Maverick Philosopher

Pluralities

To what does the plural referring expression, 'the cats in my house,' refer? Not to plurality, but to a plurality. A plurality is one item, not many items. It is one item with many members. 'The guitars in my house' refers to a numerically different plurality. It too refers to one item with many members.  It follows that a plurality cannot be identical to its members.  For if it were there would be no 'it.'

I am not saying that a plurality is a mathematical set. I am saying that a plurality is not just its members.  I am rejecting Composition as Identity. If the Londonistas do not agree with the Phoenician on this one, then I fear that there is little point to further discussion. We are at the non-negotiable.  We are at bedrock and "my spade is turned." 

Existence, Unity, Possibility, and Actuality: Are There Merely Possible Individuals?

Steven Nemes by e-mail:

Here’s a question for you about existence, perhaps one you could discuss on the blog.

In your book, you argue that existence is ontological unity. I think that’s right. But a merely possible this-such is a unity as much as an actual this-such. What then distinguishes merely possible existence from actual existence?

To put it precisely, the existence of a contingent being is the contingent unity of its ontological constituents.  Such a being is appropriately referred to as a this-such or as a concrete individual.  I assume that existence and actuality are the same: to exist = to be actual. I also assume that existence and Being are the same: to exist = to be.  Thus I reject the quasi-Meinongian thesis forwarded by Bertrand Russell in his 1903 Principles of Mathematics (449) according to which there ARE items that do not EXIST. 

It follows from these two assumptions that there are no individuals that are merely possible. For if there were merely possible individuals, they would have Being, but not existence.

Objection.   "This very table that I just finished building, was, before I built it, a merely possible table.  One and the same table went from being merely possible to being actual.  No temporal individual becomes actual unless it, that very individual, was previously possible.  Now the table is actual; hence it, that very individual, had to have been previously a merely possible table. A merely possible table is a table, but one that does not exist."

Reply. "I deny that a merely possible table is a table.  'Merely possible' here functions as an alienans adjective like 'decoy' in 'decoy duck.'  A decoy duck is not a duck, but a hunk of wood made to appear, to a duck, as a duck. A merely possible table is not a table, but the possibility that there come to exist a table that satisfies a certain description. 

The possibility of there coming to exist a table of such-and-such a description could be understood as a set of properties, or as perhaps a big conjunctive property. Either way, the possibility would not be a possible individual.

I deny the presupposition of your question, Steven, namely, that "a merely possible this-such is a unity as much as an actual this-such."  What you are assuming is that there are merely possible individuals. A merely possible individual is a nonexistent individual, and on the view I take in my existence book, there are no nonexistent individuals. 

The next post -- scroll up -- will help you understand the subtlety of this problematic.

Penultimate Draft: Meinertsen Review for Metaphysica

REVIEW ARTICLE

Bo R. Meinertsen, Metaphysics of States of Affairs: Truthmaking, Universals, and a Farewell to Bradley's Regress, Springer 2018, 174 + xviii pp.

Summary

Professor Meinertsen's detailed treatment of states of affairs agrees with the spirit and much of the letter of David M. Armstrong's middle period as represented in his A World of States of Affairs (Cambridge UP, 1997). States of affairs in this acceptation are not abstract objects, as they are for some philosophers, but concrete denizens of the natural world of space-time. They are “unified complexes that are instantiations of properties or relations by particulars.” (1) Unlike Armstrong, however, Meinertsen is not concerned to argue for their existence (3, 13), or to show their utility in different philosophical areas. His focus is on states of affairs themselves, their main theoretical role, the nature of their constituents, and the problem of their unity.

Their main role is to serve as truthmakers. Suppose it is contingently true that Tom is red, where 'Tom' denotes a tomato of our acquaintance. (The use and justification of such “toy examples” is nicely explained on p. 5) Intuitively, such a truth is not just true; it needs an ontological ground of its truth. What might that be? Rejecting both tropes (Chapter 3) and D. W. Mertz's relation instances (Chapter 4) as truthmakers, Meinertsen argues that states of affairs do the job. In this example, the truthmaker is Tom's being red. On Meinertsen's use of terms, all and only states of affairs are truthmakers (84-85).

A state of affairs is a complex, and complexes are composed of distinct constituents. The composition of a state of affairs, however, is non-mereological. Mereological complexes are governed by the unrestricted composition axiom of classical mereology. (8) What the axiom states is that any plurality of items composes something: the existence of some items entails the existence of the sum of those items. The constituents of a state of affairs, however, can exist without the state of affairs existing. For example, Tom's being red entails the existence of the sum, Tom + instantiation + the universal redness. But the existence of the sum does not entail the existence of the state of affairs. A state of affairs, then, is a non-mereological complex. We will return to this important point when we come to the problem of the unity of a state of affairs.

First-order states of affairs have as their constituents particulars, properties or relations, and instantiation. The particulars are bare or thin (Chapter 5). What makes them bare is not that they lack properties, but the way they have them. The bareness of a bare particular consists in its instantiating, as opposed to including, its properties. (73) The properties that enter into states of affairs are sparse as opposed to abundant: not every predicate picks out such a property. In addition, the properties in states of affairs are universals, and thus multiply instantiable. If an immanent (transcendent) universal is one that cannot (can) exist uninstantiated, then Meinertsen's universals are immanent. Immanence so defined admits of abstractness. Meinertsen's universals, however, are concrete. (Chapter 8) The concrete is that which is “spatially and/or temporally located.” (119) Given naturalism, which Armstrong endorses and to which Meinertsen “inclines” (119), every existent is concrete and therefore located, including universals. The locatedness of universals, which is unlike that of particulars, has three implications. The first is that a universal is “wholly located in many places at the same time.” (120) The second implication is that “the region occupied by any such universal is not a mereological part of the region occupied by the whole thick particular.” (121) The third implication is that “more than one universal can have the same spatiotemporal location.” (121)

I note in passing that the banishing of so-called abstract objects demanded by uncompromising Armstrongian naturalism exacts a high price. The price is paid in the coin of the three implications just listed. The abstract-concrete distinction is replaced by a distinction between two categories of concreta, particulars and universals. This replacement requires that one accept the view that universals are ones-in-many (as opposed to ones-over-many) not merely in the sense that a universal cannot exist uninstantiated, but also in the sense that, if it exists, it is wholly present in each of its many spatiotemporal instances without prejudice to its being one and the same universal. This is a highly counter-intuitive consequence, as philosophers from Plato to R. Grossmann have appreciated, but it must be accepted by a states-of-affairs ontologist who is both a naturalist and an upholder of universals. (121)

Chapter 7 is devoted to relations, but in the interests of brevity I will not report on this chapter but advance to Chapters 9 and 10 which treat the problem of unity and Bradley's Regress respectively. This is the most exciting and original part of the book.

Meinertsen and I agree that the problem of the unity of a state of affairs is the central problem for a states of affairs ontology. The problem arises because states of affairs have “non-mereological existence conditions” (7): the existence of the constituents does not entail the existence of the state of affairs. What then accounts for there being one state of affairs having several distinct constitutents? What makes a one out of the many? A state of affairs is not just its constituents; it is these constituents unified. Something more is needed to make of the constituents a state of affairs. “I believe that it is the relating of a unique relation that is needed.” (8)

We can call this 'something more' the unifier. On Meinertsen's approach the unifier is internal to the state of affairs: “the unifier of a state of affairs is a [proper] constituent of it.” (135, emphasis in original) I added 'proper' in brackets to underscore that Meinertsen is not maintaining that states of affairs are self-unifying either in the positive sense that they unify themselves or in the privative sense that they are not unified by another. They are truth-making unities, but not as a matter of brute fact: they need a unifier to account for their unity. The unifier U is a special sort of relation, indeed it is a unique relation as I have just quoted him as saying. It relates the material constituents in the state of affairs, but it does so by being related to them. It is not just a relator of what it relates; it is a relator of what it relates by being related to what it relates. So if U relates the constituents of R(a, b), U does this by being related to each of them, including the relation R. This implies, of course, that U is not identical to R. Some say it is the business of a material relation to relate; not so on Meinertsen's view: it is the business of the formal relation U, and it alone, to relate. We also note that a consequence of U's being related to what it relates, and not merely a relator of what it relates, is that U enters as a constituent into every state of affairs. On an externalist view, by contrast, U unifies the constituents of a state of affairs S without entering into S as a constituent.

Now U is either related by another to what it relates, or it is related by itself to what it relates. If the former, then Bradley's regress is up and running, a regress both infinite and vicious. (Chapter 10) To avoid it, Meinertsen posits that “The U-relation is related to its relata by itself.” (143). This is what makes it unique: it is the only relation that has this “ability,” a word Meinertsen employs. This view, which he dubs “self-relating internalism,” has not been maintained before as far as I know. “To emphasize this unique self-relating ability of U on self-relating unternalism, I shall call it the 'U*-relation.'” (143) Because U* is a constituent of every state of affairs whose constituents it unifies, the monadic case of a's being F may be depicted as follows: U*(U*, F, a). The occurrence of the sign 'U*' both outside and inside of the parentheses indicates that the concrete universal U* is both the bringer of unity and one of the items brought into unity. It is a constituent of every state of affairs without which there would be no states of affairs.

Is U* the same as the instantiation relation? Meinertsen waxes coy: he is “inclined” to say that it is, but this would be an “extrinsic thesis.” What he means, presumably, is that a full assay of R(a,b) might list the following constituents: U*, dyadic instantiation, R, a, and b. Or it might list the foregoing items except instantiation. In the latter case, U* is instantiation. For example, “Edinburgh's being north of London is unified if and only if the U*-relation relates itself to being north of, Edinburgh and London.”(143). Either way, it would seem that U* must be a multi-grade relation, one that can be had by a variable number of items, and which therefore has different 'adicities.' For example, if U* is the instantiation relation, then U* is tetradic in U*(U*, R, a, b) but triadic in U*(U*, F, a). If U* is distinct from the instantiation relation I, then U* is pentadic in U*(U*, I, R, a, b) and tetradic in U*(U*, I, F, a). Meinertsen is aware of all this, and of the apparent problems that arise, but he thinks that they can be adequately dealt with. (157-159) The reasoning is intricate and obscure and to save space I will not comment on it.

The main point is that U* is the master concrete universal without which no state of affairs could exist. A state of affairs exists if and only its constituents are unified, and no plurality of constituents is unified in the state-of-affairs way as a matter of brute fact; ergo, unity demands a unifier as its ground. Being a universal, the unifier U* is multiply instantiable. Being concrete implies that U* cannot exist uninstantiated. It also implies that U*, if multiply instantiated, is multiply located and 'at work' in every state of affairs as that which ties its constituents into a state of affairs. As a self-relating relation, it does its work without igniting Bradley's vicious regress. (Chapter 10) To cop a line from Armstrong, “Nice work if you can get it.”

                                                                            Critique: The Problem of Unity

I will focus my critical remarks on Meinertsen's fascinating and original internalist theory of the unifier U*. What struck me about his theory is its structural similarity to the externalist suggestion I made in a number of my writings. (I thank Meinertsen for his close attention to them.) The points of similarity are the following. Meinertsen and my earlier self both accept that there are middle-Armstrongian states of affairs; that their main role is to serve as truthmakers; that they are complexes composed of distinct constituents; that the composition of these complexes is non-mereological; that their material constituents are particulars and universals; that the unity of a state of affairs, and therewith its difference from the mere plurality of its constituents, needs accounting in terms of a unifier; and above all, that there is a very special, indeed a unique, entity that serves as unifier. The main difference is that Meinertsen's unifier is a constituent of states of affairs while mine is external to states of affairs. Not only is there a similarity, but the two theories, as different as they are, are open to some of the same objections. But before discussing these objections, I want to state my objections to Meinertsen's account of unity, and how my theory avoids them.

First Objection

If there is a constituent of a state of affairs that explains its unity, this constituent must have a unique feature: it must be self-relating. But 'self-relating' has two senses, and this duality of senses give rise to a dilemma. Either (1) U* is self-relating only in the privative sense that it is not related by another to what it relates, supposing it is actually related to what it relates, or (2) U* is self-relating in the positive sense that it actually relates itself to what it relates. If (1), then U* blocks Bradley's regress, but fails to ground unity. It fails to ground the difference between the state of affairs, which is one entity, and the corresponding plurality of its constituents, which is a mere manifold of entities. If (2), then U* is an active as opposed to an inert ingredient in the state of affairs. It is a unity-maker, if you will. It plays a synthesizing role. It brings together the constituents, including itself, which otherwise would be a mere plurality, into a truthmaking unity.

But analysis cannot render this synthesizing intelligible, and therein lies the rub. All ontological analysis can do is to enumerate the constituents of a state of affairs, or, more generally, the parts of a whole. Analytic understanding proceeds by resolving a given whole into its parts, and ultimately into simple parts. But there is more to a (non-mereological) whole than its parts. There is the unity in virtue of which the parts are parts of a whole. The whole is one entity; the parts are many entities. Now if we try to understand this 'more' analytically we can do so only by positing a further part, a unifying part. I say 'posit,' not 'find.' In Fa, one can reasonably be said to find a particular and a character, but not a distinct copulative entity that grounds the truthmaking unity of the constituents. And so Meinertsen posits a unity-grounding entity. But the attempt to understand synthesis analytically is doomed to failure. First of all, no proper part of a whole is its unity, and this for the simple reason that the unity is the unity of all the parts. What one could say, though, is that the unity of the parts, which is distinct from any part, and from all of them, is brought about by a special part, the unifier. But then that special part, without ceasing to be a proper part, would have to exercise a synthesizing function. This synthesizing is what eludes analytic understanding. Simply to posit that the unifier U* has the ability to synthesize is make a kind of deus ex machina move. Leaving God out of it, Meinertsen's U* is a principium ex machina. I will come back to this later in connection with Meinertsen's talk of “inference to the best explanation.” (144) My present point is that even if there is some occult constituent internal to states of affairs that grounds and thus explains their contingent unity, its existence and its operation must remain a mystery and cannot be rendered perspicuous by the analytic method of constituent ontology. Let me explain further.

Does Meinertsen's U* exist? If there are states of affairs as Meinertsen conceives them, then U* has to exist. But if U* exists, then it is (a) a distinct entity independent of us and our synthetic activities, and (b) a distinct item that we can single out in thought if not in perception. If I see that a book is on a table, then I see a book, a table, and possibly also the relation referred to by 'on.' What I don't see, however, is the referent of 'is': the being of the book's being on the table. Since I don't see the being of the book's being on the table, I do not see U*. I cannot single it out in perception. Can I single it out in thought? To do so I would have to be able to distinguish U* from S, the state of affairs the unity of whose constituents U* grounds. There is a problem here. The ordinary (material) constituents in a state of affairs S are weakly separable: each such constituent could exist apart from every other one in S and apart from S itself, but not apart from every other entity. For example, let S = Fa. If Fa is a Meinertsenian state of affairs, then a can exist without instantiating F, and F can exist without being instantiated by a, and each can exist without being constituents of S. (The separability is said to be weak because a cannot exist without properties, and F cannot exist uninstantiated.) Now the immanent universal relation U* can exist apart from a and apart from F provided it is instantiated elsewhere, but not if it is the actual unifier of a and F. As the latter, as the active ingredient in S, it is inseparable from a, from F, and from S. But then U* is quite unlike the material constituents in S, which are all inert, and it is unintelligible in what exact sense U* is a constituent of S. The analytic assay lays out the constituents of a state of affairs, but it can do this only because of the logically antecedent unity of the constituents in virtue of which there is a state of affairs to assay. To understand this unity analytically by positing a special unifying constituent would make sense only if said constituent were inert like the material constituents. But of course it cannot be inert if its is to be a unity-grounder.

Another way of appreciating the problem is by asking what the difference is between U* as an active ingredient in S, and S. Clearly, S cannot exist without U*. But it is also true that U*, as the active ingredient in S that unifies precisely a and F, cannot exist without S. This is because U* is a unifying unifier only when instantiated/located in a state of affairs with determinate material constituents. In every state of affairs S in which the in rebus immanent universal U* exists, it unifies precisely the constituents of S, and cannot do otherwise. So U* and S are mutually inseparable. It follows that U* both is and is not weakly separable from S. As a constituent of S, U* is weakly separable from S. As an active ingredient and unity-maker, however, U* is not weakly separable from S. We ought to conclude that it is unintelligible how a (proper) constituent of a state of affairs could serve as its unifier. As a constituent, U* must be inert in S; as unifier, U* must be active. But it can't be both because it cannot be both weakly separable from S and not weakly separable from S.

An analogy may help clarify my criticism. The existence of two boards and some glue does not entail the existence of two boards glued together. That is obvious. It is also obvious that there would be no need for super-glue to glue the glue to the boards should someone glue the boards together. If there were a need for super-glue, then one would need super-duper-glue to glue the super-glue to the glue and to the boards, and so on. We can express this by saying that ordinary glue glues itself to what it glues; it is not glued by another to what it glues. In this sense, ordinary glue is self-gluing. This is in analogy to Meinertsen's claim that U* is self-relating. But note that 'self-gluing' can only be taken in a privative, not a positive, sense. The same goes for 'self-relating.' By 'privative' I simply mean that the self-gluing glue is not glued by another. If the glue and the relation U* were self-gluing and self-relating in a positive sense, then they would be agents of an action. They would be active as opposed to passive or inert. But surely self-gluing glue does not do anything: it does not apply itself to the boards or bring it about that the two boards are glued together; self-gluing glue is merely such that if the two boards are glued together by a genuine agent, no further glue would be needed to glue the glue to what it glues. Likewise, self-relating U* does not do anything: it does not bring it about that U*, a, and F are 'cemented' into a state of affairs; it is merely such as to insure that if U*, a, and F are brought together to form a state of affairs, no further formal U-type relations are needed to do the job.

Meinertsen credits me with appreciating that the problem of regress-avoidance and the problem of unity are two and not one. “As Vallicella (2004, p. 163) . . . eloquently puts it: 'A regress-blocker is not eo ipso a unity-grounder, pace Russell, Alexander, Blanshard, Grossmann, et al.'” If I am right, however, Meinersten has not really taken this insight on board. My point against him is that his U* can do only the regress-blocking job but not the unifying job. The problem is that no constituent of a state of affairs can do the unifying job. A fortiori, no relational constituent can do the job. By my lights, Meinerten fails to appreciate this, and it may be that he fails to appreciate it because he illicitly slides from the privative sense to the positive sense of 'self-relating.'

Second Objection

On Meinertsen's internalist theory, the unifier U* is a constituent of every state of affairs. Now corresponding to every state of affairs there is the sum of its constituents. So, corresponding to a's being F, there is the sum a + U* + F. Clearly, the particular a in the state of affairs is numerically the same as the particular a in the sum, and the universal F in the state of affairs is numerically the same as the universal F in the sum. The state of affairs and the sum share these material constituents and do not differ in respect of them. But what about the concrete universal U*? Is it numerically the same entity in the state of affairs and in the sum? If yes, then trouble, and if no, then trouble.

States of affairs are contingent. The contingency of a state of affairs derives from the contingent unity of its constituents. So it must be possible that the same constituents exist either unified or not unified. Thus the state of affairs and the sum must have the same constituents. Now U* is a constituent. It follows that U* must be be numerically the same in both the state of affairs and the corresponding sum. Two items, x, y, are numerically the same just in case thay have all the same properties. So U* must be either inert in both state of affairs and sum, or active in both. Now if U* is inert in both, then no state of affairs is constituted. If, on the other hand, U* is active in both, then the unity of the state of affairs is necessary. (For if U* is active in both, then there is no difference between the state of affairs and the sum. ) Either way, no contingent state of affairs is constituted. Therefore, U* cannot be numerically the same in both state of affairs and corresponding sum.

If, on the other hand, U* is active in the state of affairs, but inert in the sum, we get the same problem. A state of affairs is contingent just in case its constituents can exist without forming a state of affairs. It must be possible for the same constituents to be either unified into a state of affairs or not so unified. But active U* is not the same as inert U*. It follows that the state of affairs and the sum do not have the same constituents, which implies that the state of affairs is not contingent, but necessary. We ought to conclude that the unifier of a state of affairs cannot be a constituent thereof.

Third Objection

The first objection focused on the existence conditions of states of affairs; the third focuses on the existence conditions of concrete universals, in particular, the existence conditions of U*. What I will try to show is that Meinertsen's theory is involved in an explanatory circulus vitiosus. Roughly, he attempts to explain the unity, and thus the existence, of a state of affairs by positing a special unifying constituent when that very constituent can exist only in a state of affairs. Here is my argument:

a) A state of affairs exists if and only if its constituents form a unity.
b) U* is a constituent of states of affairs that explains their unity.
Therefore
c) U* is a constituent of states of affairs that explains their existence. (from a, b)
d) U* cannot exercise its explanatory function unless it exists.
Therefore
e) The existence of U* explains the existence of states of affairs.
But
f) U* cannot exist except in a state of affairs.
Therefore
g) The existence of states of affairs explains the existence of U*
h) Given the asymmetry of explanation, (e) and (g) are contradictory, and Meinertsen's explanation of the existence of states of affairs in terms of U* is viciously circular.

The above argument rests on the following assumptions. First, there is such a procedure as metaphysical explanation. Second, it is asymmetrical: if x explains y, then it is not the case that y explains x. Third, a circular explanation, violating as it does the asymmetry of explanation, is not an explanation, or is not a successful explanation. Fourth, the unity/existence of states of affairs, being modally contingent, needs explanation, i.e., it cannot be a factum brutum. Meinertsen is committed to all four assumptions. He is committed to the first since he accepts truthmaking. The truthmaker metaphysically (not logically and not causally) explains the truth of the truth-bearer. He is obviously committed to the second and third. He is committed to the fourth because he takes seriously the problem of unity, which is the problem of explaining the difference between a state of affairs and the mere plurality of its constituents.

An External Unifier Avoids the Above Objections

I admit that the theory of my earlier self is not much better than Meinertsen's: in the final analysis they are both unsatisfactory, although for different reasons. But my theory does avoid the above objections. Meinertsen gets into trouble by making his unifier U* a constituent of states of affairs. This exposes him to the first objection because no constituent of a state of affairs could be an active, unity-grounding ingredient. Or at least it is unintelligible how anything like that could exercise a synthesizing function. A state of affairs is a synthetic unity the synthetic character of which cannot be understood by ontological analysis. Analytical understanding here reaches one of its limits. An ontological assay is merely a list of constituents. But the unity of these constituents is not a further item on the list. Nor can adding a special constituent to explain this unity avail anything. For either this further constituent is inert or it is active. If the former, no progress as been made in accounting for unity. If the latter, then the further constituent must be ascribed a special synthesizing power that nothing else has, and that nothing that analysis could reveal could have. How could analysis reveal such an occult power?

U*'s being a constituent opens Meinertsen to the second objection because a state of affairs is contingent only if the same constituents can exist either unified or not. But this sameness is impossible if U* is both a constituent and a unifier. U*'s being a constituent also exposes him to the third objection because no constituent can exist without being a constituent of some state of affairs or other. So if the unifier is a constituent, then it cannot exist unless states of affairs exist. This however gives rise to the explanatory circle. We ought to conclude that if there is a unifier, then it cannot be internal.

My external unifier unifies but without thereby entering into the states of affairs whose unity it brings about. It thereby evades all three of the objections lately listed. Kant's transcendental unity of apperception provides a model of an external unifier. That which brings about the synthesis of representations in the unity of one consciousness, thereby constituting an object of experience, is not itself a part of the object so constituted. One obvious objection from a realist, naturalist, and empiricist point of view to an external unifier, whether developed along transcendental lines or, as in my 2002, along onto-theological lines, is that it leads us away from realism to idealism. It brings mind into the picture as the synthesizing factor. But if (irreducible) mind is brought in, then naturalism is abandoned for some sort of 'spiritualism.' Empiricism too is abandoned if one invokes an external unifier along either transcendental or onto-theological lines.

The brings me to the deus ex machina objection that has been lodged against my proposal. Roughly, I put God to work to solve the problem of the unity of states of affairs. (“God has his uses,” my teacher J. N. Findlay once said.) Curiously, Meinertsen is open to a similar objection, call it principium ex machina. He does not call upon God, but upon a sui generis entity, U*, which is unique among concrete universals due to its synthesizing power. Well, what exactly is wrong with these ex machina moves? Meinertsen and I will be told that the moves are objectionably ad hoc. Meinertsen is sensitive to the criticism:

The U*-relation is of course an 'ad hoc' entity in the sense that it is only introduced to solve a problem, viz. the problem of unity. Some authors, such as Betti (2015), would consider that a big drawback of self-relating internalism. However, one man's 'ad hoc' - solution is another man's inference to the best explanation. (143)

If any of my three objections above are sound, however, Meinertsen's inference to the best explanation is an inference to an explanatory entity that cannot exist or at least cannot be intelligibly posited.

Van Til on Divine Simplicity and the One and the Many

(Edits added 2/10/19)

Cornelius Van Til rightly distinguishes in God between the unity of singularity and the unity of simplicity.  The first refers to God's numerical oneness. "There is and can be only one God." (The Defense of the Faith, 4th ed., p. 31) The second refers to God's absolute simplicity or lack of compositeness: ". . . God is in no sense composed of parts or aspects that existed prior to himself." (ibid.)  Van Til apparently thinks that divine simplicity is a Biblical doctrine inasmuch as he refers us to Jer. 10:10 and 1 John 1:5.  But I find no support for simplicity in these passages whatsoever.  I don't consider that a problem, but I am surprised that anyone would think that a doctrine so Platonic and Plotinian could be found in Scripture.  What surprises me more, however, is the following:

The importance of this doctrine [simplicity] for apologetics may be seen from the fact that the whole problem of philosophy may be summed up in the question of the relation of unity to diversity; the so-called problem of the one and the many receives a definite answer from the doctrine of the simplicity of God." (ibid.)

That's an amazing claim!  First of all, there is no one problem of the One and the Many: many problems come under this rubric. The problem itself is not one one but many!  Here is a partial list of one-many problems:

1) The problem of the thing and it attributes.

A lump of sugar, for example, is one thing with many properties. It is white, sweet, hard, water-soluble, and so on. The thing is not identical to any one of its properties, nor is it identical to each of them, nor to all of them taken together.  For example, the lump is not identical to the set of its properties, and this for a number  of reasons. Sets are abstract entities; a lump of sugar is concrete. The latter is water-soluble, but no set is water-soluble. In addition, the lump is a unity of its properties and not a mere collection of them.  When we try to understand the peculiar unity of a concrete particular, which is not the unity of a set or a mereological sum or any sort of collection, we get into trouble right away.  The tendency is to separate the unifying factor from  the properties needing unification and to reify this unifying factor. Some feel driven to posit a bare particular or bare substratum that supports and unifies the various properties of the thing. The dialectic that leads to such a posit is compelling for some, but anathema to others. The battle goes on and no theory has won the day.

2) The problem of the set and its members.

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)

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?  See here for more.

3. The problem of the unity of the sentence/proposition. 

The problem is to provide a satisfying answer to the following question: In virtue of what do some strings of words attract a truth-value? A truth-valued declarative sentence is more than a list of its constituent words, and (obviously) more than each item on the list. A list of words is neither true nor false. But an assertively uttered declarative sentence is either true or false.   For example,

Tom is tired

when assertively uttered or otherwise appropriately tokened is either true or false. But the list 

Tom, is, tired

is not either true or false. And yet we have the same words in the sentence and in the list in the same order. There is more to the sentence than its words whether these are taken distributively or collectively.  How shall we account for this 'more'?  

There is more to the sentence than the three words of which it is composed.  The sentence is a truth-bearer, but the words are not whether taken singly or collectively. On the other hand, the sentence is not a fourth thing over and above the three words of which it is composed. A contradiction is nigh:  The sentence is and is not the three words.

Some will say that the sentence is true or false in virtue of expressing a proposition that is true or false. On this account, the primary truth-bearer is not the (tokened) sentence, but the proposition it expresses.  Accordingly, the sentence is truth-valued because the proposition is truth-valued.  

But a similar problem arise with the proposition. It too is a complex, not of words, but of senses (on a roughly Fregean theory of propositions). If there is a problem about the unity of a sentence, then there will also be a problem about the unity of the proposition the sentence expresses on a given occasion of its use. What makes a proposition a truth-valued entity as opposed to a mere collection (set, mereological sum, whatever) of its constituents?

4) The problem of the unity of consciousness.

At Theaetetus 184 c,  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 great Plato was well aware of the problem of the unity of consciousness. (It is not for nothing that Alfred North 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 (genitivus objectivus) a self-same 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 not just any old kind of unity -- it is not the unity of a collection, even if the members of the collection are immaterial items  -- but a simple unity. Hence the unity of consciousness cannot be understood along materialist lines.  It is a spiritual unity and therefore an apt model of the divine simplicity.

Back to Van Til

He is wrong to suggest that there is only problem of the One and the Many.  The One and the Many is itself both one and many. Whether he is right that it is "the whole problem of philosophy," it is certainly at the center of philosophy. But what could he mean when he claims  that the doctrine of divine simplicity solves the problem?  It is itself one form of the problem.  The problem is one that arises for the discursive intellect, and is perhaps rendered insoluble by the same intellect, namely, the problem of rendering intelligible the unities lately surveyed.

God is the Absolute and as such must be simple.  But divine simplicity is incomprehensible to the creaturely intellect which is discursive and can only think in opposites.  What is actual is possible, however, and what is possible might be such whether or not we can understand how it is possible. So the best I can do in trying to understand what Van Til is saying is as follows. He 'simply' assumes that the God of the Bible is simple and does not trouble himself with the question of how it is possible that he be simple.  Given this assumption,  there is no problem in reality of as to how God can be both one and many.  And if there is no problem in the supreme case of the One and the Many, then there are no problems in any of the lesser cases.

The Problem of the Unity of the Proposition

Jacques writes,

I'm thinking about this problem and getting increasingly frustrated by the way in which it's discussed in philosophy.  I wonder if you have any ideas.  Let me explain what bothers me . . .

Typically, philosophers begin with the idea that 'the proposition' needs to be explained or characterized in some special way that will solve the alleged problem.  So Frege had his unsaturated concepts, Russell worried about the relating relation, etc.  And nowadays there is this vast literature about structured or unstructured propositions, acts of predication, etc.

I don't understand how anything of this kind could possibly help.  To explain, I take it that the most basic and intuitive problem here is really the problem of the nature of thought.  At least that is the most natural and paradigm case:  I think that a is F, and now we ask what is going on in my mental life that makes that happen.  How is it even possible?  But when we posit these mysterious entities, propositions, as the objects or contents of thoughts we're just pushing the question back.

I agree that introducing propositions only pushes the problem back. But what exactly is the problem?   The problem is to provide a satisfying answer to the following question: In virtue of what do some strings of words attract a truth-value? A truth-valued declarative sentence is more than a list of its constituent words, and (obviously) more than each item on the list. A list of words is neither true nor false. But an assertively uttered declarative sentence is either true or false.   For example,

Tom is tired

when assertively uttered or otherwise appropriately tokened is either true or false. But the list 

Tom, is, tired

is not either true or false. And yet we have the same words in the sentence and in the list in the same order. There is more to the sentence than its words whether these are taken distributively or collectively.  How shall we account for this 'more'?  

Some will say that the sentence is true or false in virtue of expressing a proposition that is true or false. On this account, the primary truth-bearer is not the (tokened) sentence, but the proposition it expresses.  Accordingly, the sentence is truth-valued because the proposition is truth-valued.  

But a similar problem arise with the proposition. It too is a complex, not of words, but of senses (on a roughly Fregean theory of propositions). If there was a problem about the unity of a sentence, then there will also be a problem about the unity of the proposition the sentence expresses on a given occasion of its use. What makes a proposition a truth-valued entity as opposed to a mere collection (set, mereological sum, whatever) of its constituents?

So here is one way the introduction of propositions "pushes the problem back."  So far, then I am in agreement with Jacques.

If some proposition p just inherently means that a is F, or is inherently true if a is F, regardless of any beliefs or concepts or mental activities of mine, then surely I could operate with proposition p while taking it to mean or represent some other situation--that a is not F, or that b is G, or whatever. 

This is not clear. Someone who introduces Fregean or quasi-Fregean propositions as the contents of such propositional attitudes as belief and desire will say that believing that whales are mammals involves no judgmental synthesis, no mental activity on the part of the believer, since this synthesis is already accomplished in the proposition.  (How this synthesis is accomplished is a very difficult question, an insoluble one in my opinion.)  So I could not take the proposition Whales are mammals  to mean Grass is green.  The Fregean proposition is part of the mechanism whereby I mean that whales are mammals.

The brute fact that it represents, if that even makes sense, seems to have no implications for my representational use of the proposition or relation to it (or whatever it is that I'm supposed to be doing with propositions). 

But you are not using the proposition to represent the fact.  Your intending the fact is routed through the proposition which is the sense of the corresponding declarative sentence.  (Frege of course has no truck with truth-making facts; he holds the bizarre view that the referent, Bedeutung, of the sentence is THE TRUE. I am sketching here, but not endorsing, a quasi-Fregean theory of propositions.)

Even if we could explain how it is unified, that would still seem to leave the basic problem of how I am able to think a unified thought by means of that entity.  (If I'm thinking that proposition p is true, or represents the world accurately, what is it about my activity or state of mind that somehow unifies the representational content p with the further property of being true or being-an-accurate-representation?)

I think you are missing the point that the proposition is a semantic and epistemic intermediary; it is not the direct object of a mental act. You are not thinking that Snow is white is true; you are thinking that snow is white via the propositional content Snow is white.

On the other hand, if p is such that, necessarily, in having p before my mind I entertain or grasp the thought that a is F, the basic mystery is just being described or reiterated.  What on earth am I doing when I somehow manage to think that a is F?  Postulating this thing that is supposed to enable me to think so doesn't seem like any kind of explanation.  What kind of thing is this, meaningful or representational in itself, yet also necessarily dictating my representational grasp of it?  Why not just say that I think that a is F, with no hint of any analysis or explanation of that fact about me?

Are you proposing a Wittgensteinian eschewal of theory and philosophical explanation?

Tom believes that Cicero is a Roman; Cicero is Tully. But Tom does not believe that Tully is a Roman.  Is there not a genuine puzzle here the solution to which will involve a theory of propositions? 

One view is that the ultimate truth-bearers are token acts of predication.  For example, the thing that is true is my act of predicating property F of object a, according to rules somehow determined by property F.  But this too seems hopeless as an explanation or analysis.  Phrases like 'predicating a property of an object' don't mean anything more than 'thinking that something is a certain way'.  No doubt, once I do that, I'm doing something that we might call 'correct' or 'true' depending on what the world is like.  But is there any real difference between predicating F to a, on the one hand, and just thinking that a is an F?  I have no idea what these people are talking about, or how they think this is explanatory.  Every theory seems ultimately to depend on the unexplained notion of someone having a propositional thought--that a certain proposition is true, that some possible world is actual, that a property is instantiated, or whatever.  And yet that seems to be the very notion that we want to understand here--the notion of propositional thought, thinking that something is the case.  Alternatively, they're positing these non-propositional events or activities--just the brute fact that someone 'predicates' or someone 'grasps' a proposition, without these things being taken to depend on thinking that things are thus-and-so.  But in that case, the theories are all obviously false; they just deny the phenomenon we want to explain.

Do you have a reference in the literature for me?

Suppose I say of Elliot that he is sober. That is a token act of predication: I apply the predicate 'sober' to Elliot.  But Karl can say the same thing by applying the predicate 'nuechtern' to Elliot.  So I don't see how token acts of predication could be the ultimate truth-bearers.  These acts are different. But the content expressed is the same. Besides, how can an act be true or false?

I get the impression that you are driving in a Wittgensteinian direction, We say things like 'Hillary is a liar' and we think the corresponding thoughts.  Apparently, you want to leave it at that and not seek any philosophical explanation on the ground that these explanations don't really explain anything.

Would you go so far as to say that the problem of the unity of the sentence, the problem of what makes a sentence different from a list of words, is a pseudo-problem?

Well, I don't know if that makes sense, but I'd appreciate any thoughts you might have.  I feel this is an absolutely fundamental set of problems, with important implications, but the philosophical literature just seems to confuse me . . .

It makes plenty of sense . . . 

Working Draft: The Case Against Facts

Comments appreciated if you are en rapport with the subject matter.

 

The Case Against Facts

 

Arianna Betti, Against Facts, The MIT Press, 2015, pp. 296 + xxvii

 
If Buridan's contribution to the bestiarum philosophorum was the ass, and David Armstrong's the ostrich, Arianna Betti's is the hedgehog bristling with spines. The hedgehog is an appropriate totemic animal inasmuch as her book too bristles with sharp distinctions and prickly arguments designed to inflict pain upon the friends of facts. In this penetrating and beautifully organized volume Professor Betti deploys her distinctions and arguments against two sorts of facts, compositional and propositional, as she calls them. The states of affairs of David Malet Armstrong's middle period (Armstrong 2007) are examples of the first kind of fact. These items are the main target of Betti's animadversions in the first part of her two-part book. She does not go so far as to claim that Armstrongian facts do not exist; her claim is the rather more modest one that we have no reason to posit them, since the work they do, if it needs doing at all, can be done just as well by a certain sort of mereological sum. (101) Betti ignores, however, Armstrong's very different later conception of states of affairs or facts. (Armstrong 2009; Armstrong 2010, 26-34; Vallicella 2016) This later conception also counts as compositional in her sense and ought to have been discussed for the sake of completeness, especially since it in some ways approximates to Betti's mereological  position.

 

One might wonder how a fact could fail to be compositional. Facts are complex or composite items, after all, not simples. So they must all have some internal composition or other, whether they be truthmaking facts or facts of the Chisholmian-Plantingian sort. At a bare minimum, a's being F is composed of a and F-ness. Thus I find less than felicitous Betti's talk of propositional facts in contrast to compositional facts as “noncompositional objects at the level of reference.” (24) She makes it clear, however, that she is using 'compositional' in a narrow sense that implies that compositional facts and their constituents are “part[s] of the furniture of the world.” (37) We shall soon see that being in the world involves being real as opposed to being ideal. An example of a compositional fact is the fact of Guido's being hungry. This fact has Guido himself, all 200 lbs of him, as a constituent. An example of a propositional fact is the putative referent of the that-clause in a sentence like 'Guido sees that Francesca is serving spaghetti puttanesca.' This putative referent is the fact that Francesca is serving spaghetti puttanesca. This propositional fact is like a (Fregean) proposition, though it is not a proposition, in that it does not have Francesca herself as a constituent, but rather an abstract surrogate that represents her. (170) (This fact-of vs. fact-that terminology is mine, not Betti's. I got it from Milton Fisk.)

 

Betti describes in marvellous detail seven features of compositional facts (18) and five of propositional facts (170). I will speak of C-facts and P-facts. Here are some salient differences. C-facts are in the world, and thus suited to play the truthmaking role whereas P-facts are not in the world and hence not fit for truthmaking. To be in the world is to be real where to be real is to exist “through time and in time as causes or effects in a causal chain.” (22) So C-facts are real while P-facts are ideal. The ideality of P-facts, however, is not that of propositions since P-facts are not propositions. Betti is greatly and rightly exercised by the curious in-between status of these “ghostly critters” (114) that are neither truthbearers nor truthmakers and yet are championed by such distinguished philosophers as Roderick Chisholm, Alvin Plantinga, and Kit Fine. These “ghostly critters” are not truthbearers because they are neither true nor false. But while they are not bivalent in terms of truthvalue, they are 'bipolar' (my term): while all exist, some of them obtain while some do not. They are not truthmakers since truthmakers are real and 'monopolar': if they don't exist they are nothing. Thus the fact of Guido's being hungry does not exist at all if Guido is not hungry. Propositional facts are neither fish nor fowl. The conclusion Betti arrives at strikes me as correct: “Propositional facts collapse into true propositions.” (179) Propositional facts are thus not a distinctive category of entity. We need them, she thinks, as little as we need compositional facts. Actually, her position is far more radical than this since she denies that that-clauses are referential parts of speech. So her position is best expressed conditionally by the following quotation: “If there were nominal reference to facts, facts would be true propositions . . . . (113) Her view, if I understand it, is eliminativist not identitarian: she is not saying that there are propositional facts and that what they are are true propositions; she is saying that that there are no propositional facts.

 

Leaving propositional facts to languish in their ghostly realm, the rest of this article will take issue with Betti's critique of compositional facts, the ones dear to my heart, the facts involved in the flux and shove of the real order. On a personal note, I want to thank Professor Betti for her very close attention to my articles on the topic.

 

The Case Against Compositional Facts

A compositional fact, as opposed to a propositional fact, is an entity fit to play the role of truthmaker. The truthmaker role may be introduced as follows. Consider the assertive utterance of some such contingent sentence as 'Tom is sad.' If true, this assertively uttered sentence cannot just be true: if true, it is true because or in virtue of something external to it. This use of 'because' is not causal which is why philosophers reach for the weasel phrase 'in virtue of,' which, despite its slipperiness, may well be indispensable for metaphysics. I say it is indispensable. (Or do hedgehogs eat weasels?) Roughly, there has to be something that 'makes' the sentence true. This external something cannot be another declarative sentence, even if true. More generally, a truth is a true truthbearer (a Fregean proposition, say, or perhaps an Aristotelian proposition, see pp. 31-32 for Betti's helpful explanation of the difference) and no true truthbearer is made true by another such item in the specific sense of 'makes true' in play in truthmaker theory. Nor can someone's say-so be what makes true a true truthbearer. The truthmaker has to be something 'in the world,' something extralinguistic and mind-independent in the realm of reference as opposed to the realm of sense. The friends of truthmakers are realists about truth: they are convinced that at least some truths are in need of an ontological ground of their being true.¹

 

Truthmaker maximalists hold that all truths need such grounds, but one needn't be a maximalist to be a truthmaker theorist. As for 'makes true,' this is neither entailment nor causation. Not entailment, because entailment is a relation between propositions, assuming that truthbearers are propositions, whereas truthmaking is a relation between extra-propositional reality and propositions. So if x makes true y, then y is a truthbearer, but x is not. If someone says that the proposition expressed by 'Snow is white' makes true the proposition expressed by 'Something is white,' then that person, while talking sense, is not using 'makes true' in the specific way in which the phrase is used in truthmaker theory. Truthmaking is not causation for a similar reason: causation does not connect the extra-propositional to the propositional whereas truthmaking does. As Armstrong says, truthmaking is “cross-categorial.” (Armstrong 2004b, 5) It links the extra-propositional to the propositional.

 

It is important to note, however, that while truthmakers cannot be Fregean or Aristotelian propositions, and thus must be extra-propositional, they must also be proposition-like on Armstrong's approach. This is a point I think Betti misses. Speaking of compositional facts, she tells us that “facts are neither linguistic nor languagelike entities at the lowest level of reference. (28, emphasis in original) But this is certainly not Armstrong's view, the view that is supposed to be the target of Betti's critique of compositional facts. His view is that the world is a world of states of affairs, a “totality of facts not of things” (Wittgenstein) and “sentence-like rather than list-like.” (Armstrong 2010, 34) If the world is sentence-like, then, pace Betti, it is language-like. Armstrong was profoundly influenced by his teacher in Sydney, the Scots philosopher John Anderson, who held that “reality, while independent of the mind that knows it, has a 'propositional' structure.” (Armstrong 1997, 3) Armstrong goes on to say that “the propositional view of reality which he [Anderson] championed is the facts or states of affairs view of reality.” (Armstrong 1997, 3-4) That Armstrongian facts are proposition-like and thus language-like is fairly obvious when we consider the truthmakers of contingent predications of the form 'a is F.' The truthmaker cannot be a by itself, or F-ness by itself, or the mereological sum a + F-ness. It must be a-instantiating F-ness, which has a proposition-like structure. Armstrongian facts have a logos-like and thus logical articulation contrary to what Betti says in opposition to Kit Fine. (28) But now I am getting ahead of myself.

 

Suppose you accept the legitimacy of the truthmaker role and the need for some type of entity to play it. It doesn't follow straightaway that the entities needed to play the role must be what Betti calls compositional facts or what David Armstrong calls states of affairs. This is so even if we confine ourselves to the really clear examples of truthbearers in need of truthmakers, namely, synthetic, contingent predications such as 'Guido is hungry' or the propositions expressed by assertive utterances of such sentences. Nevertheless, a powerful argument can be mounted for compositional facts as truthmakers. The argument Armstrong and I consider powerful, however, Betti calls “unsound.” (106) Surprise!

 

Although she is skeptical of the need for truthmakers, she is willing to grant the need arguendo, insisting only that if we need truthmakers, a certain type of mereological complex can do the job thus rendering Armstrong's facts, as unmereological complexes, unnecessary. (102) This is why she thinks the truthmaker argument for Armstrongian facts is unsound. As she sees it, compositional facts are not givens, but theoretical posits, and unnecessary ones at that. They were invented to solve a problem, the unity problem, that arises only because of certain optional assumptions about relations and properties that one is not bound to make. (94-95) Compositional facts are an ad hoc, indeed a “maximally ad hoc,” solution to a pseudo-problem. (64)

 

Now let me say something in exposition of Armstrong's argument for facts or states of affairs as truthmakers on the assumption that the truthmaker role is legitimate and needs to be filled by some category of entity or other. I will then consider Betti's counter-proposal.

 

If it is true that Tom is sad, could the truthmaker of this truth be the item that Betti calls (8) the sentence-subject of 'Tom is sad,' namely, Tom? No, since Tom needn't be sad. So Tom by himself cannot be what makes true 'Tom is sad.' The same goes for the property of being sad. By itself the property cannot be the truthmaker of the sentence in question. (I am assuming, with Armstrong, that properties are immanent universals. Immanent, in that they cannot exist uninstantiated; universal, in that they are repeatable.) Now if Tom exists and sadness exists, then so does the mereological sum Tom + sadness. But this sum cannot be the truthmaker either. For the sum exists whether or not Tom is sad. How so?

 

Suppose that Tom is not sad, but Shlomo is. If properties are immanent universals, then sadness cannot exist uninstantiated; suppose it exists in virtue of being instantiated by Shlomo. So Tom exists, sadness exists, and their sum exists. But this does not suffice for Tom's being sad. There is a missing ontological ingredient: something to connect sadness to Tom. You might think that the missing ingredient would have to be the worldly correlate of the 'is' of predication. But if you take this correlate to be an exemplification/instantiation relation then you ignite Bradley's relation regress which is unfortunately vicious. Other moves invoking Strawsonian nonrelational ties, Bergmannian nexus, Fregean unsaturated concepts, and benign fact-internal infinite regresses (see Vallicella 2010), are equally unavailing. The unifier of a fact's constituents cannot be a further constituent or anything internal to the fact. This leaves two possibilities: (i) the unifier is external to the fact, which Betti rejects, and (ii) Armstrong's middle-period suggestion that facts are entities in addition to their consituents and it is they who hold fact-appropriate constituents together so that they can exercise the truthmaking function. Betti has mastered the dialectic and considers the least bad solution to be Armstrong's: facts hold their constituents together. Although she doesn't say so, she considers my solution in terms of an external unifier to be the worst. The extant putative solutions to the unity problem of course presuppose that it is a genuine problem. Betti thinks it isn't.

 

Betti's Dissolution of the Unity Problem

 

After rejecting the extant putative solutions to the unity problem, Betti proposes to dissolve it by collapsing the distinction between “relations that relate relata and relations that do not: all relations relate relata and carry out their own unifying work.” (95) She means this to apply to properties as well. All properties qualify their bearers and carry out their own qualifying work. Thus there needn't be anything to hold the constituents of a relational or as monadic fact together: nothing internal to the fact, nothing external, and not the fact itself. Betti's point is that there is no need for Armstrongian facts, facts as entities in addition to their constituents. (Cf. Armstrong 1997, 117) Her point is not that there are no facts. There may well be facts; it is just that if there are, they are a special sort of mereological sum. Perhaps we can say that she is an identitarian about compositional facts, not an eliminativist, whereas she is an eliminativist about propositional facts, not an identitarian. More on this in a moment.

 

What Betti has to do is block a possibility like the following. In the actual world, call it Charley, Tim loves Tina. In a merely possible world w in which Tim and Tina both exist, Tim does not love Tina, but Tim loves Toni. In Charley we have both the relational fact of Tim's loving Tina and the mereological sum Tim + loves + Tina. In w, we have the sum Tim + loves + Tina but not the corresponding fact. This implies that there is more to the fact than the sum of its constituents: the sum can exist without constituting a fact. The something more is that which makes of the constituents a real truthmaking unity. Call it the unifier. Betti thinks that the least bad of the extant proposals as to what the unifier is is Armstrong's: facts hold their constituents together; facts are unmereological complexes over and above their constituents. In short, what Betti needs to do is counter the seductive thought that in an actual relational situation such as that of Tom's loving Tina, the constituents can exist without forming a real truthmaking unity. What she needs to maintain is that, necessarily, if all the constituents exist, then the relatedness exists. If the mere existence of the constituents ensures their connectedness, then there is no need for Armstrongian facts. You would then have real unity on the cheap, real truthmaking unity from mereology alone, or rather from mereology operating upon the right sorts of constituents. The mereological principle of the extensionality of parthood would hold for all complexes. Nice work if you can get it!

 

Betti can achieve her end if she holds that relations are relata-specific where “A relation is relata-specific if and only if it is in its nature to relate specific relata.” (89) Suppose that the relation loves as it figures in the sum Tom + loves + Tina is necessarily such that, if it exists, then it relates Tom and Tina. Then there would be no distinction in reality between loves as a relating relation and loves as an inert relation that is merely a constituent but not also a unifier of the complex into which it enters.

 

Betti's contention, then, is that all relations, just in virtue of existing, are relating relations, active ontological ingredients if you will, and none are inert ingredients. A relation cannot exist without actually relating its relata. If so, there cannot be a difference between the mereological sum a + R+ b and the fact of a's standing in R to b. Given the constituents, the fact is given: it is not an ontological extra, something over and above the constituents. There is no possibility of the constituents existing without the fact existing. It follows that there is no need for facts as unmereological compositions, facts as “additions to being,” in a phrase from Armstrong. If a fact just is a mereological complex, then it is an “ontological free lunch,” to employ yet another signature phrase of the late Australian. Of course, not just any old mereological sum is a fact; only those with the right constituents.

 

And the same goes for properties: all properties, just in virtue of existing, qualify their bearers. There is no need for a tertium quid such as an instantiation relation to tie a property to its bearer. Nor is there any need for monadic facts as entities in addition to their constituents to do this unifying work. There is no difference between the sum a + F-ness and the fact of a's being F. For this to work, all properties have to be “bearer-specific.” “A property is bearer-specific if and only if it is in its nature to be had by specific bearers.” (90) Suppose it is true that Hargle is happy, and that being happy is “bearer-specific.” We can display the property as follows: __(H) being happy. '__' indicates that the property is unsaturated or incomplete or gappy in something like Frege's sense: if it is had by an individual it is had directly without the need of a connector such as an instantiation relation or Strawsonian nonrelational tie or a Bergmannian nexus. '(H)' indicates that the property is bearer-specific or rather bearer-individuated: if the property is had, it is had by Hargle and nothing else. That the property is had follows from its existence: necessarily, if the property exists, then it is had, had by Hargle and nothing else, and had directly without the service of a tertium quid. What this all implies is that the mereological sum Hargle + __(H) being happy suffices as truthmaker of 'Hargle is happy.' There is no need for a fact over and above this sum. Indeed, as Betti points out, the property alone suffices as truthmaker since it cannot exist unless Hargle exists. (101)

 

Questions and Objections

 

1. Why is Betti's proposal superior to Armstrong's?

 

Betti presents us with an alternative way of thinking about truthmaking facts, namely, as mereological sums whose parts include relata-specific relations and bearer-specific properties. Betti's main point is that “mereological complexes are viable as truthmakers; facts are not needed for the role.” (101) When she says that facts are not needed, she means Armstrongian, middle-period facts. She is not denying that there are truthmakers. Nor is she is denying the existence of facts as long as they are assayed as mereological complexes. If a fact is a complex entity that functions as a truthmaker, then her mereological complexes containing relata-specific relations and bearer-dependent properties are facts, though not in Armstrong 's robust sense. She is denying, or rather refusing to countenance on grounds of theoretical economy, facts as unmereological complexes. Her claim is that there is no explanatory need for facts as the middle-period Armstrong conceives of them, namely, as “additions to being.” Betti may bristle at my use of 'facts' in describing her position but surely there is an innocuous and nearly datanic, as opposed to theoretical, use of 'fact' according to which an individual's having a property, or two or more things standing in a relation, is a fact. Indeed, she needs this use of 'fact' just to state her theory, according to which the fact aRb is identical to the sum a + R + b, when R is relata-specific. On her view facts are a proper subset of mereological sums. That is not a denial of facts, but an acceptance of them. Unfortunately, Betti sometimes expresses herself in a misleading way. She tells us, for example, that “the thought that the world is a world without facts – one in which there is no difference between facts and sums – is shown to be perfectly sensible.” (88) This formulation equivocates on 'fact.' What she wants to say is that the world is without Armstrongian facts, not that the world is without truthmaking facts. It is the latter that are no different from sums, namely those sums whose constituents include relata-specific relations and object-dependent properties.

 

Betti thinks her theory is preferable to Armstrong's. I question whether she is justified in this preference. We face a tough choice. Armstrong's theory violates the extensionality of parthood and countenances unmereological complexes. This is a strike against it. Betti's theory avoids unmereological complexes, thereby upholding the extensionality of parthood, but accepts relata-specific relations and bearer-dependent properties. How plausible is it that all relations are relata- specific and all properties bearer-dependent? Are these notions even coherent? Let's consider the coherence question.

 

2. Against Relata-Specific Relations and Bearer-Dependent Properties

 

Suppose Argle is two feet from Bargle. There is nothing in the nature of either relatum to necessitate their standing in this external relation. Each can exist apart from the relation. And as I see it, there cannot be anything in the nature of the relation itself to necessitate that it be precisely these two critters that the relation relates. So on my view a relational situation such as Argle's being two feet from Bargle involves a double externality: there is nothing in the nature of the terms to dictate their standing in the external relation in question, and there is nothing in the nature of the external relation to dictate the terms. But as Betti sees it, it is the nature of this relation to relate Argle and Bargle and nothing else: the relation cannot exist/be instantiated without relating precisely these two. This implies that “as soon as” (105) the relation exists, it relates Argle and Bargle. If this conception is coherent, it has the desired consequence of undercutting Bertrand Russell's distinction between actually relating relations and those same relations as inert, and with it the distinction between a fact as a real unity of fact-appropriate constituents and the 'mere' mereological sum of those very same constituents. If this works, it puts paid to Armstrong's commitment to unmereological complexes: mereology suffices for truthmakers provided the parts of the sums include relata-specific relations or bearer-dependent properties.

 

It seems to me, however, that the notion of relata-specificity reduces to absurdity by way of the following argument in which R is any relata-specific dyadic external relation, and a and b are its individual relata. (See also my critique of D. W. Mertz in Vallicella 2004.) Generalization beyond the dyadic case is straightforward but unnecessary. Betti's definition of 'external relation' is standard and perfectly serviceable: “A relation is external if and only if it is not grounded in corresponding properties of its relata, that is, is an entity over and above its relata.” (89) An internal relation is then one that is grounded in corresponding properties and is not an entity in addition to its relata. Now to the argument:

 

P1. R is entirely dependent for its existence on both a and b. (Betti's theory of relata-specificity)

 

This is because (i) R cannot exist without being instantiated and thus cannot exist without actually relating some pair of individuals or other, and (ii) R cannot, as relata-specific, relate any pair of individuals other than a, b. If dyadic R were an immanent universal, then it could not exist without relating some pair or other; but it would not necessarily have to relate the precise pair, a, b. R's existence would then not depend on its relating a and b. But as it is, R is a particular (an unrepeatable), not a universal (a repeatable); it is a non-transferable relational trope. It is as particular as the particulars it relates. Its being or existence is exhausted by its particular occurrence, unlike an immanent universal the being or existence of which is not exhausted by its instantiation in a particular case. So R, as a relational trope, is entirely dependent for its existence on the exact relata it has: its being or existence is exhausted by its relating of those exact relata, the individuals a and b. Therefore,

 

C1. R is not distinct in reality from the particular relatedness aRb: R = aRb.

 

Of course, R can be thought of in abstraction from aRb. But R in reality is identical to aRb. You cannot say that they are different because aRb has constituents a, b while R does not. For R exists when and only when it is relating a and b. Apart from them it is nothing at all.

 

P2. The particular relatedness or relational fact aRb is identical to the mereological sum a + R + b, given that R is relata-specific. (Betti's theory) Therefore,

 

C2. R is identical to the sum a + R + b. (from C1 and P2 by Transitivity of Identity)

 

P3. No proper part of a mereological sum having two or more members is identical to the sum of which it is a proper part. (Principle of mereology) Therefore,

 

C3. R is not identical to the sum a + R + b. (from P3) Therefore,

 

C4. R is and is not identical to the sum a + R + b. (from C2, C3) Contradiction! Therefore,

 

C5. Either P1 or P2 is false; either way, Betti's theory fails.

 

Betti will presumably reject (C1). But how? She tells us that it is the nature of R to relate exactly a and b. Now if it is the nature of R to relate exactly these relata, then it is intrinsic to R that it do so. But then R is intrinsically relational, relational in and of itself. If this is neither contradictory nor magical, then it involves importing mind (intentionality) into the bowels of R. For if it is intrinsic to R that it relate exactly a and b, then R, quite apart from actually relating a and b, 'pre-selects' a and b as its relata. But this is what mind in its intentional states does. Such states are intrinsically relational: it is their nature to be of or about items that need not exist for the states to be of or about them. But surely there is no intentionality within the non-transferable relational trope R!

 

But what is the alternative? Will we be told that a and b are constituents of R? But then R is identical to aRb, when it cannot be given that aRb is a + R + b.

 

Now let's consider bearer-dependent properties. Suppose we grant, along with Armstrong (2004, 49), that some mereological complexes are truthmakers. Is it not also the case that some are not? Suppose that Gargle is lachrymose but Hargle is not. Then the following sum exists: Hargle + __(G)being lachrymose. The sum exists because its two parts exist. But the parts are not connected to form a truthmaker. This implies that on Betti's account there are two sorts of mereological sum: those that are truthmakers and those that are not. It also implies that what makes a mereological sum a truthmaker is not its being a mereological sum. What makes a sum a truthmaker is the nature of its members. Thus what makes Hargle + __(H)being happy a truthmaking sum is its second member.

 

But this second member has a rather intricate and puzzling structure. It is a bearer-individuated property, a property that exists only if instantiated by Hargle. Hargle can exist without being happy, but the property in question cannot exist unless Hargle exists. It is in the nature of the property to qualify precisely Hargle “as soon as it exists,” (105) i.e., as soon as the property exists. But when does it exist? When Hargle instantiates it. So it is not as if the property has its individuated nature apart from its being instantiated; rather, it receives its individuated nature by being instantiated by Hargle. It is only the existing Hargle that can make the property individuative of precisely Hargle and nothing else. So Hargle supplies the nature that makes the property Hargle-specific, or rather Hargle-individuated.

 

Does this not smack of absurdity? The nature of an entity is intrinsic to it; it cannot consist in a relation to an item external to it. So it cannot be instantiation by Hargle that gives the property its nature. If, on the other hand, Hargle were a constituent of the property in question, namely, __(H)being happy, then it would make sense to say that it is the nature of the property to be instantiated by Hargle. But Hargle is not a constituent of the property; otherwise the property would not be a property but the fact of Hargle's being happy.

 

Betti seems to face a dilemma. Either Hargle is not a constituent of the property or he is. If Hargle is not a constituent of the property, then the property has no nature that makes it dependent on precisely Hargle and nothing else. But if Hargle is a constituent of the property, then the property is a fact.

 

If Betti's account is incoherent, as I have just argued that it is, then it cannot be superior to Armstrong's even if Armstrong's is also incoherent. I should make it clear that I am not defending Armstrong; I admit that his view of facts is problematic. In fact, I argue that it is incoherent in Vallicella 2016. My point is that Betti's theory is not an acceptable replacement for it. Even if her theory is not incoherent, it is problematic as I will now further demonstrate.

 

3. Digging Deeper: Further Questions about Betti's Theory of Relations

 

Betti faults me (92-93) for failing to distinguish between externality and relata-unspecificity. A relation is external just in case it is not “grounded in corresponding properties of its relata . . . .” (89) “A rela tion is relata-unspecific if and only if it is not in its nature to relate specific relata.” (90) I fail to distinguish externality from relata-unspecificity in that I hold that, in Betti's words, “A relation is external if and only if it could have related another pair (or triple, quadruple, etc.) of relata.” (93, citing Vallicella 2002, 14-15, 31; 2004, 164). As I see it, no external relation has a nature that dictates that it relate only a particular pair, triple, quadruple, etc. of relata. As against this, Betti envisages the following possibility: an external relation such as being two feet from that holds, if it holds at all, between Argle and Bargle but cannot hold between any other pair of relata. The relation is external in that there is nothing in the natures of the relata that dictates that they stand in the relation in question; the relation is relata-specific in that there is something in the nature of the relation to dictate that, if it holds, it holds only between Argle and Bargle.

 

Now if Betti's scenario is possible, then I have blundered by conflating externality and relata-unspecificity. But while I grant that Betti's 'possibility' is combinatorially possible given her definitions, it is not metaphysically possible. I gave an argument above. So my conflation of externality and relata-unspecificity strikes me as justified.

 

I found Betti's theory of relata-specific relations (which draws on the work of her student Jan Willem Wieland) obscure and in need of further development. One intriguing suggestion is that “relata-specific relations can still be universals.” (91) Now there is a wholly uncontroversial sense of 'relata-specific universal' which Betti does not intend. Consider the universal taller than. This is a dyadic relation that is instantiated by ordered pairs of objects, but not just by any old pair. The pairs must be pairs of things having height. Taller than is thus specific to all and only such pairs and not to pairs of numbers or pairs of sets or pairs of propositions or pairs of angels or pairs of acts of thinking. But Betti means something different. She is apparently envisaging the possibility of a relation that is universal but that, say, relates only Guido, Francesca, Giacomo, and Maria in respect of height. Unfortunately, she gives no exemples and I am not sure what she is driving at. She brings this up because she thinks that her solution to the unity problem works whether or not one assays properties as universals or as tropes. (91) But this is all very obscure and here is a lacuna that needs filling.

 

Conclusion

 

My interim verdict with respect to compositional facts is that Betti has not provided a viable mereological alternative to the admittedly untenable facts or states of affairs of Armstrong's middle period.

 

 

REFERENCES

 

Armstrong, D. M. 1978. Nominalism and Realism: Universals and Scientific Realism, vol. I. Cambridge: Cambridge University Press.

Armstrong, D. M. 1983. What is a Law of Nature? Cambridge: Cambridge University Press.

Armstrong, D. M. 1989a. Universals: An Opinionated Introduction. Boulder: Westview Press.

Armstrong, D. M. 1989b. A Combinatorial Theory of Possibility. Cambridge: Cambridge University Press.

Armstrong, D. M. 1993. “A World of States of Affairs”. Philosophical Perspectives, vol.7, 429-440.

Armstrong, D. M. 2004a. “How Do Particulars Stand to Universals?” In D. W. Zimmerman, (ed.), Oxford Studies in Metaphysics, vol. 1. Oxford: Oxford University Press, 139-154.

Armstrong, D. M. 2004b. Truth and Truthmakers. Cambridge: Cambridge University Press.

Armstrong, D. M. 2009. “Questions about States of Affairs”. In M. E. Reicher (ed.), States of Affairs. Frankfurt: Ontos Verlag, 39-50.

Armstrong, D. M. 2010a. Sketch for a Systematic Metaphysics. Oxford: Oxford University Press.

Armstrong, D. M. 2010b. “Reinhardt Grossmann's Ontology”. In Cumpa, J. (ed.), Studies in the Ontology of Reinhardt Grossmann. Frankfurt: Ontos Verlag, 29-43.

Baxter, D. 2001. “Instantiation as Partial Identity”. Australasian Journal of Philosophy, 1979, 449-64.

Bergmann, G. 1967. Realism: A Critique of Brentano and Meinong. Madison: The University of Wisconsin Press.

Butchvarov, P. 1979. Being Qua Being: A Theory of Identity, Existence, and Predication. Bloomington: Indiana University Press.

Butchvarov, P. 1986. “States of Affairs”. In Bogdan, R. (ed.), Roderick M. Chisholm. Dordrecht: D. Reidel, 113-133.

Butchvarov, P. 2010. “Facts”. In Cumpa, J. (ed.), Studies in the Ontology of Reinhardt Grossmann. Frankfurt: Ontos Verlag, 71-93.

Chisholm, R 1976. Person and Object: A Metaphysical Study. La Salle: Open Court.

Cumpa, J. and Tegtmeier, E. (eds.), 2009. Phenomenological Realism Versus Scientific Realism: Reinhardt Grossmann-David M. Armstrong Metaphysical Correspondence. Frankfurt: Ontos Verlag.

Frege, G. 1960.”On Concept and Object”. In P. Geach and M. Black (eds.), Translations from the Philosophical Writings of Gottlob Frege. Oxford: Basil Blackwell, 42-55.

Frege, G. 1976. “Der Gedanke”. In G. Patzig (ed.), Logische Untersuchungen. Goettingen:Vandenhoeck and Ruprecht, 30-53.

Grossmann, R. 1974. “Bergmann's Ontology and the Principle of Acquintance”. In Gram, M. S. and Klemke, E. D. (eds.), The Ontological Turn: Studies in the Philosophy of Gustav Bergmann. Iowa City: University of Iowa Press, 89-113.

Grossmann, R. 1983. The Categorial Structure of the World. Bloomington: Indiana University Press.

Grossmann, R. 1984. Phenomenology and Existentialism: An Introduction. London: Routledge and Kegan Paul.

Grossmann, R. 1990. The Fourth Way: A Theory of Knowledge. Bloomington: Indiana University Press.

Grossmann, R. 1992. The Existence of the World: An Introduction to Ontology. London: Routledge.

Mulligan, K., Simons, P. and Smith, B. 2009. “Truth-makers”. In Lowe, E. J. and Rami, A., Truth and Truth-Making. Montreal: McGill-Queen's University Press, 59-86.

Mumford, S. 2007. David Armstrong. Montreal: McGill-Queen's University Press.

Plantinga, A. 1974. The Nature of Necessity. Oxford: Oxford University Press.

Strawson, P. F. 1950. “Truth”. In Aristotelian Society Suplementary Volume 24, 136-137.

Vallicella, W. F. 2000. “From Facts to God: An Onto-Cosmological Argument”. International Journal for the Philosophy of Religion 48, 157-181.

Vallicella, W. F. 2002. A Paradigm Theory of Existence: Onto-Theology Vindicated. Dordrecht: Kluwer Academic Publishers.

Vallicella, W. F. 2004. “Bradley's Regress and Relation-Instances”. The Modern Schoolman, vol. LXXXI, no. 3, 159-183.

Vallicella, W. F. 2010. “Gaskin on the Unity of the Proposition”. Dialectica 64, 265-277.

Vallicella, W. F. 2016. “Facts: An Essay in Aporetics”. In Calemi, Francesco F. ed, Metaphysics and Scientific Realism: Essays in Honour of David Malet Armstrong. Boston/Berlin: Walter de Gruyter, 105-131, esp. 115-126.

 

1It is an interesting question whether one could be an idealist and also a truthmaker theorist. Consider a Kantian who holds that phenomenal objects and events are “empirically real but transcendentally ideal” to employ a signature Kantian phrase. It seems to me that such a philosopher could maintain a need for truthmakers for some truthbearers, namely those synthetic aposteriori, and thus contingent, judgments about empirical objects and events. It seems one could combine realism about empirical truth with transcendental idealism.

 

Related articles

The Ramsey Problem and the Problem of the Intrinsically Unpropertied Particular

Van Inwagen, Properties, and Bare Particulars

Bare Particulars versus Aristotelian Substances

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.)