Maverick Philosopher

Indeterminate Yet Existent? The Aporetics of Prime Matter and Pure Consciousness

Scott Roberts e-mails in reference to my post Hylomorphic Ontological Analysis and the Puzzle of Prime Matter: 

I have also been perplexed at hylomorphism's dependence on something called [prime]  'matter', for the same reason as you give. But I think there is a way out, though perhaps not one a hylomorphist will like. You say "Something bare of determinateness is unthinkable and hence nonexistent." But I can think of three words that refer to something one might consider real yet bare of determinateness, namely mass (or energy), consciousness (considered apart from all intentional objects of consciousness), and God (of classical theism). In each case you have something that can be thought of as giving form actuality. But that leads to an inversion of hylomorphism, namely, that now it is form that is potential, and what was formally [formerly?] thought of as matter is now Pure Act.  For example, a mathematical object which is not being thought of is a potential form that consciousness gives actuality as a thought. [. . .]

The reader is right to point out that there is something dubious about my claim that "Something bare of determinateness is unthinkable and hence nonexistent." Of the three counterexamples he gives, the clearest and best is "consciousness considered apart from all intentional objects of consciousness."  Consciousness so considered is not nothing, and yet it is indeterminate since all determinations fall on the side of the objects.  Consciousness is no-thing, a Sartrean theme which is also developed by Butchvarov. 

The reader has made me see that there is a certain structural analogy between prime matter and consciousness conceived of as pure of-ness bare of all determinacy.  For one thing, both, considered in themselves, are indeterminate or formless, and necessarily so.  If consciousness were determinate, it would be an object of consciousness and not the consciousness without which there are no (intentional) objects.  And if prime matter were determinate, it would be formed matter and thus not prime matter.  Second, neither can exist apart from its other.  There is no consciousness without objects, and there is no prime matter that exists on its own in the manner of a substance.  So, while consciousness is other than every object, it cannot exist except as the consciousness of objects (objective genitive).  And while prime matter is other than every form, and in itself formless, it requires formation to be something definite and substantial.

A third point of analogy is that both consciousness and prime matter give rise to a structurally similar puzzle.   Consider a mind-independent hylomorph A whose matter (H) is prime matter and whose form (F) is composed of lowest forms.  Which is ontologically prior, A, or its ontological parts H and F?  If the parts are prior in the manner of pre-existing ontological building blocks -- think (by analogy) of the way the stones in a stone wall are prior to the wall -- then H could not be a 'principle' in the scholastic sense but would have to something capable of independent existence.  And that is unacceptable: surely prime matter cannot exist on its own.  If, on the other hand, A is prior to its parts, then the parts would exist only for us, or in our consideration, as aspects which we bring to A.  But that won't do either because A ex hypothesi exists extramentally and so cannot in its ontological constitution require any contribution from us.

The consciousness puzzle is similar. Is consciousness (conceived as pure diaphanous of-ness of objects in the manner of Sartre, Butchvarov, and perhaps Moore) something really existent in itself or is it rather an abstract concept that we excogitate?  In other words, when we think of consciousness transcendentally as the sheer revelation of objects, are we thinking of a really existent condition of their revelation, or is consciousness so conceived merely a concept that we bring to the data?  If consciousness really exists, then we substantialize it (reify it, hypostatize it) in a manner analogous to the way we substantialize prime matter when we think of its as something capable of independent existence.  And that is puzzling.  How can something exist that is not an object of actual or possible awareness?  If, on the other hand, consciousness is not something that exists on its own but is a concept that we excogitate, then how do we account for the real fact that things are apparent to us, that things are intentional objects for us?  Besides, if consciousness were a mere concept, then consciousness as a reality would be presupposed: concepts are logically subsequent to consciousness.

So the two puzzles are structurally similar. 

Let us see if we can abstract the common pattern.  You have a term X and a distinct term Y.  The terms are introduced to make sense of a phenomenon Z.  Z is the analysandum whose analysis into X and Y is supposed to generate understanding.   X cannot exist without Y, hence it cannot exist on its own.  The same goes for Y.  The terms cannot exist without each other on pain of (i) hypostatization of each, and (ii) consequent sundering of the unity of Z.  (The diremption of Z into X and Y gives rise to the ancient problem of the unity of a complex which no one has ever solved.)  That the terms cannot exist without each other suggests that the unitary phenomenon Z is split into X and Y only by our thoughts such that the factoring into X and Y is our contribution.  On the other hand, however, the terms or factors must be capable of some sort of existence independent of our conceptual activities if the explanation that invokes them is an explanation of a real mind-independent phenomenon.

Here is a sharper form of the common aporia.  Both prime matter and pure consciousness are real.  But they are also both unreal.  Nothing, however,  can be both real and unreal on pain of violating Non-Contradiction.  How remove the contradiction without giving rise to a problem that is just as bad?

I don't say that the aporiai are insoluble, but I suspect that any solution proffered with give rise to problems of its own . . . .

Are There Logically Simple Propositions?

Leo Carton Mollica e-mails:

 

Your most recent post (for which many thanks) inspired the below-expressed argument, and I was curious as to your opinion of it . . . . I think it has something behind it, but right now I feel uncertain about my examples in (2).

 

0. There is something curious about the relation between a proposition or declarative sentence and the terms or words that compose it: the list L ("Christ," "Judas," "betrays") clearly differs, at the very least in not having a truth value, from the sentence "Judas betrays Christ," yet nothing immediately presents itself as the ground G of this difference. One plausible candidate for G is some kind of union or togetherness amongst the members of L present in "Judas betrays Christ" and not in L itself, but this proposal is open to a serious challenge.

 

1. Suppose we accept Barry Miller's thesis, from "Logically Simple Propositions," that some declarative sentences have only one semantic element. His favorite such sentence is the Romanian "Fulgura," whose only constituent word translates (if I remember aright) the English "brightens," and which is interesting in requiring no actual or implied subject to form a complete sentence (like "It's raining" in English, but without the dummy subject).

 

2. Now, the lone word in "Fulgura" seemingly can occur outside any proposition. If, for example, someone were to ask me to recite my favorite Romanian word, or to translate "brightens" into Romanian, it would be strange to take me as telling them something false, or to have them respond "No, it isn't," upon my replying with "fulgura." There would, however, be nothing strange about the sentence "Fulgura" being false and someone telling me as much. [. . .]

 

3. Even in such simple sentences, therefore, there is a distinction between the sentence and the words contained therein, for one can be had without the other. But the ground of this distinction cannot be any union or togetherness among the words that enter into the sentence for the simple reason that no union or togetherness amongst items can be had without distinct items to unify or bind together. It can, therefore, be at least plausibly argued that the general ground of the difference between a sentence and its constituent words is no kind of union or togetherness.

 

I take Mr Mollica's basic argument to be this:

 

a. If there are logically simple sentences/propositions, then the problem of the unity of the sentence/proposition is not one that arises for every sentence/proposition.
b. There are logically simple sentences/propositions.
Therefore

c. The problem of the unity of the proposition is not one that arises for every sentence/proposition.

 

My response is to reject (b) while granting (a).  I discussed the question of logically simple sentences/propositions with Barry Miller back in the '90s in the pages of Faith and Philosophy.  My "Divine Simplicity: A New Defense (Faith and Philosophy, vol. 9, no. 4, October 1992, pp. 508-525) has an appendix entitled "Divine Simplicity and Logically Simple Propositions."  Miller responded and I counter-responded in the July 1994 issue, pp. 474-481.  It is with pleasure that I take another look at this issue. I will borrow freely from what I have published.  (Whether this counts as plagairism, depends, I suppose, on one's views on diachronic personal identity.)

 

A.  A logically simple proposition (LSP) is one that lacks not only propositional components, but also sub-propositional components.Thus atomic propositions are not logically simple in Miller's sense, since they contain sub-propositional parts.  A proposition of the form a is F, though atomic, exhibits subject-predicate complexity.

 

B. Miller's examples of LSPs are inconclusive.  Consider the German Es regnet ('It is raining').  As Miller correctly notes, the es is grammatical filler, and so the sentence can be pared down to Regnet, which is no doubt grammatically simple.  He then argues:

 

Now there is no question of Regnet being a predicate; for as a proposition it has a complete sense, whereas as a predicate it could have only incomplete sense. Hence, Regnet and propositions like it seem logically simple. (Barry Miller, "Logically Simple Propositions," Analysis, vol. 34, no. 4, March 1974, p. 125.)

 

I find it hard to avoid the conclusion that Miller is confusing propositions with the sentences used to express them.  Regnet and fulgura are grammatically simple.  But it scarcely follows that the propositions they express are logically simple.  What makes them one-word sentences is the fact that they express propositions; otherwise, they would be mere words.  So we need a sentence-proposition distinction.  But once that distinction is in place then it becomes clear that grammatical simplicity of sentence does not entail logical simplicity of the corresponding proposition.

 

C.  It is also unclear how any intellect like ours could grasp a proposition devoid of logical parts, let alone believe or know such a proposition.  To believe that it is snowing, for example, is to believe something logically complex, albeit unified, something formulatable by some such sentence as 'Snow is falling.'  So even if there were logically simple propositions, they could not be accusatives of minds like ours.  And if propositions are defined as the possible accusatives of propositional attitudes such as belief and knowledge, then the point is stronger still: there cannot be any logically sinple propositions.

 

D.  So it seems to me that 'the problem of the list' or the problem of the unity of the sentence/proposition is one that pertains to every sentence/proposition.  It is a problem as ancient as it is  tough, and, I suspect, absolutely intractable.  For a glimpse into the state of the art, I shamelessly recommend my June 2010 Dialectica article, "Gaskin on the Unity of the Proposition."

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

Note to Steven Nemes:  Tell me if you find this totally clear, and if not, point out what is unclear.  Tell me whether you accept my overall argument.

The day before yesterday in conversation Steven Nemes presented a challenge  I am not sure I can meet.  I have maintained (in my book, in published articles, and in these pages) that the difference between a fact and its constituents cannot be a brute difference and must therefore have a ground or explanation.  But what exactly is my reasoning?

Consider a simple atomic fact of the form, a's being F.  This fact has two primary constituents, the individual a, and the monadic property F-ness, which a possesses contingently.  But surely there is more to the fact than these two primary constituents, and for at least two reasons.  I'll  mention just one, which I consider decisive:  the constituents can exist without the fact  existing.  The individual and the property could each exist without the former exemplifying the second.  This is so even if we assume that there are no propertyless individuals and no unexemplified properties.  Consider a world W which includes the facts Ga and Fb.  In W, a is propertied and F-ness is exemplified; hence there is no bar to saying that both exist in W.  But Fa does not exist in W.  So a fact is more than its primary constituents because they can exist without it existing.

A fact is not its constituents, but those constituents unified in a particular way.  Now if you try to secure fact-unity by introducing  one or more secondary constituents such  an exemplification relation, then you will ignite Bradley's regress.  For if the constituents include a, F-ness, and EX, then you still have the problem of their unity since the three can exist without constituting a fact.

So I take it as established that a fact is more than its constituents and therefore different from its constituents.  A fact is different from any one of its constituents, and also from all of them taken collectively, as a mereological sum, say.    The question is:  What is the ontological ground of the difference?  What is it that makes them different?  That they are different is plain.  I want to know what makes them different.  It won't do to say that one is a fact while the other is not since that simply underscores that they are different.  I'm on the hunt for a difference-maker.

To feel the force of the question consider what makes two different sets different.  If S1 and S2 are different sets, then it is reasonable to ask what makes them different, and one would presumably not accept the answer that they are just different, that the difference is a brute difference.  Let S1 be my singleton and S2 the set consisting of me and Nemes.  It would not do to say that they are just different.  We need a difference-maker.  In this case it is easy to specify: Nemes.  He is what makes S1 different from S2.  Both sets contain me, but only one contains him.  Generalizing, we can say that for sets at least,

DM. No difference without a difference-maker.

So I could argue that the difference between a fact and (the sum of) its constituents cannot be a brute difference because (i) there is no difference without a difference-maker and (ii) facts, sets, and sums, being complexes, are relevantly similar.  (I needn't hold that the numerical difference of two simples needs a difference-maker.) But why accept (DM) in full generality as applying to all types of wholes and parts?  Perhaps the principle, while applying to sets, does not apply to facts and their constituents.  How do I answer the person who argues that the difference is brute, a factum brutum, and that therefore (DM), taken in full generality, is false?  As we say in the trade, one man's modus ponens is another's modus tollens.

Can I show that there is a logical contradiction in maintaining that facts and their constituents just differ?  That was my strategy in the book on existence.  The strategy is to argue that without an external ground of unity -- an external unifer -- one lands in a contradiction, or rather cannot avoid a contradiction.  That the unifier, if there is one, must be external as opposed to internal is established by showing that otherwise a vicious infinite regress ensues of the Bradley-type.  I cover this ground in my book and in articles in mind-numbing detail; I cannot go over it again here.  But I will refer the reader to my 2010 Dialectica article  which discusses a fascinating proposal according to which unity is constituted by an internal infinite, but nonvicious, regress.  But for now I assume that the unifier, if there is one, must be external.  If there is one, then the difference between a fact and its constituents cannot be brute.  But why must there be a unifier?

Consider this aporetic triad:

1. Facts exist.
2. A fact is its constituents taken collectively.
3. A fact is not its constituents taken collectively.

What I want to argue is that facts exist, but that they are contradictory structures in the absence of an external unifier that removes the contradiction.  Since Nemes agrees with me about (1), I assume it for present purposes.  (The justification is via the truth-maker argument).

Note that (2) and (3) are logical contradictories, and yet each exerts a strong claim on our acceptance.  I have already argued for (3).  But (2) is also exceedingly plausible.  For if you  analyze a fact, what will you uncover?  Its constituents and nothing besides.  The unity of the constituents whereby it is a fact as opposed to a nonfact like a mereological sum eludes analysis.  The unity cannot be isolated or located within the fact.  For to locate it within the fact you would have to find it as one of the constituents.  And that you cannot do.

Note also that unity is not perceivable or in any way empirically detectable.  Consider a simple Bergmann-style or 'Iowa' example, a red round spot.  The redness and the roundness are perceivable, and the spot is perceivable.  But the spot's being red and round is not perceivable.  The existence of a fact is the unity of its constituents.  So what I am claiming is equivalent to claiming that existence is not perceivable, which seems right: existence is not an empirical feature like redness and roundness.

So when we consider a fact by itself, there seems to be nothing more to it than its constituents.

Each limb of the triad has  a strong claim on our acceptance, but they cannot all be true as formulated.  The contradiction can be removed if we ascend to a higher point of view and posit an external unifier.  What does that mean? 

Well, suppose there is a unifier U external to the fact and thus not identifiable with one or more of its primary or secondary constituents.  Suppose U brings together the constituents in the fact-making way.  U would then be the sought-for ground of the fact's unity.  The difference between a fact and its constituents could then be explained by saying that  the difference is due to U's 'activity':  U operates on the constituents to produce the fact.  Our original triad can then be replaced by the following all of whose limbs can be true:

1. Facts exist
2*. A fact, considered analytically, is its constituents taken collectively.
3.  A fact is not its constituents taken collectively.

This triad is consistent.  The limbs can all be true.  And I think we have excellent reason to say that each IS true.  The truthmaker argument vouches for (1).  (2*) looks to be true by definition.  The argumentation I gave for (3) above strikes me as well-night irresistible.

But if you accept the limbs of the modified triad, then you must accept that there is something external to facts which functions as their unifier.  Difficult questions about what U is and about whether U is unique and the same for all facts remain; but that U exists is 'fallout' from the modified triad.  For if each limb is true, then a fact's being more than its constituents can be accounted for only by appeal to an external unifier.

But how exactly does this show that the difference between a fact and its constituents is not a brute difference?   The move from the original to the modified triad is motivated by the laudable desire to avoid contradiction.  So my argument boils down to this:  If the difference is brute, then we get a logical contradiction. So the difference is not brute. 

But it all depends on whether or not there are facts.  If facts can be reasonably denied, then my reasoning to a unifer can be reasonably rejected.  But that's a whole other can of worms: the truthmaker argument.

Analytically considered, a fact is just its constituents.  But holistically considered it is not.  Unity eludes analysis, and yet without unities there would be nothing to analyze!  Analytic understanding operates under the aegis of two distinctions: whole/part, and complex/simple.  Analysis generates insight by reducing wholes to their parts, and complex parts to simpler and simpler parts, and possibly right down to ultimate simples (assuming that complexity does not extend 'all the way down.')  But analysis is a onesided epistemic procedure.  For again, without unities there would be nothing to analyze. To understand the being-unified of a unity therefore requires that we ascend to a  point of view external to the unity under analysis. 

Richard Gaskin on the Unity of the Proposition

The current issue of Dialectica (vol. 64, no. 2, June 2010) includes a symposium on Richard Gaskin, The Unity of the Proposition (Oxford 2008).  Gaskin's precis of his work is followed by critical evaluations by William F. Vallicella ("Gaskin on the Unity of the Proposition"), Manuel Garcia-Carpintero ("Gaskin's Ideal Unity"), and Benjamin Schnieder ("Propositions United: Gaskin on Bradley's Regress and the Unity of the Proposition").  The symposium concludes with Gaskin's replies ("The Unity of the Proposition: Replies to Vallicella, Schnieder, and Garcia-Carpintero"). 

Are the Souls of Brute Animals Subsistent? Considerations Anent the Unity of Consciousness

We have been discussing the view of Thomas Aquinas according to which (i) the soul is the form of the body, and (ii) the souls of some animals, namely rational animals, are subsistent, i.e. capable of an existence independent of matter. I have registered some of my misgivings. Here is another. If our souls are subsistent forms, then why are not the souls of non-human animals also subsistent? If that in us which thinks is a life-principle and the substantial form of our bodies, and subsistent to boot, by what principled means do we not ascribe subsistent souls to all living things or at least to many non-human living things?

Aquinas discusses this question in Summa Theologica, Q. 75, art. 3. He attempts to navigate a middle course between a form of materialism according to which sense and intellect are both "referred to a corporeal principle," and the view he takes to be Platonic according to which both sense and intellect are "referred to an incorporeal principle." On the Platonic view, both sensing and understanding "belong to the soul as such." Thomas points us to Theaetetus 184 c. This is a fascinating passage which, according to Paul Natorp, anticipates Kant's transcendental unity of apperception.

In this passage, Socrates puts the following question to Theaetetus: ". . . which is more correct — to say that we see or hear with the eyes and with the ears, or through the eyes and through the ears?" Theatetus obligingly responds with through rather than with. Socrates approves of this response:

Yes, my boy, for no one can suppose that in each of us, as in a sort of Trojan horse, there are perched a number of unconnected senses which do not all meet in some one nature, the mind, or whatever we please to call it, of which they are the instruments, and with which through them we perceive the objects of sense. (Emphasis added, tr. Benjamin Jowett)

The issue here is the unity of consciousness in the synthesis of a manifold of sensory data. Long before Kant, and long before Leibniz, the Plato was well aware of the problem of the unity of consciousness. (It is not for nothing that Whitehead described Western philosophy as a series of footnotes to Plato.)

Sitting before a fire, I see the flames, feel the heat, smell the smoke, and hear the crackling of the logs. The sensory data are unified in one consciousness of a selfsame object. This unification does not take place in the eyes or in the ears or in the nostrils or in any other sense organ, and to say that it takes place in the brain is not a good answer. For the brain is a partite physical thing extended in space. If the unity of consciousness is identified with a portion of the brain, then the unity is destroyed. For no matter how small the portion of the brain, it has proper parts external to each other. Every portion of the brain, no matter how small, is a complex entity. But consciousness in the synthesis of a manifold is a simple unity. Hence the unity of consciousness cannot be understood along materialist lines.

This argument from the unity of consciousness, which of course needs to be more rigorously developed, is present in nuce in Plato in the passage cited. According to Aquinas, if this argument is sound, ". . . it follows that even the souls of brute animals are subsistent." This seems to be a correct inference.

Aquinas hopes to block the inference with the help of Aristotle's De Anima 429 a 24. Thomas gives an argument that I interpret as follows:

1. Although understanding alone is performed without a corporeal organ, as Aristotle maintains, sensation and the operations of the sensitive soul are accompanied by changes in the body at our sensory receptors.

Therefore

2. The sensitive soul has no per se operation of its own, and every operation of the sensitive soul belongs to the soul-body composite.

Therefore

3. The souls of brute animals, having no per se operations, are not subsistent.

Unfortunately, I cannot see that this is a good argument. The gist of the argument is that while there are specific corporeal organs for seeing, hearing, smelling, tasting, and touching, namely, eyes, ears, etc., there is no corporeal organ for understanding. From this it is concluded that there is a crucial difference between sensing and understanding: it is broadly logically possible that there be understanding without a body; but it is not broadly logically possible that there be sensing without a body. And since we alone among animals are rational, or capable of understanding, we alone have subsistent souls.

What this ignores is that sensing is not merely a mechanical or material process. When my cat simultaneously sees, smells, and tastes her food (or my food as she much prefers) there is a unity of consciousness in her no less than there is one in me when I lay into my food. There is no specific corporeal organ that does this unifying of sensory data, neither in me nor in my cat. The unity-of-consciousness argument against materialism can be 'run' both for man and cat. If it works for me it should work for her. So if the possibility of my disembodied existence follows from there being no physical organ that unifies my consciousness, then we get the same result for my cat, and the difference between man and brute in respect of subsistence of souls cannot be maintained.

To sum up. Thomas wants to say that men, but no brutes, have subsistent souls. This is because men, but no brutes, understand. But sensing is a form of consciousness, and consciousness cannot be understood in materialist terms. Sensing is not a mere collision of atoms in the void. Sensory consciousness, besides displaying unity across its several modalities, reveals qualia. And qualia are a well-known stumbling block to materialism. It is difficult to see why, if understanding supports the possibility of disembodied existence, sensing should not also support this possibility. There is after all only one soul which both senses and understands. The phrases 'sensitive soul' and 'intellective soul' are not to be taken to refer to distinct souls.

Richard Gaskin on the Unity of the Proposition

The following is my contribution to a symposium on Richard Gaskin's The Unity of the Proposition. The symposium, together with Gaskin's replies, is scheduled to  appear in the December 2009 issue of Dialectica.

GASKIN ON THE UNITY OF THE PROPOSITION

William F. Vallicella

While studying Richard Gaskin’s The Unity of the Proposition (Oxford 2008), the word ‘magisterial’came repeatedly to mind. Gaskin’s mastery of the history, literature, and dialectical intricacies of the problem of the unity of the proposition in all its ramifications is in evidence on every page. More than a treatment of a particular problem, Gaskin’s book is a systematic treatise in the philosophy of language organized around a particular but centrally important problem. To my knowledge, it is the most thorough and penetrating discussion of the unity of the proposition ever to appear. The fact that Gaskin’s solution to the unity problem is set within a systematic philosophy of language contributes to the book’s depth and richness, but also makes the task of the critic difficult. In a few pages, the critic cannot properly convey the systematic underpinnings of Gaskin’s formulation of the problem and his solution to it. And when the critic evaluates, he is forced to acknowledge that he is evaluating a solution embedded in a far-flung system whose ideas are mutually reinforcing. His critical points may then appear as ‘dialectical potshots’ if he cannot, as he cannot in a few pages, bring a competing system of mutually reinforcing ideas onto the field. These caveats having been registered, I proceed to sketch Gaskin’s project and raise some questions about his formulation of the unity problem. After conceding that Gaskin has solved the problem as he understands it, I will suggest that the problem lies deeper than he recognizes, and that the linguistic idealism in which he embeds his solution is problematic.

On the Elusive Notion of a Set: Sets as Products of Collectings

In an important article, Max Black writes:

Beginners are taught that a set having three members is a single thing, wholly constituted by its members but distinct from them. After this, the theological doctrine of the Trinity as "three in one" should be child's play. ("The Elusiveness of Sets," Review of Metaphysics, June 1971, p. 615)

1. A set in the mathematical (as opposed to commonsense) sense is a single item 'over and above' its members. If the six shoes in my closet form a mathematical set, and it is not obvious that they do, then that set is a one-over-many: it is one single item despite its having six distinct members each of which is distinct from the set, and all of which, taken collectively, are distinct from the set.   A set with two or more members is not identical to one of its members, or to each of its members, or to its members taken together, and so the set  is distinct from its members taken together, though not wholly distinct from them: it is after all composed of them and its very identity and existence depends on them.

In the above quotation, Black is suggesting that mathematical sets are contradictory entities: they are both one and many.  A set is one in that it is a single item 'over and above' its members or elements as I have just explained.  It is many in that it is "wholly constituted" by its members. (We leave out of consideration the null set and singleton sets which present problems of their own.)  The sense in which sets are "wholly constituted" by their members can be explained in terms of the Axiom of Extensionality: two sets are numerically the same iff they have the same members and numerically different otherwise. Obviously, nothing can be both one and many at the same time and in the same respect.  So it seems there is a genuine puzzle here.  How remove it?

Bradley's Regress as the Metaphysical Ground of the Unity of the Proposition: Notes on Gaskin

Having recently returned from the Geneva conference on Bradley's regress, I have much to ruminate upon and digest.  I'll start my ruminations with some comments on Richard Gaskin's work. 

In an earlier post I suggested that we ought to make a tripartite distinction among vicious, benign (harmless), and virtuous (helpful) infinite regresses. To put it crudely, a vicious regress prevents an explanatory job from getting done; a benign regress does not prevent an explanatory job from getting done; and a virtuous regress makes a positive contribution to an explanatory job's getting done.  I gave an example of a putative virtuous regress in the earlier post which example I will not repeat here.  In this post I draw your attention to a second putative example from the work of Richard Gaskin, whom I was happy to meet at the Geneva conference on Bradley's Regress.  Gaskin's proposal is that "Bradley's regress is, contrary to to the tradition, so far from being harmful that it is even the availability of the regress which guarantees our ability to say anything at all.  Bradley's regress is the metaphysical ground of the unity of the proposition." ("Bradley's Regress, the Copula, and the Unity of the Proposition," The Philosophical Quarterly, vol. 45, no. 179, April 1995, p. 176)  In terms of my schema above, Gaskin is claiming that Bradley's regress is positively virtuous (not merely benign) in that it plays a positive explanatory role: it explains (metaphysically grounds) the unity of the proposition.

I will now attempt to summarize and evaluate Gaskin's position on the basis of two papers of his that I have read, and on the basis of his presentation in Geneva.  (I should say that he has just  published a book, The Unity of the Proposition, which I have not yet secured, so the following remarks may need revision in light of his later work.)