(1) There is a real difference between the sum a + R + b and fact aRb.
(2) This difference isn't brute1. That is, it must have an ontological ground.
(3) This ground is in (i) constituents a, R, or b; (ii) one or more additional constituents in aRb; (iii) aRb itself; or (iv) something outside aRb.
(4) The ground isn't in (i), (ii), or (iii).
(5) From (1) – (4), something outside aRb grounds its difference from a + R + b.
His argument implies that without God the world would fall apart.2
I begin my attempt to exorcise Bradley's ghost by supporting Vallicella's premises.
Premises (1), (2), and (3)
Vallicella starts by distinguishing the sum a + R + b from the fact aRb. The sum exists as long as a, R, and b exist; in contrast, the fact only exists if a, R, and b are unified or “together”. The sum of John, a tea cup, and the two feet from relation exists as long as John, the tea cup, and the relation exist; the fact of those constituents only exists if John is two feet from the tea cup. In short, since John + the tea cup + the two feet from relation can exist without its corresponding fact existing, sums are different from facts.
Vallicella argues that this difference has an ontological ground. He argues that, one, if the difference between a + R + b and aRb is brute, they're both composed of nothing more than a, R, and b; two, if a + R + b and aRb are both composed of nothing more than a, R, and b, they're identical; three, since aRb is the unity of a + R + b's constituents, a + R + b isn't identical to aRb; thus four, if the difference between a + R + b and aRb is brute, a + R + b both is and isn't identical to aRb; thus five, the difference between a + R + b and aRb has an ontological ground. It follows from the last two paragraphs that the difference between sums and facts has an ontological ground.
The foregoing and some analysis entail that the difference between a + R + b and aRb is grounded in (i) the constituents a, R, or b, (ii) one or more additional constituents in aRb, (iii) aRb itself, or (iv) something outside aRb.
Premise (4)
Vallicella argues that this difference isn't grounded in (i), (ii), or (iii). First, he argues that a + R + b and aRb are both composed of a, R, and b; if a + R + b and aRb are both composed of a, R, and b, they're identical in respect of a, R, and b, and neither a, R, nor b can ground their difference; thus, neither a, R, nor b can ground the difference between a + R + b and aRb. In other words, he argues that assumptions behind the sum-fact distinction rule out (i).
Second, Vallicella argues that aRb can only ground its own unity if it exists logically prior to its existing; it therefore can't ground its own unity; the difference between the sum and its fact is that the sum isn't relevantly unified and the fact is; therefore, since aRb can't ground its own unity, it also can't ground the difference between a + R + b and itself. In brief, he argues that (ii) is incoherently circular.
Third, Vallicella argues that if one adds a constituent (C) to aRb to try grounding aRb's unity, this results in a further fact (aRCb) that needs its unity grounded. And if one adds another constituent (C*) to that fact, this results in another fact that needs its unity grounded, and so on with each new constituent ultimately failing to ground its corresponding fact's unity. In fewer words, he argues that (iii) leads to a vicious, infinite regress. It follows from the last three arguments that the difference between a + R + b and aRb isn't grounded in (i), (ii), or (iii).
If the foregoing arguments are right, (5) follows. In future posts, I shall argue that some of them are wrong, and build an ontology that grounds the unity of facts in particularized relations.
1. I use brute, here, to mean "lacking an ontological ground".
2. Or, if you're truly brave, you can accept fact infinitism. I won't be developing the inference from external unifier to God in this post, though I think it right.
Bibliography
Betti, Arianna. Against Facts. The MIT Press, 2015.
Betti, Arianna, and Jan Willem Wieland. “Relata-specificity: A Response to Vallicella”. Dialectica, vol. 62 no. 4, 2008, pp. 509-524.
Betti, Arianna, and Jan Willem Wieland. “Relata-specificity: A Response to Vallicella”. Dialectica, vol. 62 no. 4, 2008, pp. 509-524.
Vallicella, William F. A Paradigm Theory of Existence: Onto-Theology Vindicated. Kluwer Academic Publishers, 2002.
---. “Bradley's Regress and Relation-Instances”. The Modern Schoolman, LXXXI, 2004.
---. “Relations, Monism, and the Vindication of Bradley's Regress”. Dialectica, vol. 56 no. 1, 2002, pp. 3-35.
From what I understand, even something like the truth regress would require an infinity of entities to make the propositions true; since each proposition would have to have a truthmaker outside of the proposition, to make it true. However, this is non-vicious in the sense that none of the propositions are made true by the previous member in the series, but because of entities that make them true. Neither a vicious, nor a non vicious regress seem to be palatable, since the former demonstrates an explanatory failure (nothing in the series is able to explain the fact), and the latter implies that there are an infinity of entities. What's the difference between fact infinitism and a vicious regress?
ReplyDeleteHi, Dennis,
DeleteThe difference is that one is a philosophical theory and the other is a type of regress, but I don't think that's what you really want to know. Could you rephrase your question?
By the way, according to truthmaker theory, one entity can serve as truthmaker for even an infinite number of truths.
Hi Cyrus,
DeleteIf the reason a regress is unpalatable is because it is an explanatory failure, what makes fact infinitism more acceptable but still unpalatable? I’m guessing fact infitism is the thesis where you have to accept an infinite amount of entities to uphold the unity of a fact, if not, then what?
Hi, Dennis,
DeleteYou ask: If the reason a regress is unpalatable is because it is an explanatory failure, what makes fact infinitism more acceptable but still unpalatable?
I would say nothing. I argue that if one brings a further fact (a2Rb2) in to try grounding aRb's unity, one then needs a yet further fact (a3Rb3) to try grounding a2Rb2's unity, and so on ad infinitum without ever finally unifying aRb. In other words, I think that trying to unify facts with an infinite regress of further, external facts leads to a vicious regress.
Francesco Orilia, however, thinks that the regress is benign. I might write a post on it sometime.
Pardon an elementary question. The *ground of* aRb; is that distinct from the old Platonist realism v. Aristotelian realism v. nominalism debate? If not, then 3(iii) and 3(iv) are not mutually exclusive. *Being a doll* is nowhere but in the doll, tho' Gepetto is the ground of being a doll?
ReplyDeleteChris Kirk
Hello Chris,
DeletePardon an elementary question. The *ground of* aRb; is that distinct from the old Platonist realism v. Aristotelian realism v. nominalism debate?
It is! Instead of aRb, I could have put the argument in terms of the mere sum of Gepetto-particles and those Gepetto-particles-unified-into-Gepetto. The former exists even if the particles are in different galaxies. The latter only if they're unified into Gepetto. Whether the Gepetto-particles are nominalist “blobs” or structured “layer cakes” of substances and properties or properties makes no difference.
*Being a doll* is nowhere but in the doll, tho' Gepetto is the ground of being a doll?
Could you clarify what you're asking in this question?
Hm, maybe it is just a poor example. Gepetto is the source of the being of the doll he creates - is that a good synonym for ground? *Being a doll* opens a question about the status of the universal. Yes?
ReplyDeleteI admit I am a poor ontologist. Like Brother Francis in *A Canticle for Leibowitz*, it sometimes makes the boulders roll around in my head.
Hello Chris,
DeleteGepetto is the source of the being of the doll he creates - is that a good synonym for ground?
Vallicella thinks that the Being of an individual is its unity. He would say yes. Barry Miller, however, thinks that the Being of an individual is a property-instance it has. He would say that the property-instance has to be unified with the rest of the individual and that its Being is therefore distinct from its unity. I think Miller's view has more problems with it than Vallicella's.
*Being a doll* is nowhere but in the doll, tho' Gepetto is the ground of being a doll?
Yes. If being a doll unifies the doll's other constituents into a doll, it does so by itself being unified with those constituents, and hence needs a unifier. Gepetto is that unifier.
Hm, maybe it is just a poor example.
It's a fine example. Probably safest to avoid names easily confused with fictions when talking about Being though.