Naturalness vs. "Arbitrariness" and "Simplicity" in Mereology

There are three answers one can give to the question: "When does composition occur?"

(1) Always.
(2) Sometimes.
(3) Never.

The first view is something like David Lewis's view: Any plurality of objects composes a third. Hence, for example, there is an object consisting of Barack Obama, my left leg, an orange, and half of the beach in Santa Monica. (We could call it the BLOB.) This is the view encompassed in classical mereology.

The third view is something like Peter Van Inwagen's view in 'Material Beings'. This view holds that (with maybe a few very specific exceptions), there are not, literally, any composite objects. There are just "simples" -- atoms in the void, physically proximate to each other and arranged in various ways.

The second view encompasses all other possibilities. One of these possibilities is "common sense" ontology, or something like it. One such view might hold that things like physical organisms, tables and chairs, rocks, planets, stars, maybe even galaxies, etc. are composite objects. But not just any plurality of things constitutes an object on this view; for instance, there is definitely no object such as the BLOB.

One argument (I think due to Van Inwagen) says that (2) can be ruled out rather easily because it is arbitrary and/or overly complicated. Hence, we must choose between (1) and (3).

However, it seems to me that people who hold to (2) might argue that their ontology only encompasses what is natural; just as there is a distinction between natural properties (like 'having mass') and gerrymandered properties (like 'being Barack Obama-or-my leg-or-an orange-or-half of Santa Monica Beach'), there may well be a distinction between natural composites and gerrymandered composites. And just as one might choose to privilege the natural properties by saying they are the only ones that exist (as D.M. Armstrong does), so one might choose to privilege the natural composites by saying they are the only ones that exist.

Obviously more needs to be said than this and this view would need to be fleshed out. But I'm more interested in the methodological question, and all I need granted is that it is a distinction one could coherently use so as to avoid (1) or (3).

Now, people like Van Inwagen might (probably, would) respond to this view by claiming that it is arbitrary, that it multiplies distinctions, that the notion of "naturalness" is mysterious and vague, and so on.

But I think it is worth noting here an "arbitrariness" in this objection: Claiming that some entity is more natural than another (or, by extension, that one's theory is more natural) is no more mysterious than claims that that (2) is arbitrary and complex, and that (1) and (3) are non-arbitrary and more simple. Defining the sense in which (1) and (3) are "non-arbitrary" and "simpler" is no easier than defining the sense in which (2) is "more natural."

Frankly, simplicity and arbitrariness, as used in this way, seem to me to be just as bad off as the other notions that anti-hyper-intensionalists use as criteria of theory choice; they are themselves hyperintensional notions in fact. That's not to say that they are bad off -- I do think there is an intuitive sense in which theories can be "simpler" and "less arbitrary" than other theories. But it is arbitrary to use "arbitrariness" and "simplicity" as criteria for selecting between metaphysical theories, and then pretend you don't know what it means when one says that his theory is more "natural" than others or, relatedly, posits entities that are "more natural."

Modernizing (and Medievalizing) Analyticity

A project I've been hoping to do eventually is to re-work the concept-containment notion of analyticity. Something has always seemed to me intuitive about it, at least in the "Bachelors are unmarried" sorts of cases. (From the 19th century onward, for various reasons, the analytic truths seem to have become equated with the logical truths; this seems wrong to me.)

I'd also like to see whether the notion of analyticity comes up at all in medieval philosophy, and whether any of the tools of medieval philosophy could be of use for this project (or, what would be just as interesting, whether they would find the concept-containment notion of analyticity hopelessly confused).

There are several problems for the concept-containment approach, but a big one is this:

1. Forms of Analytic Judgments: Kant (sometimes) defined analyticity in terms of conceptual containment, roughly as: A judgment of the form 'A are B' is analytic iff the concept B is contained in the concept A.

The worry is that there are many judgments that do not seem to have this form, but where they seem to also be true in virtue of 'meaning' or 'concepts' (or something close). Some examples, taken from SEP:

(11) If Bob is married to Sue, then Sue is married to Bob.
(12) Anyone who's an ancestor of an ancestor of Bob is an ancestor of Bob.
(13) If x is bigger than y, and y is bigger than z, then x is bigger than z.
(14) If something is red, then it's colored.

Other examples, from Jerrold Katz:

(15) Mary walks with those with whom she herself walks.
(16) Mary walks with those with whom she herself strolls.
(17) Poor people have less money than rich people.
(18) Rich people have more money than poor people.

It's not totally clear how all of these examples can be analytic (assuming they all are) if we take analytic truth to mean that the predicate-concept is contained in the subject-concept.

I don't have a worked-out answer to this yet, but I suspect that some of the work in cognitive linguistics might be helpful. In fact, Katz' own work might be helpful here, though from what I understand Katz is a Platonist (rather than a "conceptualist") about meaning, and so it would have to be properly adapted.

In addition to these strategies, where medieval philosophy might be useful here is in seeing how we might, in fact, be able to reformulate all "basic" sentences and then parse them out so that they technically obey the constraint of "subject-copula-predicate" form.

As Terence Parsons points out, medieval scholastic Latin is unique in that it is a natural language and yet there is no distinction between a sentence's ordinary surface grammar and its logical form.

Now, if one had a close enough association between words and mental concepts, one might then be able to get a nice conceptualist-type semantics going. And it seems certain medieval thinkers did have precisely this sort of close association between mental concepts and meaning, viz., in the theory of "subordination" (I'm thinking of Buridan and Ockham right now).

This suggests that we could translate basic ordinary-language sentences into medieval subject-copula-predicate sentences, and the concept-containment idea could become more useful again.

I'm not sure it will be as simple as that or that this will solve everything, but I suspect it will make things easier.

There are some other issues for a conceptual containment theory of analyticity too:

2. Conceptual Containment: There are really at least two problems here: (a) a theory of concepts, and (b) a notion of containment. Can we give a plausible and clear theory of both? (And, what would be even better: Can we give a theory of both that is mathematizable and subject to rigor and computation once we are given a case?) And how neutral can we be here with respect to different theories of concepts and containment?

How can medieval philosophy help here? Medieval philosophy certainly contains much discussion of concepts, and that should certainly be useful.

As for the notion of containment, I can't help but think of Scotus' theory of "repugnance" and "non-repugnance" by which he assesses the modal status of basic propositions -- the kinds of propositions concept-containment seems to be after (see page 162, here). What's interesting is that Scotus seems to define repugnance as a relation holding between terms. That seems to make it a semantic relation rather than a conceptual relation for Scotus; moreover, the relation's holding is said to be grounded in "notae," which are in some sense objective features of the external world.

So this isn't exactly concept-containment analyticity; but still, in terms of its formal/logical properties, non-repugnance/repugnance behaves similarly to concept-containment/exclusion. (This seems to be an instance of a more "externalist," metaphysical picture of containment and exclusion relations; I get the sense that this sort of externalism is the norm in medieval philosophy, especially pre-Nominalism, though even after that as well.) Moreover, like repugnance-relations, concept-containment relations are supposed to ground the modal status of propositions, and moreover, they both seem to deal with the same sorts of propositions. So I can't help but think Scotus will be helpful here, even if he probably wouldn't have a view of analyticity like Kant's.

3. Rigor: How would a rigorous conceptual semantics go? Can we make it as formal, precise and mathematical as the non-conceptualist semantics have been? Some work has already been done on this sort of thing, but there's more to be said. Again, I wonder if the medieval logic might help us here, since Parsons and others have shown it to be entirely rigorous and fit for mathematical treatment. Medieval logic at its height was generally far more sophisticated than anything after it -- certainly more sophisticated than anything Kant did on logic -- and so I can only imagine it will make this project easier.

4. Externalism: Although the conceptual-containment approach seem plausible in certain cases, so does semantic externalism. Gillian Russell, a professor here at UNC, has done some brilliant work on updating analyticity to take these post-Kripkean insights into account. However, she tends toward the more externalist side of things, and I'd like to see whether we can salvage more of the connections between meaning, analyticity and concepts than she does, while still giving a reasonable account of the externalist insights (something I worry cognitive semantics a la Peter Gardenfors hasn't quite done -- see 4.1 here, for instance).

One thing I worry about in trying to find analyticity in medieval philosophy is that medieval philosophy seems to tend much more toward externalism about semantic content (though this is only a hunch I get -- I can't point to anything specific). But maybe I'm wrong and there is room for analyticity in medieval philosophy; and even if not, the project may still be worthwhile, since maybe we will find new reasons to either abandon or revise our conception of analyticity in interesting ways we've never thought of.

So I plan to do some research on medieval logic and semantics in the next few weeks, and maybe this will help my concept-containment project. Moreover, I think it is an interesting historical project in its own right to see whether something like analyticity can be found (or reformulated) in terms of medieval semantic categories.

Russell on Existence in TPLA III: The Argument from Transferability

In the last post we explained what Russell's views on existence are and how they entail a "higher-order" theory of existence according to which existence is not a feature of individuals but of some "higher-order" things, viz. propositional functions. Since this is, initially, a very counter-intuitive proposal ("Socrates exists" is meaningless on Russell's view!), Russell ought to have some arguments to defend his view. This is going to be a long series of posts, so we'll discuss several of Russell's arguments from The Philosophy of Logical Atomism, but in the next two posts we'll discuss one of his arguments in particular: What I will call the "Transferability Argument." But before that I'll briefly mention Russell's motivation for having a theory of existence like his in the first place.

In the first place, the whole notion of existence comes up in connection with what we might call “negative existential” statements. A negative existential statement is a statement saying that something does not exist: For instance, that Socrates does not exist, or that dogs do not exist. These present an initial puzzle. On the one hand, if they are true, then it seems “Socrates” and “dogs” do not refer to anything, and so it’s not clear what could make the sentences true. On the other hand, they seem to be saying that something, “Socrates” or “dogs,” has the feature of “not existing.”

Now, this doesn’t immediately support Russell’s view on existence, but it does give one impetus to develop some sort of view that would address the question of negative existentials. It is interesting to see how Russell’s view deals with the problem. In the first place, ‘Socrates does not exist’ is simply meaningless according to Russell, since it doesn’t make sense to attribute existence to an individual, and so neither does it make sense to deny existence of an individual. On the other hand, since existence is a property of propositional functions, “dogs do not exist,” is easy to deal with: it is the same as saying ‘x is a dog’ is impossible. This involves no shady references to non-existent dogs or anything of that sort. One need only say that ‘x is a dog’ is never true.

With that said, it is not enough to point out that Russell’s view gives an answer to this question. Russell’s view is still prima facie implausible, and there might also be other positions available. Hence, Russell needs to give some direct arguments specifically for his view and arguments against alternatives. We will discuss just one of the arguments that Russell gives, which I call “the Transferability Argument.” The argument is quite subtle in fact, and it is rather complicated. But I think it is worth thinking through because it incorporates several interesting assumptions from logic and the philosophy of language.

Before delving into it, I want to define what we will call a ‘transferable predicate’. Russell does not use this terminology himself, but he uses the concept, and his argument is easier to state with this terminology. Now, a predicate F is transferable in my sense just in case (i) F can  be meaningfully applied to some kind G, and (ii) for any kind G that F applies to, ‘G’s are F’ is true only if every individual x that is a G is also F. For instance, the predicate ‘green’ is transferable: It applies to a generic kind term like ‘men’, since we can say ‘men are green’, and ‘men are green’ is true only if each man is himself green. The predicate ‘green’ “transfers” to the individual men. The predicate ‘numerous’ on the other hand is non-transferable: While we can say ‘men are numerous’, it does not imply any particular man is himself numerous. Indeed, this last statement is meaningless.

With that said, Russell’s Argument from Transferability can be reconstructed as follows:

• (1’) ‘Unicorns exist’ is false, but meaningful. [Premise]
• (2’) If there is an individual sense of ‘exists’, then ‘exists’ is transferable. [Premise]
• (3’) If ‘exists’ is transferable, then ‘Unicorns exist’ implies ‘a exists’, for some proper name ‘a’ of some particular unicorn. [Premise]
• (4’) So, if there is an individual sense of ‘exists’, then ‘Unicorns exist’ implies ‘a exists’, for some proper name ‘a’ of some particular unicorn. [By 2’ and 3’]
• (5’) If ‘a’ is a proper name then ‘a is F’ is meaningful only if ‘a’ refers. [Premise]
• (6’) So ‘a exists’ is meaningful only if ‘a’ refers. [5’, Universal Instantiation]
• (7’) Suppose there is an individual sense of ‘exists’. [Supposition for Reductio]
• (8’) Then ‘Unicorns exist’ implies ‘a exists’ for some proper name ‘a’ of some particular unicorn. [By 4’ and 7’]
• (9’) If ‘unicorns exist’ is false, then ‘a’ does not refer. [Premise]
• (10’) So ‘a’ does not refer. [By 1’ and 9’]
• (11’) So ‘a exists’ is meaningless. [By 10’ and 6’]
• (12’) No meaningful statement can imply a meaningless statement. [Premise]
• (13’) So, ‘unicorns exist’ is meaningless. [By 8’, 11’, and 12’]

But this contradicts our assumption in (1’). Hence, we must reject our assumption in 7’:

• (14’) There is no individual sense of ‘exists’. [By 7’ – 13’ and Reductio ad Absurdum]

This is an extremely interesting and rich argument. It is the best reconstruction I can give of Russell’s argument. The argument is clearly valid. It has a total of six premises: 1’, 2’, 3’ 5’, 9’, and 12’. I think it is useful to isolate the premises so that we can see precisely the principles at work here:

• (1’) ‘Unicorns exist’ is false, but meaningful.
• (2’) If there is an individual sense of ‘exists’, then ‘exists’ is transferable.
• (3’) If ‘exists’ is transferable, then ‘Unicorns exist’ implies ‘a exists’, for some proper name ‘a’ of some particular unicorn.
• (5’) If ‘a’ is a proper name then ‘a is F’ is meaningful only if ‘a’ refers.
• (9’) If ‘unicorns exist’ is false, then ‘a’ does not refer.
• (12’) No meaningful statement can imply a meaningless statement.

The first premise is uncontroversial I assume. The third premise seems to follow from the definition of ‘transferable’.  12’ also seems straightforward: If, by hypothesis, p is meaningful, then it does not imply anything meaningless, and this is just what 12’ says. That leaves 2’, 5’, and 9’ as the crucial premises.

I take it that the motivation behind 2’ is that if ‘existence’ is just another predicate of individuals, like ‘green’, say, then it should be transferable in precisely the way they are. After all, how could it be that ‘frogs are green’ is true but that ‘green’ does not transfer to all of the individual frogs? But if ‘exists’ is just like ‘green’ then it should behave in the same way.

5’ seems to be motivated by the fact that we are supposing ‘a’ to be a proper name in Russell’s sense. Recall that, according to Russell, a logically proper name is a word whose meaning just is a particular object; in other words, the proper name ‘a’ is meaningful only if, and because, ‘a’ refers. So if ‘a’ is meaningless, then the whole sentence ‘a is F’ will be meaningless too.

Finally, 9’ is motivated by the fact that if ‘unicorns exist’ is false then there simply aren’t any unicorns for ‘a’ to refer to, and so ‘a’ cannot have a reference.

On the face of it, there is some reasonableness about all of these premises. However, I think there are worries for all of them. In the next post I will try to raise some of those worries.

Geach on Good and Evil: Some Counterexamples?

In Peter Geach’s paper “Good and Evil” Geach draws a distinction between attributive adjectives and predicative adjectives. An adjective A, as in the phrase “is an A B,” is predicative just in case the phrase can be broken down into “is a B” and “is A.” Otherwise A is attributive. For instance, “This is a sweet pastry” can be broken down into “This is a pastry” and “This is sweet.” So “sweet” is a predicative adjective. On the other hand “This is a small elephant” cannot be broken down into “This is an elephant” and “This is small,” so “small” is an attributive adjective.

Geach wants to argue for the thesis that “’good’ and ‘bad’ are always attributive, not predicative, adjectives.” I would like to bring up three intelligible, legitimate uses of the word “good” that are not obviously attributive, and suggest that they may provide counter-examples to Geach’s thesis. The first is what I will call “comparative goodness.” The second is what I will call “relative goodness.” The third is what I will call “global goodness.”

In the first case, consider the claim that it is better to be a Socrates dissatisfied than a pig satisfied. Or consider the claim that God is the greatest conceivable being and its apparent implication that it is even better than being a dissatisfied Socrates to be God. Both of these claims seem, on the face of it, intelligible. They may be open to dispute, but if they are open to dispute then that presupposes they are intelligible.

Now, ‘better’ and ‘greater’ are not, by themselves, the same word as ‘good’. But these claims presuppose that there is some scale of being according to which a satisfied pig is somewhere below dissatisfied Socrates, dissatisfied Socrates is presumably below satisfied Socrates, and satisfied Socrates is somewhere below God. Now, if we suppose, just for argument’s sake, that the satisfied pig is at the very bottom of the spectrum, and that God is at the very top, it seems intelligible to say that being satisfied Socrates – this being somewhere in the middle – is good. This is what I have called the “comparative sense” of goodness. But in this sentence, “Being satisfied Socrates is good,” there is not even another adjective for “good” to modify. Hence, this appears to be a case where “good” is used in a predicative sense.

The second case, which I have called “relative goodness,” is the type of goodness we have when something is good for something else. It is what we express by saying “X is good for Y.” For example, “This spaghetti is good for me,” or “my dog Paco is good for me.” It is interesting to note that both of these sentences might be true even if this spaghetti is neither good food nor good spaghetti and even if Paco is not a good dog. This spaghetti might be terribly undercooked. It might be incredibly cheap. But the relief it gives me may be enough to make it good for me. And Paco may be a crooked, maimed, and disobedient beast – hardly a good dog – but the licking he gives me at the end of the day makes him good for me still.

So things that are good in this sense can’t be likened to cases where I eat spaghetti and say “Oh, this is good!” In that case the adjective that “good” is supposed to modify is implicit (e.g., “Oh, this is good [spaghetti]!”). Whereas here it is not clear at all what the implicitly modified adjective would be; nor would it be clear what the meaning of such a construction might be (what does it mean to say “This spaghetti is good [spaghetti] for me”?); and as we’ve just shown, it is false that, in general, the F that is good for me is a good F (the spaghetti that is good for me need not be good spaghetti). So it doesn’t seem that “good” modifies any adjective in this case; so relative goodness seems predicative.

The third case is what I call “global goodness.” This is the type of goodness we attribute to whole facts or propositions. For instance: “It is good that God created the universe,” or “It is bad that animals suffer needlessly in factory farms.” Of course, these constructions could be turned into subject-predicate form too (that-p is good), in which case it will be clear that global goodness is prima facie predicative. Note that these are not just roundabout ways of saying “It is morally bad;” for even if nobody were responsible for the suffering of beasts – say, if they were harmed by some natural disaster – it would still be bad that they suffered (an objective tragedy, if you will).

But in these cases, it is not clear what the implicit adjective would be that “good” is supposed to modify. Should we say that-p is a bad proposition? This doesn’t seem to make much sense. Or that it is a bad state of affairs? This doesn’t seem to make much sense either: It’s not clear what counts as a good state of affairs or a bad one. States of affairs just are what they are. (If a state of affairs consists of an object having a property, as some philosophers say, then is a good state of affairs one where the object really has the property? Or maybe it must have the property well?). Besides, even if one did not believe there were states of affairs at all (an open question in metaphysics), one could still affirm that it is bad that animals needlessly suffer. This isn’t the case with genuinely attributive uses of “good,” since one cannot consistently believe “he is a good robber” and at the same time believe there are no robbers. Hence, this cannot be an attributive use of goodness. So this sense of “goodness,” global goodness, seems to be predicative: We can say, in a seemingly intelligible manner, “It is good that-p” or “that-p is good,” good simpliciter.

Russell on Existence in TPLA II: Russell's Second-Order View of Existence

In my last post I introduced the topic of Russell on existence. Now I'll deliver. Let’s see what Russell thinks.

First, it is helpful to understand some of Russell’s technical vocabulary. In particular, for our purposes, we should consider his notion of a name, of a definite description, of a proposition, and of a propositional function.

For Russell, a logically proper name (or, for short, just a name) is a word whose meaning is a particular, i.e., an individual object or entity. For instance, intuitively, the name “Socrates” directly denotes the particular object, Socrates. Or the name “Paco” directly denotes my Chihuahua, Paco. Now, this is simplifying a little bit, since Russell has a whole theory of what a particular is and which words actually are proper names, but this isn’t really essential to his account of existence. One could hold to views about existence that are basically the same as Russell’s even if one modified his account of particulars and the extent of the proper names.

What is important, however, is that proper names be contrasted with definite descriptions. A definite description is some phrase that is meant to describe a particular, unique individual. For instance “the Chihuahua that I have had since 6th grade” is a definite description. (As it turns out, it does successfully denote something: my dog Paco.) “The dragon flying above my head” is a definite description too, though to my knowledge it is one that does not refer to anything.

Note: Names are not definite descriptions and definite descriptions are not names. The meaning of a name is just the object it refers to; the meaning of a definite description includes all of the predicates mentioned in the description (for instance, in the last example, "dragon," "flying", and "above my head" are all part of the meaning of the description).

It is important to bring up this contrast between definite descriptions and proper names because Russell gives a separate account of existence statements for each. What we are interested in when talking about “individual existence” statements is existence statements whose subject term is a proper name. This is the type of existence statement Russell will say is meaningless.

A proposition for Russell is, in essence, something that can be asserted, or something that can be true or false. For instance, that it is raining is a proposition, or that Paco is black is a proposition. Once again, this is simplifying a bit, but the particular details of Russell’s views on propositions are not essential here.

Finally, there is the notion of a propositional function. Russell says that a propositional function is “any expression containing an undetermined constituent, or several undetermined constituents, and becoming a proposition as soon as the undetermined constituents are determined.” Examples include ‘x is a man’ or ‘n is a number’ or ‘(x+y)(x-y)=x2-y2’. So, if we were to “fill in the blanks” so to speak we would have a full proposition. For instance, replacing ‘x’ with ‘Paco’ gives the proposition that Paco is a man. Replacing 'n' with '2' gives the proposition that 2 is a number.

Russell's propositional functions can be necessary, possible, or impossible. Russell defines this as follows. A propositional function is:

• Necessary, when it is always true;
• Possible, when it is sometimes true;
• Impossible, when it is never true.

Russell technically says that we have to take at least one of these locutions – “always true,” “sometimes true,” etc. – as undefined. But intuitively, “always true” means that every instance of the propositional function is true. For example, ‘x is x’ is a propositional function that is “necessary’ in Russell’s sense, since it is “always true,” whereas ‘x is a man’ is a propositional function that is possible but not necessary. These locutions are clearly not meant in a temporal sense.

(Interesting side-note: Obviously Russell's definition of "possible" and the like is not at all the definition we would immediately think of when we hear these words. What's interesting is that it's not clear whether he even meant to capture what we do with possible worlds semantics. He makes it explicit that he thinks previous thinking about modality is confused and problematic in some way, but it's not clear whether his discussion of modality is trying to capture some sort of traditional modal phenomenon as opposed to just making stipulations, nor whether his attitude toward traditional notions of modality is one of revision or rejection. Another interesting question: Is there any way to modernize Russell here? Is he on to anything at all? Anyway, enough of this digression...)

That brings us finally to Russell’s theory of existence. Russell’s official view is that “existence is a predicate of a propositional function.” In particular, if F is a type or kind of entity, then to say that F’s exist is just a shorthand way of saying that the propositional function ‘x is F’ is possible:

• (EXIST): F’s exist iff ‘x is F’ is possible (in Russell’s sense above).

For instance, dogs exist iff ‘x is a dog’ is possible. Or men exist iff ‘x is a man’ is possible.

This makes Russell's view a "second-order" or "second-level" view of existence. If we think of individual objects or entities as the "first level" and we think of things that apply to individuals -- propositional functions -- as the second level, then existence is a property of things at the second level, since it is a property of propositional functions. Hence Russell's view has been variously described as a "second-order", "higher-order", or "higher-level" view of existence.

So, according to Russell, “It is of propositional functions that you can assert or deny existence.” On the other hand, to say of a particular thing in the world that it is exists or not is “strictly nonsense.” After all, it doesn’t make sense to say of a particular object a that it is “possible” or “sometimes true.” Hence, individual existence statements are meaningless.

This is of course rather shocking on the face of it. We seem to make true individual existence claims all the time. But on Russell’s view, “John exists” isn’t simply false. It isn’t even a loose way of speaking. It’s simply nonsense. Moreover, the seemingly indubitable inference from “I think” to “I exist” is not invalid on this view; it isn’t even an argument, since arguments have to have propositions as their conclusions, and “I exist” isn’t even a comprehensible thought. What one might have thought incorrigible turns out to be unintelligible.

Nonetheless, as repugnant to common sense as this might seem at first, common sense is not infallible. And to be fair, we have only laid out Russell’s views and have not presented his arguments for them. In the next post I'll consider some of the reasons why, exactly, Russell might have come to this conclusion.

[Part III is here!]

Russell on Existence in TPLA I: Why Care?

In the next few posts I'm going to talk about Bertrand Russell's views on existence as one finds them in his The Philosophy of Logical Atomism (TPLA for short). (Note: I have already written the posts, so I will actually deliver!)

In TPLA Bertrand Russell offers a brief but intriguing account of the notion of existence. Russell holds forcefully to the view that existence cannot be said to apply to individual objects – at least, not without descending into nonsense. According to Russell we cannot meaningfully say this or that particular thing exists; instead, only types or kinds of things can be said to exist.

I will first try to make clear what, exactly, Russell’s views on the matter of existence are, at least insofar as he talks about it in TPLA, and I will clarify his technical terminology along the way. I will then attempt to lay out what are, so far as I can tell, Russell’s arguments for his views, as well as some of the problems concerning existence that motivate him to have a view in the first place. After questioning the soundness of Russell’s arguments I will lay out an alternative view that deals with some of the problems of existence he has identified. This alternative view of existence is more similar to that held by the majority of people before him, including the medieval Scholastics. Ironically, it turns out that this view is actually similar to some of what Russell says about propositions and propositional functions (as well as his own earlier view before TPLA).

Before I begin, however, I’d like to explain why I think it is worthwhile to think about Russell’s views on existence and to bother to critique them. After all, Russell gave the Lectures for TPLA nearly a hundred years ago, and hardly anyone would agree with the precise details of his account of existence (let alone his general metaphysic).

It is probably true that Russell’s precise views are not generally accepted, and arguably parts of his technical “machinery” are archaic. Nevertheless, Russell’s spirit lives on. Russell’s claim that existence is not a predicate of individuals and that existence should ultimately be defined in a “higher-order” way, in terms of quantification, has been widely accepted by many prominent philosophers.  Indeed, the slogan that “existence is what is expressed by ‘existential quantification’” is standard orthodoxy nowadays. (See, for instance, Frege’s  Foundations of Arithmetic sec. 53, Quine’s “On What There Is,” C.J.F. Williams’ What is Existence?, and Peter van Inwagen’s “Being, Existence and Ontological Commitment,” just for a few examples.)

So, aside from the fact that Russell was a great thinker, and the general guideline that it is worthwhile to interact with great thinkers, we should think about his views on existence because views like his are held in one form or another even today.

[Part II is here.]

Link: Amazing Philosophy Interviews with Bryan Magee

I just wanted to share a very special link with any readers who happen upon my blog.

Several years ago (probably about five or so years ago) I worked as a mascot for Liberty Tax Service in southern California. At the same time I was going to community college, and I had decided by this point that I wanted to study philosophy. I had only begun to learn about analytic philosophy. While waving a sign dressed up in a statue of liberty costume can be fun at first, after several hours one might feel a need for intellectual stimulation. Hence, I would download philosophy talks from several different sources, and one of them was here.

There are many full-length interviews on this Youtube channel, all available for free. They each consist of a dialogue between Bryan Magee and one of the greatest philosophers of the twentieth century. They are very interesting, and are especially helpful in the case that one is not already familiar with the concepts being discussed (though even then they are still fun to listen to). If you're not familiar with some area of philosophy they can give you a quick crash-course on the topic. I really recommend checking them out. Here is one I remember enjoying a lot, with A.J. Ayer talking about logical positivism. One of the best lines is when Magee asks, "What do you think was the biggest issue with logical positivism?" and Ayer replies, "Well, it was all false." (Part 4, 6:26)

Modal Realism and the Serviceability Argument

Here's a quote from David Lewis: "Why believe in a plurality of worlds? -- Because the hypothesis is serviceable, and that is a reason to think that it is true."

Question for David Lewis and other modal realists: Lots of worlds are serviceable, not just the metaphysically possible ones. Many times when we do semantics, discuss language, give thought experiments, etc., worlds which are strictly logically possible but not metaphysically possible are helpful. For example, one of the ways that intensional semantics deals with oblique transitive verbs, control verbs, etc. is by invoking worlds where, for instance, water is not H2O, or where Hesperus is not Phosphorus. Presumably these are not metaphysically possible worlds, but rather 'logically' possible worlds. (Sometimes metaphysically possible worlds are called 'broadly' logically possible worlds; by 'logically' possible worlds I mean what are sometimes called 'strictly' logically possible worlds.)

Do these exist too, in exactly the same way as the metaphysically possible ones? If yes, then we run into problems. After all, isn't it only the metaphysically possible worlds which can exist? If not, then what is the distinction between metaphysical possibility and mere logical possibility supposed to mean? In fact, if merely logically possible worlds exist just like the metaphysically possible ones then there is no distinction. But there is, of course, a distinction.

At the very least, aren't the metaphysically possible worlds the only ones which could be actual? But if 'actual' is indexical as Lewis thinks, and the logically possible worlds exist on a par with the metaphysically possible ones, then any of these worlds could be actual.

Personally, I think there's just as good reason to admit the existence of logically impossible worlds as there is to admit the existence of possible worlds (though I don't think there's much reason to admit the existence of either).  If we really needed possible worlds, I think we'd need impossible ones too. But if logically impossible worlds are serviceable too then that makes things even worse for the modal realist. After all, what would it mean to say that a logical contradiction actually holds true in a concrete world just like ours? Clearly there are no such concrete worlds, since whatever concretely exists must at least be possible. But even if one resists the need for impossible worlds, the metaphysically possible worlds are a proper subset of the strictly logically possible ones, and it should be clear that these latter are "serviceable" too.

In sum, if Lewis's argument works for the existence of concrete metaphysically possible worlds, then it works for the existence of metaphysically impossible worlds too. But these can't exist concretely; that's the whole point of making some metaphysically possible and others not. Hence, Lewis's argument does not work. This can be taken as either reason to abandon the 'serviceability' criterion of existence, or as reason for rejecting concrete possible worlds. I'm inclined to reject both.

Quantifier Variance and the Semantics of Quantifiers

In my previous post I explained the basic idea behind quantifier variance. Now I want to criticize it. In particular, I said I want to point out some problems with the quantifier variantist's simultaneously affirming the following two statements:

(i) the different quantifiers behave the same logically; and

(ii) the different quantifiers have different meanings.

Let's do a little basic semantics. Let's define the truth function τ[ψ]^U,g relative to models U and g for the cases of quantified formulas ψ as follows. The following definitions are true for all models M, all variable assignments s, all variables x, and all formulas φ. If a formula is not assigned to T it is assigned to F:


τ : {<ψ,U,g>|ψ is a formula, U a model, g a var. assign.} → {T,F}

• (τ-∀): τ[∀xφ]^M,s = T ⇔ for all variable assignments s′, if for all variables v, s(v) ≠ s′(v) ⇒ v = x, then τ[φ]^M,s′ = T 
• (τ-∃): τ[∃xφ]^M,s = T ⇔ for some variable assignment s′, for all variables v, s(v) ≠ s′(v) ⇒ v = x, and τ[φ]^M,s′ = T 

Basics of Quantifier Variance

When I say that there are tables is it unambiguous what I'm saying? Quantifier variantists say no. Or at least they would say that in certain contexts it is not. In particular, the sentence is ambiguous when we are engaging in metaphysical debate about the existence of the table, as in the following case.

Consider the debate between what I will call compositionalism and anti-compositionalism. Compositionalism is the thesis that there are composite material objects, while anti-compositionalism is the thesis that there are not. Take the case of a world with just a table and its parts, and suppose we are considering a form of compositionalism which says there are tables. Assume further that there are exactly n atoms which, according to this form of compositionalism, are proper parts of the table. Note that we are using a philosophical definition of 'atom', according to which an atom is a material object which has no proper parts. Anti-compositionalism says there is no table; there are just the n atoms. 

In essence, compositionalism says (A) there are n+1 distinct things (viz. the n atoms, plus the table), while anti-compositionalism says (B) there are n things and there are no more than n things. Note that (A) and (B) can be adequately translated into a quantified language which only contains variables, quantifiers, sentential connectives, and the identity sign with the usual interpretation. For example, (A) would be translated as follows:

∃x₁∃x₂...∃x_n((x₁≠x₂ ∧ ... ∧ x₁≠x_n+1) ∧ (x₂≠x₃ ∧ ... ∧ x₂≠x_n+1) ∧ ... ∧ (x_n≠x_n+1))

One More Reason Why Russellian Descriptivism is False

Russellian descriptivism about proper names can be summarized rather roughly in terms of the following four theses. For any object O, where 'O' is a proper name of O:

(1) There is a unique definite description D associated with the term 'O'.
(2) The speaker believes that D is uniquely true of O.
(3) D uniquely picks out O.
(4) The proposition expressed by "If O exists, then O is D" is knowable by the speaker a priori.

So, very roughly, in the case of Barack Obama one might associate with this name the definite description 'the president of the United States from 2008 to 2016' and believe that this picks out Barack Obama uniquely; this is how one refers to Barack Obama, by means of the associated description.

There are many excellent reasons to believe a theory like this is false. Kripke, Donnellan, and others have pretty much put it to rest. But one more reason is that it entails another false thesis known as the identity of indiscernibles (or at least a somewhat modified and equally false version of this thesis). The identity of indiscernibles basically states that if two things share all the same features then they are the same object. [On the falsity of this thesis, check out Max Black's famous paper.]

The basic line of reasoning which leads me to say descriptivism of the described sort entails this principle is, informally, as follows (taking Barack Obama again as our example): By clause (3), 'the president of the United States from 2008 to 2016' uniquely picks out Obama; and by Russell's analysis of definite descriptions it follows from this that anything having the feature *being the president of the United States from 2008 to 2016* will be Barack Obama. Now, suppose two things x and y both have all the same features, and x has this feature. Then so does y. But since anything which has this feature is Obama, y is Obama. We can apply similar reasoning in any other case, since by (3) everything will have a feature P which uniquely picks it out, so if two things x and y have the same features then both of them will have P, and thus both will be identical to x.

There are two qualifications to be made. First, there is a sense in which the identity of indiscernibles can be trivially true. If we include among the features of a thing x the property *being identical to x* then it is obviously and trivially true that two things having all the same features will be identical. Even excluding features such as these the argument still goes through though, since presumably on a descriptivist theory the relevant description for, say, Barack Obama is not going to be 'the thing which has the feature of being Barack Obama'. Descriptivist theories aim to not be blatantly circular.

Second, the descriptivist might say that his thesis only applies to those referents which are nameable, whereas the identity of indiscernibles applies to all things regardless as to whether they can have names applied to them. However, the identity of indiscernibles is still false even when restricted to nameable things. You can give names to Max Black's two spheres and this provides a counter-example to the restricted form of the identity of indiscernibles.

For those not satisfied with my rather informal "proof" I've made a more formalized proof (with cheap symbols and lines, since OpenOffice does not appear to have any quantifiers). It should be pretty easy to interpret but if not please tell me. The first premise says for all x, if x is nameable, then there is a feature P such that for all y, if y is P then y = x, and x is P. The conclusion states that for any two nameable objects x and y, the identity of indiscernibles holds. Hence, if I have made no mistakes, descriptivism entails a restricted but still false identity of indiscernibles.

Reply to William Lane Craig on Divine Simplicity

Dr. William Lane Craig has made a response to my previous post where I argued that his own view of divine sovereignty entails the truth of divine simplicity. Now, Craig is actually correct about one thing: My argument does not by itself entail that God is identical to all his parts. This only follows from the conclusion of my argument if you grant that God really has a will, intellect, etc. Craig does not grant this, since he doesn't think talk about things having parts is metaphysically substantive.

There are a lot of things to say about Craig's response here. Maybe the first is to simply note that he is denying that anything really, in the metaphysically deepest sense, has any parts. This is surely an unacceptable conclusion. Personally I would think it's better to simply deny God has any parts rather than to deny anything has parts. Absent this option, if I didn't believe in divine simplicity I would even modify my account of divine sovereignty just to save parthood. For otherwise I honestly don't know how Craig explains kidneys, brains, legs and their relations to the people who have them. This is just a datum of experience, that there are at least some parts.

Craig tries to use an argument by Peter van Inwagen to back up his thesis. However, the problem is that Van Inwagen's argument only demonstrates the falsity of the doctrine of arbitrary undetached parts, which is the idea that any region of a body can be taken to be a proper part. His argument can only go through if we are dealing with 'parts' like Dottie* which are constituted by enough matter in such a form that a person can survive by becoming identical to them. It's not obvious though that I could ever become identical to, say, my heart. So his argument would not go through with those sorts of proper parts.

Now, I'm inclined to reject the doctrine of arbitrary undetached parts anyway so I'm happy to accept the soundness of the argument. But it just doesn't demonstrate that there are no proper parts. And if it did entail that, then--like Peter Geach did with Tibbles the Cat--I would just take the argument to establish the relativity of identity rather than the complete lack of proper parthood. More importantly, it's not even obviously sound. We might just deny the premise that Dottie becomes identical to Dottie*, since Dottie seems to be an animal (or a soul) and Dottie* seems to be a 'lump'. In virtue of their falling under different sortals these two objects have different identity conditions associated with them, and thus by Leibniz's law they are non-identical. They are merely constituted by the same matter.

There's also something to be said about Craig's underlying Carnapian sympathies. There is intense debate about taking this sort of view about language and metaphysical methodology (cf. the Chalmers volume on metametaphysics), and suffice it to say for now that I'm not too sympathetic. I will criticize this neo-Carnapian line of thought later, but this post should be enough to see why Craig's response is inadequate.

William Lane Craig Responds

...to my post on divine simplicity, here.

William Lane Craig on God and Analogy

William Lane Craig, as with most contemporary analytic philosophers of religion, objects to the classical Thomistic idea that God cannot be said to be a being in the sense that we can. I aim to argue that at least some of his claims here are unreasonable.

Craig objects: "One of the aspects of Thomas Aquinas’ thought that I find most disturbing is his claim that we can speak of God only in analogical terms. Without univocity of meaning, we are left with agnosticism about the nature of God, able to say only what God is not, not what He is."

This does not follow in the slightest; in fact, I wonder if Craig actually understands what analogy is, since it is one of the main points of Aquinas's theory of analogy to avoid this problem. Aquinas sought to show, in contrast to Maimonides, that though we can't predicate attributes of God in the same sense as us we can still speak meaningfully and make positive predications about him. Craig fails utterly to show how from the semantic analogy of the term 'being' we are left only with negative theology.

Next, Craig says: "When in discussions with atheists I affirm, 'God exists' and they reply, 'God does not exist,' we may need to be sure that we mean the same thing by 'God,' but there is no equivocation on the meaning of 'exists.'"

I guess what Craig is trying to say here is something like this: If the word 'exists' is analogical, then when I affirm God exists and when atheists affirm God does not exist, we are both equivocating past each other. But this is a genuine ontological dispute and so there is no equivocation; hence, 'exists' is not analogical. The problem is that the main premise is simply not true; if analogy is true, then we affirm that God exists in one sense, and the atheist simply denies that God exists in any sense, including the one I am predicating of God.

In the next paragraph, Craig says this: "The problem you pose brings us to the heart of my current work on divine aseity. What makes God more than just one being among many is precisely His aseity: God alone is self-existent; everything else exists contingently. Only God exists of Himself (a se); everything else exists through another (ab alio). That makes God the source of being for everything apart from Himself."

Now, I really like this, and I agree with this completely. The only problem is that Craig himself doesn't; for if what Craig says is literally true then divine simplicity is true, from which it is a small step to the doctrine that talk about God is analogous. Here's why:

(1) Whatever is non-identical to God is created by God. [conceded by Craig]
(2) If God has metaphysical proper parts ('parts' hereafter), then at least one of these parts is not created by God. [prem]
(3) Either God has parts or he doesn't. [LEM]
(4) Suppose he does have parts. [assp]
Then
(5) All of God's parts are created by God. [by 1]
But
(6) One of God's parts is not created by God [by 2,4]
This is a contradiction. Hence, we must reject our assumption. Hence:
(7) God has no parts.

So by 'metaphysical proper parts' here I mean things like ontological constituents, such as a property-instance (or trope or accident or whatever). (1) is just Craig's own thoughts on the matter, and (2) is true because clearly God doesn't create his essential properties; he depends on those for his existence, since if they didn't exist then neither would he. The rest follows by the meanings of the terms and the rules of logic.

Craig says that he considers God to be a substance, presumably in the same manner we are: "Not a physical substance, of course, but a spiritual substance like a mind."

However, the case is even more clear if Craig thinks God's mind and will are distinct; for if he does, granting Craig's doctrine of aseity, then from (1) it follows God's will must be created by God. But it is absurd to suppose God creates his own will; after all, he must have a will to do that! So, either Craig's doctrine of aseity is false (which I agree with Craig it isn't) or God is not distinct from his will (which I think is right, but is really only intelligible given divine simplicity).

Craig thinks getting rid of Platonism will solve the problems concerning God's aseity; but it doesn't, since even if there are no abstract properties in us there are clearly ontological constituents (my brownness, my height, my shape, etc.). Even taking 'parts' in this sense, I think the above argument shows that if he wants to hold on to the strong doctrine of aseity set out in the quote above he needs to get rid of the idea that God has any parts at all. And if God has no parts in the metaphysical sense then it can be shown speech about God is analogical; for in our case, to say I am good is to say the quality of goodness inheres in me as an accident (or is exemplified as a property, or inheres as a trope or whatever). But since God has no parts in any of these senses, to say God is good cannot be to say this about him. And the same with any of the divine attributes. Thus our terms must be said analogically of God.

[Edit: Craig's reply here. My reply here.]

Is 'Existence' Univocal Because 'All' Is Univocal?

In this post, Bill Vallicella presents another argument by Peter van Inwagen for the univocity of existence and questions it (he posted and refuted the first argument here). I think Vallicella has a point. Still, I might grant that the Quinean like Van Inwagen can translate a singular existential statement so as to have the same form as a general existential statement and argue the conclusion still does not follow. Quine, in his famous paper "On What There Is," proposes that we treat for instance the relation '__ = Pegasus' as a single-place predicate '=Pegasus'; one can call this 'pegasizing' or formally 'P'. Then 'Pegasus exists' will just be 'something pegasizes', which will just be translated to, '(Ex)(Px)'. Even ignoring the problematic aspects here I would pose a different objection. I would accuse Van Inwagen's argument of being a 'non sequitur'. Vallicella states the argument thus:

(1) 'Every' is univocal.

(2) 'Exist(s)' and 'every' are interdefinable: 'Fs exist' is equivalent to 'It is not the case that everything is not an F.'

Therefore

(3) 'Exist(s)' is univocal.

Clearly, as is, this argument is not valid. To make it valid we need some further premise. I'm not sure what sort of plausible premise Van Inwagen is using to get to his conclusion, but maybe it is something like

(2.5) If two terms are interdefinable then each of the terms' uses share the same sense relation.

(Just a clarificatory point: Sense relations are things like 'univocity' or 'equivocity', and Van Inwagen thinks that all the uses of 'exists' are univocal.) How are we to understand 'interdefinable' here? Surely not as meaning that for each 'exists' statement there is a semantically identical 'every' statement, i.e. one with the exact same meaning, for that would be utterly question-begging. We must construe it then as something like 'for each 'exists' statement there is a logically equivalent 'every' statement'. The problem is that (2.5) is not obviously true on this interpretation. I'll explain.

I think we can admit that 'some' and 'every' are univocal, that these two are interdefinable in the sense that logically equivalent statements can be expressed in terms of each, but still say that 'some' doesn't fully capture the meaning of 'exists', and thus neither does 'every'. Of course, every 'some' statement is logically equivalent to another 'there exists' statement, but that does not imply they are semantically identical.

On the idea that 'exists' is analogical, the natural language quantifier 'there exists' has many senses, but all beings can be said to exist in one of those senses; thus the range of this quantifier includes all beings (regardless as to which sense of 'being' can be said of them). And since there are no non-existent beings, the range of the quantifier 'some' is over all beings. So the two quantifiers range over the same domain of discourse; and since for any 'some' statement there is a logically equivalent 'there exists' statement, it follows that we can translate logically equivalent statements involving either of them with the same symbol in predicate-logic, '(Ex)'. This is also why they are each logically equivalent to at least one 'all' statement. But it simply doesn't follow that they all share the same sense relation (univocal, equivocal, etc.). It is true that our 'some' quantifier ranges over only and all beings, but it ranges over them regardless as to which of the many analogous senses of 'being' can be said of them. So it's consistent with both 'some' and 'all' being univocal that 'being' or 'exists' are not.

Classical Theism vs. Neo-Theism I: Divine Simplicity

In contemporary debates about the existence of God it is common to hear reference to 'the traditional divine attributes.' These include properties like omniscience, omnipotence, omnibenevolence, immateriality, eternality, and personality. It is supposed that if God exists he 'exemplifies all of these great-making properties'. This is the 'orthodox' conception of God in contemporary philosophy of religion and philosophical theology as heard from Craig, Plantinga, Swinburne, and most others.

Unfortunately, right from the get-go, there is a perfectly good sense in which this conception of God is unorthodox. According to the Fourth Lateran and First Vatican Councils of the Catholic Church, the doctrine that God is a perfectly simple being--one without any composition--is defined as infallible, binding dogma, denial of which amounts to heresy. Hence, the doctrine has some degree of pedigree in that it has been held by billions of Christians to be a very important doctrine. But even aside from this I would argue that the contemporary view--what I will call 'neo-theism'--is directly contrary to the truly 'classical theistic' view of God's nature. Classical theism has been the majority opinion for thousands of years. It is the view of the great pagan philosophers like Aristotle and Plotinus, the Christian Saints Athanasius, Augustine, Anselm, Bonaventure, Thomas Aquinas, and Bl. Duns Scotus, as well as other monotheistic thinkers like Maimonides, Averroes, and Avicenna. Such classical theists would deny that God is 'personal' or 'perfectly good' or 'eternal' in the sense that neo-theists take God to be. Distinctively classical theistic doctrines which are unpopular among the neo-theists of today include divine immutability, timelessness, and simplicity. I will focus on this last doctrine as an example of a fundamental difference between the two views, and argue that the classical theist view maintains God's perfection in a way which the neo-theist view does not.

The way that God's attributes are defined in contemporary philosophy of religion as above implicitly contradicts divine simplicity from the start. According to the contemporary view, when we predicate perfect moral goodness of God as in the sentence 'God is good', the referent of the term 'God's goodness' is the property of goodness. Likewise, if we say 'God is omniscient', the referent of the term 'God's omniscience' is the property of omniscience, and similarly for omnipotence, immateriality, and so on. However divine simplicity says that the referents of all intrinsic predications about God are identical, for to say otherwise would be to introduce metaphysical complexity into God. Hence, it is common to hear classical theists saying that God's goodness IS his omniscience, which IS his omnipotence, and so on. But it would seem to follow that omnipotence and goodness are the same property, which is clearly false; indeed, it would follow that God is himself a property!

Obviously the classical theist doesn't want to commit himself to such seemingly absurd claims, and it would be stupid to suppose 2,000 years of great thinkers were simply willing to accept a manifest falsehood. The more reasonable inference is that contemporary and classical thinkers are working with very different metaphysical presuppositions, and this is correct.

One neo-theist assumption is the Platonist, relational ontology within which Plantinga phrases the objection presented above. For Plantinga and other contemporary detractors reality consists of concrete individuals, platonic properties, and relations of exemplification. The platonic properties are abstract objects, which means they lack efficient causal power, while the causally efficacious concrete individuals exemplify these properties. Clearly God is an individual, since as creator of the universe he possesses causal power, in which case it follows he could not be an abstract object; hence he could not be identical to any of his properties, and thus divine simplicity is false. But certainly none of the classical presenters of simplicity accepted this ontological framework. Rather, following Aristotle, they would take a thing's features to be ontological constituents of a subject. This is the picture found in Aristotle's Categories for instance, where accidents such as color or size are said to be 'present in' a subject. Among contemporary philosophers D.M. Armstrong's theory of universals seems to be an example of a constituent ontology as well. Within such a framework it's not obviously incoherent to suppose that God is identical with his constituents so long as we can admit the idea of an improper constituent (analogous to an improper part or improper subset), since it doesn't follow from the very meaning of the term 'ontological constituent' that the constituent in question is a property; 'ontological constituent' is a category-neutral term, and doesn't necessarily imply Plantinga's relational ontology.

More generally though we can make sense of divine simplicity in terms of truthmakers. The neo-theist assumes that the referents of abstract singular terms like 'Alfredo's audacity', or in our case 'God's goodness', are platonic properties. This is what makes it impossible for God's to be identical with his goodness, for this to be identical to his omniscience, and so on. However, those who embrace divine simplicity can deny this account of predication. Rather, a classical theist will accept a truthmaker account, which says that if an intrinsic predication of the form 'a is F' is true, then a’s F-ness exists, where this entity is to be understood as the truthmaker for 'a is F.' So divine simplicity says God is identical with the truthmakers for each of his intrinsic predications. This makes sense because a truthmaker is an entity in the world in virtue of which a proposition is true. Clearly by this understanding truthmakers need not be properties (they can sometimes be). They can also be substances, as is the case with God--to deny this would at least have to be argued for and such a denial is on the face of it implausible. Hence, it is perfectly coherent to say God is his omniscience, which is his omnipotence, and so on. All this is saying is that God is identical to that in virtue of which he is omnipotent, that he is identical to that in virtue of which he is omniscient, and so on; and moreover, by the transitivity of identity, these things are each identical to each other. This picture shows that divine simplicity is not obviously contradictory and deserves much more than the charges of 'unintelligibility' and 'incoherence' ignorantly thrown at it today.

With these charges of absurdity put to one side we can see that divine simplicity is at least prima facie coherent. Certainly we will need to be given better arguments than Plantinga's cavalier dismissal of 2000 years of philosophy based on the presupposition of his own anachronistic ontology. But to argue something is logically coherent isn't to argue that it's true. In another post I will provide an argument to the effect that only a  simple God can truly be said to exist of himself and thus be perfect.