday, November 30, 2008 at 03:15 AM
Hi Bill!
Basically, I tend to see relatedness and complexity on a par. The fact that there is a whole or complex implies that there is relatedness and vice versa,although I think that different kinds of complexes must be sharply distinguished. And it seems to me obvious that there is relatedness,although a philosophical analysis of what relatedness is must be offered somehow. So perhaps your final picture of our disagreement is not far from the truth. It has been most useful for me to trace back some of my implicit basic assumptions and I hope that this exchange has been useful to you as well. Pretty soon we'll be packing for Geneva and happily we can continue our discussion there. I'll look at you paper and the addendum on adicity before I leave. Looking forward to meeting you in Geneva
Francesco
Posted by: Francesco Orilia | Wednesday, December 03, 2008 at 12:17 AM
Francesco,
The discussion has been very useful to me, and I hope we can reach greater clarity when we meet face to face. I will have studied your latest paper by then. I am finishing a post on Richard Gaskin which I will upload to this weblog today. Please take a look at it if you get a chance. There are some similarities between his approach and yours. Basically, you both see the regress as virtuous.
I studied Maurin's paper "Why There are Tropes?" this morning and I will be interested in your response to it.
It will be good to meet you and hear some Castaneda stories. Have a safe trip.
Posted by: Bill Vallicella | Wednesday, December 03, 2008 at 12:19 PM