Following A. N. Prior, Sainsbury sets up the problem of intentionality as follows:
We are faced with a paradox: some intentional states are relational and some are not. But all intentional states are the same kind of thing, and things of the same kind are either all relational or all non-relational. (Intentional Relations, 327)
Cast in the mold of an aporetic triad:
1) Some intentional states are relational and some are not.
2) All intentional states are the same kind of thing.
3) Things of the same kind are either all relational or all non-relational.
These propositions are individually plausible but jointly inconsistent. Sainsbury solves the problem by rejecting (1). He maintains that all intentional states are relational. Whether I am thinking about Obama, who exists, or about Pegasus, who does not exist, a relation is involved. In both cases, the relation connects the subject or his mental state to a representation. The representation, in turn, either represents something that exists 'in the world' or it does not. In the first case, there is me, my intentional or object-directed mental state, the concept OBAMA, and the man himself in the external world. In the second case, there is me, my intentional or object-directed mental state, the concept PEGASUS, and that's it: there is nothing in reality that the Pegasus representation represents.
Sainsbury is not saying that when I think about Obama, I am thinking about a representation. Plainly, I am thinking about a man, and a man is not a representation in a mind. While Sainsbury advocates a representationalist theory of mind (RTM), he essays to steer clear of ". . . a disastrous turn that a representationalist view may take: instead of saying that the intentional states are about what their representations are about, the fatal temptation for British Empiricist thinkers (and others) is to regard the intentional states as about the representations (“ideas”) themselves." (330) On Sainsbury's RTM,
For representationalists, all intentional states, including perceptual states, are relational, but the representations are not the “objects” of the states in the sense of what the states are about. Rather, the representations are what bring represented objects “before the mind”. Analogously, we see by using our eyes, but we do not see our eyes. Using our eyes does not make our vision indirect. (330)
This implies that representations are not representatives or stand-ins or epistemic deputies or cognitive intermediaries interposed between mind and world. They are not like pictures. A picture of Obama is an object of vision just as Obama himself is. But Sainsburian representations "neither react appropriately with light nor emit odiferous molecules." (330) Pictures of Obama and Obama in the flesh do both. Representations are in the mind but not before the mind. They are "exercised" in intentional states without being the objects of such states:
Intentional states are not normally about the representations they exercise. The representation is not the state’s “object”, as that is often used. Rather, the state’s object is whatever, if anything, the representation refers to, or is about. The notion of “aboutness” needed to make this true is itself intensional: a representation may be about Pegasus, and a thought about Pegasus involves a representation about him. (338)
Sainsbury's solution to the problem codified in the above inconsistent triad involves two steps. The first is to reject (1) and hold that all intentional states are relational. They are genuine relations, not merely relation-like. The second step is to import relationality into the mind: every intentional state is a relational state that connects two intramental existing items, one being the intentional state itself, the other being the representation, whether it be a truth-evaluable representation, which S. calls a thought, or a non-truth-evaluable representation, which S. calls a concept.
It is easy to see that one could take the first step without taking the second. One could hold that all intentional states are relations but that these relations tie intentional states to mind-transcendent items, whether existent, like Obama, or nonexistent, like Pegasus. But this is the way of Meinong or quasi-Meinong, not the way of Sainsbury. He argues in the paper in question against Meinong for reasons I will not go into here.
In sum, intentional states are relations, but they are neither relations to mental objects nor are they relations to extramental objects. They are relations to representations which are neither. A mental object is (or can be) both in the mind and before the mind. And extramental object is (or can be) before the mind but not in the mind. A Sainsburian representation is in the mind but not before the mind (except in cases of reflection as when I reflect on the concept OBAMA as opposed to thinking about him directly).
The article ends as follows:
Metaphysical relationality is the fundamental feature of intentional states, the nature they all share. In the original puzzle, it was claimed that Raoul’s thinking about Pegasus is not relational, since there is no such thing as Pegasus, whereas his thinking about Obama is relational, since there is such a thing as Obama. But in both cases the claims are made true by Raoul being in a two-place relational state, involving a Pegasus-representation in one case and an Obama representation in the other. The metaphysical underpinning of thinking about Pegasus is just as relational as his thinking about Obama. For the Pegasus case, that is not because there really is such a nonexistent object as Pegasus, but because the truth-making state is a relational one, holding between Raoul and, in the typical case, the concept PEGASUS. For the Obama case, the state is relational in the relevant way not because there is such an object as Obama, but because the truth-making state is a relational one, holding between Raoul and, in the typical case, the concept OBAMA.
CRITIQUE
Does this solve our problem? I don't see that it does. First of all, we are left with the problem of the intentionality of representations. What makes an Obama representation about Obama? Sainsbury's solution to the Prior puzzle is to reject the first limb of the aporetic triad by maintaining that ALL intentional states are relational. But since these relations are all intramental we are left with the problem of external reference. We are left with no account of the of-ness or aboutness of representations. We need an account not only of noetic intentionality but of noematic intentionality as well, to press some Husserlian jargon into service.
Second, it is not clear from this article what exactly representations are. We are told that "representations are what bring represented objects 'before the mind'." How exactly? Talk of the "exercise" of representations suggests that they are dispositions. Is the concept OBAMA in Raoul his being disposed to identify exactly one thing as Obama? But how could an occurrent episode of thinking-of be accounted for dispositionally? Besides, the concept OBAMA would have to be a haecceity-concept and I have more than once pointed out the difficulties with such a posit.
Bill, you said by email earlier that the sentence “Jake is thinking of Zeus” would be true if Jake was indeed thinking of Zeus.
BV: That's what I said, although I would put 'is' where you have 'was.' Is what I said a shocking thing to say?
I have questions for you about the terms ‘obtains’ and ‘satisfies’.
(1) If “Jake is thinking of Zeus” is true, and assuming there is no such thing as Zeus, then does the relation “– is thinking of –” obtain? According to what you said earlier, a relation cannot obtain if any its relata do not exist. But we normally think of a relation obtaining precisely in the case where the sentence which asserts the relation is true. What do you think?
BV: We cannot assume that thinking-of is a relation if every relation is such that its obtaining entails the existence of all its relata. For in the case of Jake and Zeus only one of the relata exists, and it's not Zeus. And yet it is true that Jake is thinking of Zeus. I conclude that the sentence 'Jake is thinking of Zeus,' although grammatically relational, does not express a relational proposition. The sentence needs a truth-preserving analysis that does not commit one to the existence of nonexistent things.
Here are two different candidate analysantia. 'Jake is thinking Zeus-ly.' 'Jake is a Zeus-entertainer.' Neither of these sentences is grammatically relational, and both seem to preserve the truth of the analysandum without commitment to nonexistent things. I do not endorse either analysans.
(2) Is the relational expression “– is thinking of –” satisfied when “Jake is thinking of Zeus” is true? For example, is it satisfied by the two things Jake and Zeus respectively? If not, why not?
a) Lions are smaller than dragons. b) Mice are smaller than elephants.
From this datanic base a puzzle emerges.
1) The data sentences are both true. 2) 'Smaller than' has the same sense in both (a) and (b). 3) In both (a) and (b), 'smaller than' has the same reference: it refers to a dyadic relation. 4) No relation holds or obtains unless all its relata exist.
What we have here is an aporetic tetrad. The four propositions just listed are individually plausible but collectively inconsistent: they cannot all be true. What we have, then, is a philosophical problem in what I call canonical form. Any three of the above four, taken in conjunction, entails the negation of the remaining one. Which limb of the tetrad should we reject?
One might reject (4) while upholding (1), (2), and (3). Accordingly, some relations connect existents to non-existents. It is true that lions are smaller than dragons despite it being the case that dragons do not exist. The sense of 'smaller than' is the same in both (a) and (b). And 'smaller than' picks out one and the same dyadic relation in both (a) and (b).
The idea here is that there is nothing in the nature of a relation to require that its obtaining entails the existence of all its relata. Contrast thinking about the Trevi Fountain in Rome and thinking about the Fountain of Youth. Some will say that in both cases the intentional nexus is a genuine relation since there is nothing in the nature of a relation (to be precise: a specific relatedness) to require that all of its relata exist. It is the same relation, the intentional relation, whether I think of an existing item or think of a non-existent item.
If you don't like this solution you might try rejecting (2) while upholding the remaining limbs: 'smaller than' does not have the same sense in our data sentences. Accordingly, 'are smaller than' in (b) picks out a relation that actually connects mice and elephants. But in (a), 'are smaller than' does not pick out that relation. In (a), 'is smaller than' has the sense 'would be smaller than.' We are thus to understand (a) as having the sense of 'Lions would be smaller than dragons if there were any.'
(2)-rejection arguably falls afoul of Grice's Razor, to wit: one ought not multiply senses beyond necessity. Here is what Grice himself says:
[O]ne should not suppose what a speaker would mean when he used a word in a certain range of cases to count as a special sense of the word, if it should be predictable, independently of any supposition that there is such a sense, that he would use the word (or the sentence containing it) with just that meaning. (Grice, 1989, pp. 47-48, Quoted from Andrea Marchesi, "A radical relationist solution to intentional inexistence," Synthese, 2021.)
I am a first year Jesuit novice of the USA Midwest province. I'm from Cincinnati, OH. I have interests in philosophy. I know Thomism well. My hope is to do metaphysics and philosophical logic within the analytic tradition.
I saw that you wrote a paper on external relations and Bradley's Regress. Can I ask you a couple questions regarding external relations? Do you think that first order logic is ontologically committed to external relations? Also, if all relations are external, would this entail a sort of bare particularism about objects? In other words, would all necessary properties be conceived of as something added, rather than as the essence?
It is good to make your acquaintance, K. V. Best wishes for your studies.
First we need to clarify 'internal and 'external' as applied to relations.
External Relations. My coffee cup rests on a coaster which rests on my desk. Consider first the dyadic on top of relation the relata of which are the cup and the coaster. This is an external relation in the sense that both the cup and the coaster can exist and have the intrinsic (non-relational) properties they have whether or not they stand in this relation. Removing the cup from the coaster need not induce an intrinsic change (a change in respect of an intrinsic property or change in existential status) in the cup or in the coaster. One could also put the point modally. In the actual world, the cup is on the coaster at time t. But there is a merely possible world W in which the cup is not on the coaster at t. In W, cup and coaster both exist and possess the same intrinsic properties they have in the actual world, but the cup does not bear the external on top of relation to the coaster.
Now consider the triadic between relation that relates the members of the ordered triple <coaster, cup, desk>. This relation is also external. The terms (relata) of the relation can exist and have the intrinsic properties they have whether or not they stand in the relation.
A-Internal Relations. If a relation is not external, then it is non-external. One sort of non-external relation is an A-internal relation, where ‘A’ honors David M. Armstrong:
Two or more particulars are internally related if and only if there exist properties of the particulars which logically necessitate that the relation holds. (Universals and Scientific Realism, II, 85)
Consider two balls, A and B. Each has the property of being red all over. Just in virtue of each being red, A and B stand in the same color as relation. Each ball's being (the same shade of) red logically suffices for them to stand in the relation in question. This relation is internal in that the non-obtaining of the relation at a later time or in a different possible world would induce an intrinsic change in one or both of the balls. In other words, the two balls could not cease to be the same color as one another unless one or both of the balls changed color. But the two balls could cease to be ten feet from each other without changing in any intrinsic or non-relational respect. Spatial relations are clear examples of external relations.
In a theological image, for God to bring it about that Mt. Everest is higher than Mt. Kiliminjaro he need do only two things: create the one mountain and then create the other. He doesn't have to do a third thing, namely, bring them into the higher than relation.
A-internal relations can be said to be founded relations in that they are founded in intrinsic (non-relational) properties of the relata. Thus the relational fact of A’s being the same color as B decomposes into a conjunction of two non-relational facts: A’s being red & B’s being red. These non-relational facts are independent of each other in the sense that each can obtain without the other obtaining. A-internal relations reduce to their monadic foundations. They are thus an "ontological free lunch" in Armstrong's cute phrase. They do not add to the ontological inventory. They are no "addition to being." So if every relation were A-internal, then the category of Relation, as an irreducible category of entities, would be empty.
B-internal relations. To say that two or more particulars are B-internally related, where ‘B’ honors Bradley and Blanshard, is to say that there is no possible world in which the particulars exist but do not stand in the relation in question. Thus two B-internally related particulars cannot exist without each other. Each is essential to the other. Here is an example. Set S has five members essentially (as opposed to accidentally) , while set T has seven members essentially. These essential properties of S and T found the relation larger than (has a greater cardinality than) that obtains between them. Although there are possible worlds in which neither set exists, there is no possible world in which both sets exist but fail to stand in the relation in question. So S and T are B-internally related.
Here is a simpler example, Socrates and his singleton {Socrates}. The first is an element of the second, and cannot fail to be an element of the second. And the second cannot fail to have Socrates as its sole element. So Socrates and his singleton stand in a B-internal relation.
Go back to the cup and the coaster. The first is on top of the second. If they were B-internally related, then that very cup could not have existed without that very coaster, and vice versa. In every possible world in which the cup exists, the coaster exists. That strikes me as preposterous. So while I grant that there are B-internal relations, not all relations are B-internal. There are external relations.
In sum, external relations are not founded in the non-relational properties of their relata. A-internal relations are founded in accidental non-relational properties of their relata. B-internal relations are founded in essential non-relational properties of their relata.
My reader asks a question that I will precisify as follows: Is standard first-order predicate logic with identity ontologically committed to external relations? I should think so. The quantifiers range over a domain of existents. If that were not the case, 'Cats exist' could not be replaced salva veritate with 'For some x, x is a cat.' For the particular quantifier to be an existential quantifier, the domain of quantification must be a domain of existents.
So modern predicate logic includes a commitment to ontological pluralism, to a plurality of numerically distinct individual existents. This is a totality of "independent reals" (to borrow a phrase from Josiah Royce). Each of these independent existents has no need of any other one for its existence. In Humean terms, they are "distinct existences," i.e., numerically distinct existents. No doubt they stand in external relations. The cat is on the mat but it has no need of the mat to exist and the mat pays the same compliment to the cat. The relation that connects them is external.
The reader's second question is none too clear. He may be asking this: If all relations are external, does it follow that concrete particulars that stand in such relations are bare particulars? First of all, what is a bare particular?
A bare particular is not a particular without properties. As a matter of metaphysical necessity, everything has properties. What make a bare particular bare is not its lack of properties, but the way it has the properties it has. It has them by exemplifying/instantiating them, where (first-order) exemplification is -- or is modelled on -- an asymmetrical external relation. Thus the bare particular in a red round spot -- to use a typical Bergmannian, 'Iowa,' example -- stands in an external relation to the property of being red and the property of being round in the same spot. A bare particular is not an Aristotelian primary substance; it is not an individual essence or nature. It has properties but they are all accidental properties. It cannot not have properties, but there is no necessity that it have the very properties it has. So, from 'Necessarily, every bare articular has properties' one cannot validly infer 'Every bare particular has the properties it has necessarily.' By contrast, an Aristotelian primary substance (prote ousia) is an individualized essence or nature.
The answer to the second bolded question, I think, is in the affirmative. But to explain this with any rigor would take more time than I presently have to invest.
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
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Armstrong, D. M. 1983. What is a Law of Nature? Cambridge: Cambridge University Press.
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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.
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Armstrong, D. M. 2004b. Truth and Truthmakers. Cambridge: Cambridge University Press.
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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.
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Chisholm, R 1976. Person and Object: A Metaphysical Study. La Salle: Open Court.
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Frege, G. 1976. “Der Gedanke”. In G. Patzig (ed.), Logische Untersuchungen. Goettingen:Vandenhoeck and Ruprecht, 30-53.
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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.
Each of the following three propositions strikes me as very reasonably maintained. But they cannot all be true.
A. Worship Entails Reference: If S worships x, then S refers to x. B. Reference Entails Existence: If S refers to x, then x exists. C. Worship Does Not Entail Existence: It is not the case that if S worships x, then x exists.
It is easy to see that the triad is inconsistent. The conjunction of any two limbs entails the negation of the remaining one. For example, (A) and (B), taken in conjunction, entail the negation of (C).
What makes the triad a very interesting philosophical problem, however, is the fact that each of the constituent propositions issues a very strong claim on our acceptance. I am inclined to say that each is true. But of course they cannot all be true if they are logically inconsistent, which they obviously are.
Why think that each limb is true?
Ad (A): While there is much more to worship than reference, and while reference to a god or God can take place without worship, it is surely the case that whatever one worships one refers to, whether publicly or privately, whether in overt speech or in wordless thought.
Ad (B): Unless we make a move into Meinong's jungle, it would seem that reference is reference to what exists. There are different ways for reference to fail, but one way is if the referent does not exist. Suppose I think Scollay Square still exists. Trying to say something true, I say, 'Scollay Square is in Boston.' Well, I fail to say something true because of the failure of reference of 'Scollay Square.' My sentence is either false or lacks a truth-value. Now if one way for a reference to fail is when the referent does not exist, then reference entails existence.
Here is a second consideration. Philosophers often speak of reference as a word-world relation. Better: it is a relation between a word of phrase thoughtfully deployed by a person and something that exists extralinguistically. But surely if a genuine relation R holds, then each of R's relata exists. In the dyadic case, if x stands in R to y, then both x and y exist. A weaker principle is that of existence-symmetry: if x stands in R to y, then either both relata exist or neither exists. Both principles rule out the situation in which one relatum of the reference relation exists and the other doesn't.
So if reference is a genuine relation, and a person uses a word or phrase to refer to something, then the thing in question, the referent, exists. So again it seems that (B) is true and that reference entails existence. If the referent does not exist, then the reference relation does not hold in this case and there is no reference in this case. No referent, no reference. If reference, then referent.
Ad (C): Some say that the Christian God and the Muslim God are the same. But no one this side of the lunatic asylum says that all gods are the same. So at least one of these gods does not exist. But presumably all gods have been worshipped by someone; ergo, being worshipped does not entail existence.
So how do we solve this aporetic bad boy? We have three very plausible propositions that cannot all be true. So it seems we must reject one of them. But which one?
(A) is above reproach. Surely one cannot worship anything without referring to it. And I should think that (C) is obviously true. The idolater worships a false god, something that does not exist. As Peter Geach points out, the idolater does not worship a hunk of gold, say, but a hunk of gold as God, or God as a hunk of gold. But then he worships something that does not exist and indeed cannot exist. The only hope for solving the triad is by rejecting (B). For (B) does not share in the obviousness of (A) and (C). (B) is very plausible but not as plausible as the other two limbs.
London Ed will presumably endorse (B)-rejection as the solution since he is already on record as saying that one can successfully refer to purely fictional (and thus nonexistent) individuals and that one also be confident that it is numerically the same fictional individual to which different people are referring in different ways. Thus if London Ed brings up in conversation the fictional detective who lives on Baker Street, has an assistant named 'Watson,' etc. , then I know he is referring to Sherlock Holmes. And referring successfully. We are talking about one and the same individual. Successful reference thus seems not to require the existence of the referent.
But notice. If there is successful reference to nonexistent individuals, then it would seem that reference is an intentional state just like worshiping is. Or to put the point in formal mode: it would seem that 'refers' is an intentional verb just like 'worship' is. What one worships may or may not exist without prejudice to one's being in a state of worship. On (B)-rejection, what one refers to may or may not exist without prejudice to one's being in the state of referring.
By the way, it is not words that refer, but people using words. Of course, one can say that 'cat' in English refers to furry, four-legged mammals, but that is elliptical for saying that competent English speakers who are using 'cat' in a standard, non-metaphorical, way refer by the use of this word to furry, four-legged mammals. Linguistic reference is grounded in and parasitic upon thinking reference, intentional reference. And not the other way around. Not everyone agrees, of course. (Chisholm and Sellars famously disagreed about this.) This is yet another bone of contention at the base of the Same God? controversy. And one more reason why it is not easily resolved.
Well, suppose that linguistic reference is like mental reference (intentionality) in this respect: just as the intentio is what it is whether or not the intentum exists, the reference is what it is whether or not the referent exists. This makes sense and it solves the above aporetic triad. We simply reject (B).
Now where does my solution to the above triad leave us with respect to the question, Does the Christian and the Muslim worship the same God? My solution implies that they do not worship the same God. For it implies that reference to an individual or particular is not direct but mediated by properties. Let's consider private, unverbalized worship in the form of discursive prayer. Suppose I pray the Jesus Prayer, or some such prayer as 'Lord, grant me light in my moral and intellectual darkness.' Such prayer is on the discursive plane. It is not a matter of infused contemplation or any state of mystical intuition or mystical union. On the discursive plane I have no knowledge of God by acquaintance, and certainly not by sensory acquaintance. My knowledge, if knowledge it is, is by description. I refer to God mentally via properties as that which satisfies, uniquely, a certain identifying description. Obviously, I cannot have God before my mind as a pure, unpropertied particular; I can have God before my mind only as 'clothed' in certain properties, only as an instantiation of those properties.
Now if the properties in terms of which I prayerfully think of God include the property of being triune, and the properties in terms of which a Muslim thinks of God include the property of not being triune, then no one thing can be our common mental referent. For in reality outside the mind nothing can be both triune and not triune.
If you object that there is a common God but that the Muslim has false beliefs about it, then I say you are either begging the question or assuming a causal theory of reference. It is certainly true that different people can have contradictory beliefs about one and the same thing. But if you say that this is the case with respect to the Muslim and Christian Gods, then you assume that there is one God about whom there are contradictory beliefs -- and that is precisely to beg the question. This is the very mistake that Beckwith and Tuggy and others make.
If, on the other hand, you are assuming a casual theory of reference, then how will you solve my triad above? Besides, you take on board all the problems of the casual theory. The notion that reference can be explained by causation is a very questionable one, about which I will have more to say later.
Here is London Ed's most recent version of his argument in his own words except for one word I added in brackets:
1. There is no such thing as Caesar any more.
2. The predicate 'there is no such thing as -- any more' is satisfied by Caesar.
3. If a relation obtains [between] x and y, then there is such a thing as y.
4. (From 2) the relation 'is satisfied by' obtains between the predicate '-- is not a thing any more' and Caesar.
5. (3, 4) There is such a thing as Caesar.
6. (1, 5) contradiction.
Premiss (1) is Moorean. There is no longer any such thing or person as Caesar. (Or if you dispute that for reason of immortality of Caesar, choose some mortal or perishable object). (2) is a theoretical. (3) is a logical truth, and the rest is also logic. You must choose between (1) and (2), i.e. choose between a Moorean truth, and a dubious theoretical assumption.
(1) is indeed 'Moorean,' i.e., beyond the reach of reasonable controversy. (2) is indeed theoretical inasmuch as it involves an optional albeit plausible parsing in the Fregean manner of the Moorean sentence.
Ed tells us that (3) is a logical truth. I deny that it is. A logical truth is a proposition true in virtue of its logical form alone. 'Every cat is a cat' is an example of a logical truth as are 'No cat is a non-cat' and 'Either Max is a cat or Max is not a cat.' One can test for logical truth by negating the proposition to be tested. If the result is a logical contradiction, then the proposition is a logical truth. For example, if we negate 'Every cat is a cat' we get 'Some cat is not a cat.' The latter sentence is a logical contradiction, so the former sentence is a logical truth. The latter is a logical contradiction because its logical form -- Some F is not an F -- has only false substitution-instances.
Negating (3) yields 'A relation obtains between x and y, but there is no such thing as y.' But this is not a logical contradiction in the strict and narrow sense defined above. Suppose I am thinking about the Boston Common which, unbeknownst to me, ceases to exist while I am thinking about it. I stand in the 'thinking about' relation to the Common during the whole period of my thinking despite the fact that at the end of the period there is no such thing as the Boston Common. There are philosophers who hold that the intentional relation is a genuine relation and not merely relation-like as Brentano thought, and that in some cases it relates an existing thinker to a nonexisting object.
Now there are good reasons to reject this view as false, but surely it is not false as a matter of formal logic. If it is false, it is false as a matter of metaphysics. A philosopher such as Reinhardt Grossmann who holds that the intentional relation is a genuine relation that sometimes relates an existent thinker to a nonexistent object is not contradicting himself.
Since (3) is not a logical truth, one way to solve Ed's problem is by rejecting (3) and holding that there are genuine relations that relate the existent to the nonexistent. One could hold that the relation of satisfaction is such a genuine relation: it relates the existing predicate to the nonexistent emperor: Caesar satisfies the predicate despite his nonexistence.
Note that I am not advocating this solution to the puzzle; I am dismissing Ed's dismissal of this putative solution. I am rejecting Ed's claim that one is forced to choose between (1) and (2). One can avoid the contradiction by denying (3), and one is not barred from doing so by logic alone.
Ed claims that (1) and (5) are logical contradictories. But they are not. Just look carefully at both propositions and you will see. Ed thinks they are contradictories because he assumes that 'There is no such thing as y any more' is logically equivalent to 'There is no such thing as y.' But to make that assumption is to to assume the substantive metaphysical thesis known in the trade as
Presentism: Necessarily, only temporally present concrete objects exist.
Given Presentism, (1) and (5) are indeed contradictory. This is why I said earlier that Ed's argument cannot get off the ground without Presentism. For suppose we reject Presentism in favor of the plausible view that both past and present concreta exist, i.e., are within the range of our unrestricted quantifiers. Then Ed's puzzle dissolves. For then there is such a thing as Caesar, it is just that he is past. The relation of satisfaction connects a present item with a past item both of which exist. Or, since Ed is allergic to 'exist': both of which are such that there such things as them.
So a second way to solves Ed's puzzle is by rejecting the Presentism that he presupposes.
So I count at least three ways of solving Ed's puzzle: reject (2), reject (3), reject the tacit assumption of Presentism which is needed for (1) and (5) to be contradictory.
My inclination is to say that the puzzle is genuine, but insoluble. And this because the putative solutions sire puzzles as bad as the one we started with. Of course, I haven't proven this. But this is what my metaphilosophy tells me must be the case.
The locus classicus of the Euthyphro Dilemma (if you want to call it that) is Stephanus 9-10 in the early Platonic dialog, Euthyphro. This aporetic dialog is about the nature of piety, and Socrates, as usual, is in quest of a definition. Euthyphro proposes three definitions, with each of which Socrates has no trouble finding fault. According to the second, "piety is what all the gods love, and impiety is what all the gods hate." To this Socrates famously responds, "Do the gods love piety because it is pious, or is it pious because they love it?" In clearer terms, do the gods love pious acts because they are pious, or are pious acts pious because the gods love them?
What interests me at the moment is the notion of metaphysical grounding which I want to defend against London Ed and other anti-metaphysical types. (For it is his failure to understand metaphysical grounding that accounts for Ed's failure to appreciate the force of my circularity objection to the thin theory of existence.) Thus I will not try to answer a question beyond my pay grade, namely:
Q. Does God command X because it is morally obligatory, or is X morally obligatory because God commands it?
My concern is with the preliminary question whether (Q) is so much as intelligible. It is intelligible only if we can make sense of the 'because' in it. Let' s start with something that we should all be able to agree on (if we assume the existence of God and the existence of objective moral obligations), namely:
1. Necessarily, God commands X iff X is morally obligatory.
(1) expresses a broadly logical equivalence and equivalence is symmetrical: if p is equivalent to q, then q is equivalent to p. But metaphysical grounding is asymmetrical: if M metaphysically grounds N, then it is not the case that N metaphysically grounds M. For example, if fact F is the truth-maker of sentence s, then it is not the case that s is the truth-maker of F. Truth-making is a type of metaphysical grounding: it is not a causal relation and its is not a logical relation (where a logical relation is one that relates propositions, examples of logical relations being consistency, inconsistency, entailment, and logical independence.)
(1) leaves wide open whether God is the source of the obligatoriness of moral obligations, or whether such obligations are obligatory independently of divine commands. Thus the truth of (1) does not entail an answer to (Q).
The 'because' in (Q) cannot be taken in a causal sense if causation is understood as a relation that connects physical events, states, or changes with other physical events, states, or changes. Nor can the 'because' be taken in a logical sense. Logical relations connect propositions, and a divine command is not a proposition. Nor is the obligatoriness of the content of a command a proposition.
So I say this: if the content of a command is morally obligatory because God issued the command, then the issuing of the command is the metaphysical ground of the the moral obligatoriness of the content of the command. If, on the other hand, the content of the command is morally obligatory independently of the issuing of the divine command, then the moral obligatoriness of the command is the metaphysical ground of the correctness of the divine command.
Either way, there is a relation of metaphysical grounding.
My argument in summary:
1. (Q) is an intelligible question.
2. (Q) is not a question about a causal relation.
3. (Q) is not a question about a logical relation.
4. There is no other ordinary (nonmetaphysical) candidate relation such as a temporal relation or an epistemic relation for (Q) to be about.
5. (Q) is an intelligible question if and only if 'because' in (Q) expresses metaphysical grounding.
Therefore
6. 'Because' in (Q) expresses metaphysical grounding.
Therefore
7. There is a relation of metaphysical grounding.
OK, London Ed, which premise will you reject and why?
Last Thursday, Steven N. and I had a very enjoyable three-hour conversation with ASU philosophy emeritus Ted Guleserian on Tempe's Mill Avenue. We covered a lot of ground, but the most focused part of the discussion concerned the subject matter of this post. If I understood Guleserian correctly, he was questioning whether there is any such problem as the problem of the unity of a fact. I maintained that there is such a problem and that it is distinct from the problem of order.
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The problem of order arises for relational facts and relational propositions in which there is a relation R that is either asymmetrical or nonsymmetrical. If dyadic R is asymmetrical, and x stands in R to y, then it follows that y does not stand in R to x. For example, greater than and taller than are asymmetrical relations. If I am taller than you, then you are not taller than me. If dyadic R is nonsymmetrical, and x stands in R to y, then it does not follow, though it may be the case, that y stands in R to x. For example, loves and hates are nonsymmetrical relations. If I love you, it does not follow that you love me, nor does it follow that you do not love me. But if I weigh the same as you, then you weigh the same as me: 'weigh the same as' picks out a symmetrical relation.
Well, suppose R is either asymmetrical or nonsymmetrical. Then the relational facts Rab and Rba will be distinct. For example, Al's loving Bill, and Bill's loving Al are distinct facts. A fact is a complex. Now the following principle seems well-nigh self-evident:
P. If two complexes, K1 and K2, differ numerically, then there exists a constituent C such that C is an element of K1 but not of K2, or vice versa.
In other words, if two complexes differ, then they differ in a constituent. 'Complex' is intended quite broadly. Mathematical sets are complexes and it is clear that they satisfy the principle. There cannot be two sets that have all the same members. Ditto for mereological sums.
Now if Rab and Rba are distinct, then, by principle (P), they must differ in a constituent. But they seem to have all the same constituents. Both consist of a, b, and R, and if you think there must also be a triadic nexus of exemplification present in the fact, then that item too is common to both. And if you think there is a benign infinite regress of exemplification nexuses in the fact, then those items too are common to both. Since both facts have all the same constituents, what is the ontological ground of the numerical difference of the two facts? What makes them different? The question is not whether they differ; it is obvious that they do. The question concerns the ground of their difference. What explains their difference? Of course, I am not asking for an explanation in terms of empirical causes. Consider {1, 2} and {1, 2, 3}. What is the ontological ground of the difference of these two sets? It would be a poor answer to say that they just differ, that their difference is a factum brutum. The thing to say is that they differ in virtue of one set's having a member the other doesn't have. When I say that 3 makes the difference between the two sets I am obviously not giving a causal explanation. I am specifying a factor in reality that 'makes' the two entities numerically different.
So what, if anything, is the ontological ground of the difference between aRb and bRa when R is either asymmetrical or nonsymmetrical? This, I take it, the problem of order, or, in the jargon of Gustav Bergmann, the problem of providing an 'assay' of order. It may be that no assay is possible. It may be that the difference is a brute difference. But that cannot be assumed at the outset.
It seems to me that the problem of unity is different although related. What is the difference between the fact aRb and the set or sum of its constituents? If a contingently stands in R to b, then it is possible that a, R, and b all exist without forming a relational fact. So what is the difference between aRb and {a, R, b}? Here we have two complexes that share all their constituents, but they are clearly different complexes: one is a fact while the other is not. What is the ground of fact-unity, that peculiar form of unity found in facts but not it other types of complex?
Suppose you deny that they share all constituents. Suppose you maintain that the fact includes a triadic exemplification nexus that is not present in the set. I will then re-formulate the problem as follows. What is the difference between aRb and {a, R, NEX, }?
The problem of order is different from the problem of unity. The latter is the problem of accounting for the peculiar unity of those complexes that attract such properties as truth, falsity, and obtaining. For some of these complexes, no problem of order arises. For example, a monadic fact of the form, a's being F, precisely because it is nonrelational does not give rise to any problem of order. Since the problem of unity can arise in cases where the problem of order does not arise, the two problems are distinct.
The unity problem is the more fundamental of the two. The question as to the ground of the difference of a fact and the mere collection of its consituents is more fundamental than the question as to the ground of the difference between two already constituted facts which appear to share all their constituents.
What is (linguistic) reference? Is it a relation? Edward the Ockhamist assumes that it is and issues the following request: "To clarify, could I ask both you and Bill whether you think the reference relation is ‘internal’ or ‘external’?"
Here is an inconsistent tetrad:
1. 'Frodo' refers to Frodo 2. 'Frodo' exists while Frodo does not. 3. Reference is a relation. 4. Relations are existence-symmetrical: the terms (relata) of a relation are such that either all exist or none exist.
Since the members of this quartet cannot all be true, which one will Edward reject? Given what he has said already, he must reject (4). But (4) is exceedingly plausible, more plausible by my lights than (1). I myself would reject (1) by maintaining that there is no linguistic reference to the nonexistent. It is not there to be referred to!
For me, reference is a relation. Is it internal or external? Being the same color as is an example of an internal relation. If a and b are both red, then that logically suffices for a and b to stand in the same color as relation. Suppose I paint ball a red and then paint ball b (the same shade of) red; I don't have to do anything else to bring them into the aforementioned relation. You could say that an internal relation supervenes upon the intrinsic properties of its relata.
But to bring the two balls into the relation of being two feet from each other, I will most likely have to do more than alter their intrinsic properties. So being two feet from is an external relation. If the balls fall out of that relation they needn't change in any intrinsic respect. But if the balls cease to stand in the same color as relation, then they must alter in some intrinsic respect.
In sum, internal relations supervene on the intrinsic properties of their relata while external relations do not.
Suppose 'Max' is the name of my cat. Then 'Max' as I use it has a definite meaning. The sound I make when I say 'Max' and the cat are both physical items. Surely they do not stand in a semantic relation. No physical item by itself means anything. So the semantic relation must connect a meaningful word (a physical item such as a sound or marks on paper 'animated' by a meaning) with the physical referent, the cat in our example. Suppose the meaning (sense, connotation) of 'Max' is given by a definite description: the only black male feline that enjoys linguine in clam sauce. Then the relation between the meaningful word 'Max' and the cat will be external since that meaning (sense, connotation) is what it is whether or not the cat exists.
If, on the other hand, the meaning of 'Max' = Max, then the semantic relation of reference is internal. For then the relation is identity, and identity is an internal relation.
So it seems that whether reference is external or internal depends on whether reference is routed through sense or is direct. I incline toward the view that reference, since routed through sense, is an external relation.
There are philosophers who think that 'Cambridge' changes and real changes are mutually exclusive. Thus they think that if a change is Cambridge, then it is not real. This is a mistake. Real changes are a proper subset of Cambridge changes.
Consider an example. Hillary gets wind of some tomcat behavior on the part of Bill and goes from a state of equanimity to that lamp-throwing fury the Bard spoke about. ("Hell hath no fury like a woman scorned!"). Bill, on the other hand, as the object of Hillary's fury, also changes: at one time he has the property of being well thought of by Hillary, and the contradictory property at a later time. Common to both the real change (in Hillary) and the relational change (in Bill) is the following: x changes if and only if there are distinct times, t1 and t2, and a property P such that x exemplifies P at t1 and ~P at t2, or vice versa. Change thus defined is Cambridge change. The terminology is from Peter Geach:
The great Cambridge philosophical works published in the early years of this [the 20th] century, like Russell's Principles of Mathematics and McTaggart's Nature of Existence, explained change as simply a matter of contradictory attributes' holding good of individuals at different times. Clearly any change logically implies a 'Cambridge' change, but the converse is surely not true. . . . (Logic Matters, University of California Press, 1980, p. 321.)
In sum, every (alterational) change is a Cambridge change, but only some of the latter are real changes. The rest are mere Cambridge changes. It is therefore a mistake to think that Cambridge and real changes form mutually exclusive classes. What one could correctly say, however, is that mere Cambridge changes and real changes form mutually exclusive classes.
But what about existential (as opposed to alterational) change, as when a thing comes into existence, or passes out of existence? Are such changes real changes in the things that pass in and out of existence? Are they merely Cambridge changes? Or neither?
It is plausibly maintained that all relations are existence-entailing. To illustrate from the dyadic case: if R relates a and b, then both a and b exist. A relation cannot hold unless the things between which or among which it holds all exist. A weaker, and hence even more plausible, claim is that all relations are existence-symmetric: if R relates a and b, then either both relata exist or both do not exist. Both the stronger and the weaker claims rule out the possibility of a relation that relates an existent and a nonexistent. (So if Cerberus is eating my cat, then Cerberus exists. And if I am thinking about Cerberus, then, given that Cerberus does not exist, my thinking does not relate me to Cerberus. This implies that intentionality is not a relation, though it is, as Brentano says, relation-like (ein Relativliches).)
But if presentism is true, and only temporally present items exist, then no relation connects a present with a nonpresent item. This seems hard to accept for the following reason.
I ate lunch an hour ago. So the event of my eating (E) is earlier than the event of my typing (T). How can it be true that E bears the earlier than relation to T, and T bears the later than relation to E, unless both E and T exist? But E is nonpresent. If presentism is true, then E does not exist. And if E does not exist, then E does not stand in the earlier than relation to T. If, on the other hand, there are events that exist but are nonpresent, then presentism is false.
How will the presentist respond? Since E does not exist on his view, while T does, and E is earlier than T, he must either (A) deny that all relations are existence-symmetric, or deny (B) that earlier than is a relation. He must either allow the possibility of genuine relations that connect nonexistents and existents, or deny that T stands in a temporal relation to E.
To fully savor the problem we cast it in the mold of an aporetic tetrad:
1. All relations are either existence-entailing or existence-symmetric.
2. Earlier than is a relation.
3. Presentism: only temporally present items exist.
4. Some events are earlier than others.
Each limb of the tetrad is exceedingly plausible. But they cannot all be true: any three, taken together, entail the negation of the remaining limb. For example, the first three entail the negation of the fourth. To solve the problem, we must reject one of the limbs. Now (4) cannot be rejected because it is a datum.
Will you deny (1) and say that there are relations that are neither existence-entailing nor existence-symmetric? I find this hard to swallow because of the following argument. (a) Nothing can have properties unless it exists. Therefore (b) nothing can have relational properties unless it exists. (c) Every relation gives rise to relational properties: if Rab, then a has the property of standing in R to b, and b has the property of standing in R to a. Therefore, (d) if R relates a and b, then both a and b exist.
Will you deny (2) and say that earlier than is not a relation? What else could it be?
Will you deny presentism and say that that both present and nonpresent items exist? Since it is obvious that present and nonpresent items cannot exist in the present-tense sense of 'exists,' the suggestion has to be that present and nonpresent (past or future) items exist in a tenseless sense of 'exist.' But what exactly does this mean?
The problem is genuine, but there appears to be no good solution, no solution that does not involve its own difficulties.
What is (linguistic) reference? Is it a relation? Edward the Ockhamist assumes that it is and issues the following request: "To clarify, could I ask both you and Bill whether you think the reference relation is ‘internal’ or ‘external’?"
Here is an inconsistent tetrad:
1. 'Frodo' refers to Frodo
2. 'Frodo' exists while Frodo does not.
3. Reference is a relation.
4. Relations are existence-symmetrical: the terms (relata) of a relation are such that either all exist or none exist.
Since the members of this quartet cannot all be true, which one will Edward reject? Given what he has said already, he must reject (4). But (4) is exceedingly plausible, more plausible by my lights than (1). I myself would reject (1) by maintaining that there is no linguistic reference to the nonexistent. It is not there to be referred to!
For me, reference is a relation. Is it internal or external? Being the same color as is an example of an internal relation. If a and b are both red, then that logically suffices for a and b to stand in the same color as relation. Suppose I paint ball a red and then paint ball b (the same shade of) red; I don't have to do anything else to bring them into the aforementioned relation. You could say that an internal relation supervenes upon the intrinsic properties of its relata.
But to bring the two balls into the relation of being two feet from each other, I will most likely have to do more than alter their intrinsic properties. So being two feet from is an external relation. If the balls fall out of that relation they needn't change in any intrinsic respect. But if the balls cease to stand in the same color as relation, then they must alter in some intrinsic respect.
In sum, internal relations supervene on the intrinsic properties of their relata while external relations do not.
Suppose 'Max' is the name of my cat. Then 'Max' as I use it has a definite meaning. The sound I make when I say 'Max' and the cat are both physical items. Surely they do not stand in a semantic relation. No physical item by itself means anything. So the semantic relation must connect a meaningful word (a physical item such as a sound or marks on paper 'animated' by a meaning) with the physical referent, the cat in our example. Suppose the meaning (sense, connotation) of 'Max' is given by a definite description: the only black male feline that enjoys linguine in clam sauce. Then the relation between the meaningful word 'Max' and the cat will be external since that meaning (sense, connotation) is what it is whether or not the cat exists.
If, on the other hand, the meaning of 'Max' = Max, then the semantic relation of reference is internal. For then the relation is identity, and identity is an internal relation.
So it seems that whether reference is external or internal depends on whether reference is routed through sense or is direct. I incline toward the view that reference, since routed through sense, is an external relation.