The exclusion of so-called abstract entities or abstract objects such as mathematical sets, unexemplified universals, and numbers from the roster of the real is because of their lack of causal power. What causal role could they play?
And then I quoted Armstrong: "And if they play no causal role it is hard to see how we can have good reasons for thinking that they exist." (2)
Woland's Cat objects:
This reasoning is missing a step, I think. Abstract entities do exist when they are contemplated by a mind: assuming minds are 'real' (i.e. part of organisms, which are part of the space-time continuum of reality), then mathematical sets etc. become real when represented in the mind.
How would Armstrong reply? As follows. To exist is to exist extra-mentally. That is the only way anything can exist. If so, there cannot be two or more ways or modes of existing. He here follows, as other Australian philosophers do, his and their teacher John Anderson. Hence there is no such way of existing as existing intra-mentally, in the mind. Whatever I do when I think about something, I do not, in thinking about it, or contemplating it, confer upon it existence-in-the mind.
The following are candidate abstract entities: the number 7, the set {7}, the proposition expressed by '7 is prime,' the property of being prime. To say that they are abstract is to say that they are not in space or in time, and that they are 'causally inert,' which is to say that they do not enter into causal relations with anything: they neither cause nor are caused. Armstrong rejects the whole lot of them. Their existence is ruled out by his metaphysical naturalism according to which reality is exhausted by the space-time system and its contents. They don't exist outside the mind and, since that is the only way anything can exist, they don't exist inside the mind either.
So what am I thinking about then I think of {Max the cat, Manny the cat}? Sets or "classes supervene on their members -- that is to say, once you are given the members, their class adds nothing ontologically, is no addition of being." (Sketch, 8) But then what am I thinking about when I think about the intersection of two disjoint sets? A set theorist will say: the null set, { }! You will also recall that in set theory, the null set is a subset of every set, and a member of every power set. Don't confuse subset and member as Armstrong does on p. 8, n. 1.
This presents a bit of a problem for Armstrong. He cannot say that the null set supervenes on its members since it doesn't have any. So of course he bites the bullet: he rejects the existence of the null set. "It would be a strange addition to space-time!" (p. 8., n. 1) The more I think about this, the more problematic it seems. If there is no null set, then there are no power sets. And if there is no null set, why should we think that there are unit sets or singletons such as {Quine} or {Max}? What is the difference between Max and the set whose sole member is him? If Max's singleton supervenes on him, then there is no singleton! If there are no singletons, then there is no intersection of {Max, Manny} and {Max, Maya}!
What would Woland's Cat say about that?
Memo to self: Re-read the section "Mysterious Singletons" in David Lewis, Parts of Classes. And blog it! You are not spreading yourself thin enough!
0) What David Armstrong calls truthmaker maximalism is the thesis that every truth has a truthmaker. Although I find the basic truthmaker intuition well-nigh irresistible, I have difficulty with the notion that every truth has a truthmaker. Thus I question truthmaker maximalism (TM). Alan Rhoda has recently come out in favor of TM in a penetrating weblog entry. After sketching my position, I will try to pinpoint my disagreement with Rhoda.
1) Compare *Peter is tired* and *Every cygnet is a swan.* I will argue that truths like the first need truthmakers while truths like the second do not. A declarative sentence enclosed in asterisks names the primary truthbearer expressed by the sentence when assertively uttered or, more generally, assertively tokened. A truthbearer is anything appropriately characterizable as either true or false when 'true' and 'false' are used in their sentential as opposed to their ontic senses. ('True friend' and 'false teeth' feature ontic senses of 'true' and 'false'.) Candidate truthbearers include assertively tokened sentences in the indicative mood, statements, asseverations, judgments, Fregean Gedanken, Bolzanian Saetze an sich and more. By definition, a truth is a true truthbearer, whatever truthbearers are taken to be.)
2) Intuitively, *Peter is tired,* being contingently true, both due to its dependence on the existence of Peter, and on Peter's accidentally possessing the property of being tired, is in need of something external to it that 'makes' it true or determines it to be true, or serves as the ontological ground of its truth. (An ontological ground is not the same as an empirical cause.) *Peter is tired* can't just be true. This is because its truth-value depends on the way the world is. It needs a truthmaker external to it. By 'external to it,' I don't just mean that the truthmaker of a truth must be distinct from it: this condition is satisfied by a distinct proposition (or other type of truthbearer) that entails *Peter is tired.* Entailment, however, is not truthmaking: entailment connects propositions to propositions; truthmaking connects extra-propositional entities (states of affairs for Armstrong) to propositions. What I mean when I say that a contingent truth needs something external to it to 'make' it true is that the truthmaker must be both distinct from the truthbearer and not, like the truthbearer, a 'representational entity' where the latter term covers such items as assertively uttered sentences, judgments, Fregean thoughts/propositions (the senses of context-free sentences in the indicative mood), and whatever else counts as a truthbearer. In other words, a truthmaker of a contingent atomic truth such as *Peter is tired* must be outside the sphere of representations: it must be extralinguistic, extramental, and extra-propositional. Thus the truthmakers of propositions like *Peter is tired* cannot belong to the category of propositions. The ontological ground of a contingent proposition's being true cannot be an entity within the sphere of propositions.
3) The truthmaker of *Peter is tired* cannot be a proposition; but it also cannot be utterly unlike a proposition. Consider Peter himself, that very concrete individual. It is clear that he could not be the truthmaker of *Peter is tired.* Granted, if Peter were not to exist, then the proposition in question could not be true. There are no truths about what does not exist. But although Peter or Peter's existence is a necessary condition of the truth of every true proposition about him, that very individual, it is not the case that Peter or Peter's existence is a sufficient condition of the truth of contingent propositions about him if these propositions are predications such as *Peter is tired.* (I am open to the suggestion that Peter himself suffices for the truth of *Peter exists.*) That Peter by himself cannot be the truthmaker of contingent predications about him can be proven or at least argued as follows.
Argument from Necessitation. Assume for reductio that Peter by himself can serve as truthmaker of contingent predications about him. Now, by truthmaker necessitarianism, whatever truthmakers are, they broadly logically necessitate the truth of their corresponding truthbearers. So if X is the truthmaker of *Peter is tired at t,* then there is no possible world in which X exists and *Peter is tired at t* is not true. But there are plenty of worlds in which Peter exists but *Peter is tired at t* is not true. So Peter by himself cannot be the truthmaker of *Peter is tired at t.*
Argument from Selection. Consider any two true affirmative atomic contingent monadic propositions about Peter such as *Peter is tired at t* and *Peter is hungry at t.* If Peter by himself can serve as the truthmaker of one, then he can serve as the truthmaker of the other. But they obviously require numerically different truthmakers. So Peter is the truthmaker of neither of them. Although different truths can have the same truthmaker, this is not the case when both truths are atomic, even if both are about the same individual. The truthmakers of such atomic propositions as that Peter is a philosopher and that Peter is a violinist must be distinct and they must match up with, or select, their truthbearers. To do this, the truthmakers must have an internal structure isomorphic to the structure of the truthbearers. In other words, the truthmakers must be proposition-like despite their not being propositions. Extra-propositional but proposition-like! What may look like a 'bug' is a 'feature' of truthmaker theory. It follows that Peter by himself cannot be the truthmaker of atomic contingent propositions about him.
4) If Peter by himself cannot serve as truthmaker of the accidental predication *Peter is F,* then neither can F-ness by itself. The same goes for the set {Peter, F-ness}, the mereological sum (Peter + F-ness) and the ordered pair [Peter, F-ness]. For what is needed in addition to Peter and F-ness is a link in the truthmaker that corresponds to the copulative link in the proposition. After all, not every possible world in which both Peter and F-ness exists is a world in which Peter is F. There could be a world in which Peter exists and F-ness exists (by being instantiated by Paul) but in which Peter does not instantiate F-ness. I am assuming that F-ness is a universal, but not that F-ness is a transcendent universal (one that can exist uninstantiated). This is why concrete states of affairs are plausible candidates for the office of truthmaker, as in middle-period Armstrong.
5) But even if one balks at the admission of concrete states of affairs or facts, one will have to admit that Peter himself -- assuming that this concrete individual is not assayed as a state of affair but as an individual -- cannot be the truthmaker of contingent propositions of the form *Peter is F.* Some will say that tropes can serve as truthmakers. Fine, but they too have a proposition-like structure. If the trope Peter's-tiredness-at-t is the truthmaker of *Peter is tired at t,* then it is made true by an entity that has a proposition-like structure, a structure isomorphic to, and mirroring, the structure of the truthbearer.
6) It seems to me that I have just definitively established that the truthmakers of accidental atomic predications like 'Peter is a philosopher' cannot be concrete individuals lacking a proposition-like structure. I have also made it clear that we should not confuse the principle that there are no truths about nonexistent objects with the truthmaker principle. We can call the first principle veritas sequitur esse (truth follows being). What it says is that a truth cannot be true unless there are one or more items it is about. Thus VSE requires that if Milo kicked Philo, this is true only if both Milo and Philo exist or have some mode of being other than existence. The truthmaker principle (TMP) goes beyond this in requiring the instantiation of the dyadic relation ---kicks___ by Milo and Philo, in that order.
7) Consider now the analytic proposition *Every cygnet is a swan.* As analytic, it is true solely in virtue of the meanings of 'cygnet' and 'swan.' It is true ex vi terminorum. Its truth is not contingent on the existence of any cygnets. Why does it need a truthmaker? It certainly does not need anything external to it to make it true. The concept cygnet includes the concept swan, so that, by sheer analysis of the subject concept, one can arrive at the truth in question. That's why we call it, following Kant, 'analytic.' Clearly, nothing external to an analytic proposition is required to make it true. It follows that it cannot have a truthmaker. Or rather it follows if a truthmaker of a first-order truthbearer is an entity that is external to the truthbearer and resident in the realm of reality beyond the sphere of representations broadly construed.
Does this not decisively refute truthmaker maximalism? There are plenty of analytic truths, but none of them has or can have a truthmaker. For if you say that an analytic truth needs a truthmaker, then you are saying that it needs something external to it to 'synthesize,' to bring together, subject and predicate concepts. But analytic truths are precisely not synthetic in that (Kantian) sense. But I hear an objection coming.
8) "*Every cygnet is a swan* does have a truthmaker, namely, the fact that cygnet includes swan." This is a confused response. There would not be a analytic truthbearer at all if cygnet did not include swan. The very existence of the proposition *Every cygnet is a swan* requires that the first concept include the second. So there is no need of an ontological ground of the truth of this proposition. One could of course say that in the analytic case the truthbearer is its own truthmaker. But it is better to say that in the analytic case there cannot be a truthmaker as 'truthmaker' was defined in #2 above.
Some philosophers say that truthmaking is asymmetric rather than anti-symmetric, but that is a mistake. Asymmetry disallows the possibility of self-grounding truthbearers. Anti-symmetry allows for that possibility. And this is something we should allow, because conceptually necessary propositions (e.g., all triangles have three sides) are their own truthmakers. If the proposition exists—whether it exists [as] a Platonic object, an idea in God’s mind, or something else—its very existence supplies a parcel of reality sufficient to explain and ground its own truth.
10) For me, truthmaking is an asymmetric relation whereas for Alan it is an antisymmetric relation. Thus I am maintaining that, for any x, y, if x makes-true y, then it is not the case that y makes-true x. This implies that no truthbearer is its own truthmaker or truth-ground. It implies that in no case is the truthmaker of a truth (a true truthbearer) that very truth. It implies that the truthmaker of a truth is in every case 'external' to that truth in the manner explained above.
Now a relation R is said to be antisymmetric just in case: for any x, y, if x stands in R to to y, and y stands in R to x, then x = y. The antisymmetry of 'makes-true' allows for cases in which a proposition (or other truthbearer) is its own truthmaker. Thus Every cygnet is a swan is its truthbearer that is its own truthmaker. This is Alan's position.
11) Here is a consideration in favor of my position. Truthmakers play an explanatory role. Now explanation is asymmetric: if x explains y, then it is not the case that y explains x. This holds for causal explanation, but also for metaphysical explanation or metaphysical grounding. It is the existence of Milo that metaphysically grounds the truth of Milo exists. And not the other way around. No one -- I hope! -- will say that that the truth of Philo's belief that Milo exists is what makes it the case that Milo exists or that Shlomo's sincere assertive utterance of 'Milo is sleeping' is what makes it the case that Milo is sleeping.
Now if truthmakers play an explanatory role, and metaphysical explanation is asymmetric, then no truthbearer is its own truthmaker. So in the case of analytic or conceptually necessary truths, we should say that they do not have and do not need truthmakers. To maintain this is to reject truthmaker maximalism.
It is worth noting that my position is consistent with saying that a truthbearer (whether a Platonic proposition, a divine thought, whatever) can serve as a truthmaker for a different truthbearer. The Platonic proposition expressed by '7 is prime,' for example, makes-true the general Platonic proposition that there are Platonic propositions.
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.
But, while David has never aspired to put the world right by philosophy, the world for its part has not been equally willing to let him and philosophy alone in return. Quite the reverse. His tenure of the Chair turned out to coincide with an enormous attack on philosophy, and on humanistic learning in general: an attack which has proved to be almost as successful as it was unprecedented.
This attack was begun, as everyone knows, by Marxists, in support of North Vietnam’s attempt to extend the blessings of communism to the south. The resulting Marxisation of the Faculty of Arts was by no means as complete as the resulting Marxisation of South Vietnam. But the wound inflicted on humanistic learning was a very severe one all the same. You could properly compare it to a person’s suffering third-degree burns to 35 per cent of his body.
After the defeat of America in Vietnam, the attack was renewed, amplified, and intensified, by feminists. Their attack has proved far more devastating than that of the Marxists. Lenin once said, “If we go, we shall slam the door on an empty house”; and how well this pleasant promise has been kept by the Russian Marxists, all the world now knows. It is in exactly the same spirit of insane malignancy that feminists have waged their war on humanistic learning; and their degree of success has fallen not much short of Lenin’s. Of the many hundreds of courses offered to Arts undergraduates in this university, what proportion, I wonder, are now not made culturally-destructive, as well as intellectually null, by feminist malignancy and madness? One-third? I would love to believe that the figure is so high. But I cannot believe it.
David did all that he could have done, given the limits set by his position and his personality, to repel this attack. Of course he failed; but then, no one could have succeeded. What he did achieve was a certain amount of damage-limitation. Even this was confined to the philosophy-section of the front. On the Faculty of Arts as a whole, David has had no influence at all—to put it mildly. In fact, when he spoke at a meeting of the Faculty, even on subjects unrelated to the attack, you could always have cut the atmosphere with a knife. It is a curious matter, this: the various ways inferior people have, of indirectly acknowledging the superiority of others, even where no such acknowledgment is at all intended by the inferior, or expected by the superior.
By the end of 1972, the situation in the philosophy department had become so bad that the splitting of the department into two was the only way in which philosophy at this university could be kept alive at all. In this development, David was the leading spirit, as his position and personality made it natural he should be. Of course he did not do it on his own. Pat Trifonoff’s intelligence and character made her an important agent in it. Keith Campbell’s adhesion to our side, after some hesitation, was a critical moment. But while I and certain others were only casting about for some avenue of escape, David never gave up. He battled on, and battled on again, and always exacted the best terms, however bad, that could be got from the enemies of philosophy.
The result of the split was far more happy than could have been rationally predicted at the time. In fact it was a fitting reward for David’s courage and tenacity. For the first twenty years of the new Department of Traditional and Modern Philosophy have been fertile in good philosophy, to a degree unparalleled in any similar period in this or any other Australian university. The department has also enjoyed a rare freedom from internal disharmony. As I have often said, it is the best club in the world, and to be or have been a member of it is a pleasure as well as a privilege.
There will certainly be no adequate official acknowledgment, from anyone inside the university, of what is owed to David. What could someone like the present Vice-Chancellor possibly care about the survival of humanistic learning, or even know about philosophy, or history, or literature? Anyone who did would never have got a Vice-Chancellor’s job in the first place. If there is any acknowledgment forthcoming from the Faculty of Arts, David will be able to estimate the sincerity of it well enough. It will be a case of people, who smiled as they watched him nearly drowning in the boiling surf of 1967–72, telling him how glad they were when, against all probability, he managed to make it to the beach.
But anyone who does know and care about philosophy, or does care about the survival of humanistic learning, will feel towards him something like the degree of gratitude which they ought to feel.
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.
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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.
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