Category: Predication

Collective Inconsistency and Plural Predication

We often say things like

1. The propositions p, q, r are inconsistent.

Suppose, to keep things simple, that each of the three propositions is self-consistent.  It will then be false that each proposition is self-inconsistent. (1), then, is a plural predication that cannot be given a distributive paraphrase.  What (1) says is that the three propositions are collectively inconsistent.  This suggests to many of us  that there must be some one single entity that is the bearer of the inconsistency.  For if the inconsistency does not attach distributively to each of p, q, and r, then it attaches to something distinct from them of which they are members.  But what could that be?

If you say that it is the set {p, q, r} that is inconsistent, then the response will be that a set is not the sort of entity that can be either consistent or inconsistent.  Note that it is not helpful to say

A set is consistent (inconsistent) iff its members are consistent (inconsistent).

For that leaves us with the problem of the proper parsing of the right-hand side, which is the problem with which we started.

And the same goes for the mereological sum (p + q + r).  A sum or fusion is not the sort of entity that can be either consistent or inconsistent.

What about the conjunction p & q & r?  A conjunction of propositions is itself a proposition.  (A set of propositions is not itself a proposition.) This seems to do the trick. We can parse (1) as

2. The conjunctive proposition p & q & r is (self)-inconsistent.

In this way we avoid construing (1) as an irreducibly plural predication.  For we now have a single entity that can serve as the logical subject of the predicate ' . . . is/are inconsistent.'  We can avoid saying, at least in this case, something that strikes me as only marginally intelligible, namely, that there are irreducible monadic non-distributive predicates.  My problem with irreducibly plural predication is that I don't know what it means to say of some things that they are F if that doesn't mean one of the following: (i) each of the things is F; (ii) there is a single 'collective entity' that is F; or (iii) the predicate 'is F'  is really relational. 

One could conceivably object that in the move from (1) to (2) I have 'changed the subject.'  (1) predicates inconsistency of some propositions, while (2) predicates (self)-inconsistency of a single conjunctive proposition.  Does this amount to a changing of thr subject?  Does (2) say something different about something different?

A Problem With the Multiple Relations Approach to Plural Predication

Consider

1. Sam and Dave are meeting together.

2. Al, Bill, and Carl are meeting together.

3. Some people are meeting together.

Obviously, neither (1) nor (2) can be decomposed into a conjunction of singular predications.  Thus (2) cannot be analyzed as 'Al is meeting together & Bill is meeting together & Carl is meeting together.'  So it is natural to try to analyze (1) and (2) using relational predicates.  (1) becomes

1R. Meeting(Sam, Dave)   In symbols: Msd

But if 'meeting' is a dyadic (two-place) predicate, then we should expect (2) to give way to

2R. Mab & Mbc & Mac.

Unfortunately, (2R) is true in circumstances in which (2) is false.  Suppose there are three separate meetings.  Then (2R) is true and (2) false.  To get around this difficulty, we can introduce a triadic relation M* which yields as analysans of (2):

2R*. M*abc.

But then we need a tetradic relation should Diana come to the meeting.  And so on, with the result that 'meeting together' picks out a family of relations of different polyadicities.  But what's wrong with that?  Well, note that (1) and (2) each entail (3) by Existential Generalization in the presence of the auxiliary premise 'Al, Bill, Carl, Dave, and Sam are people.' 

But then we are going to have difficulty explaining the validity of the two instances of Existential Generalization.  For the one instance features a dyadic meeting relation and  the other a triadic.  If two different relations are involved, then what is the logical form of (3) — Some people are meeting together — which is the common conclusion of both instances of Existential Generalization?  If 'meeting together picks out a family of relations of different 'adicities, then (3) has no one definite logical form.

Does this convince you that the multiple relations approach is unworkable?

REFERENCE:  Thomas McKay, Plural Predication (Oxford 2006), pp. 19-21.

 

Irreducibly Plural Predication: ‘They are Surrounding the Building’

Let's think about the perfectly ordinary and obviously intelligible sentence,

1. They are surrounding the building.

I borrow the example from Thomas McKay, Plural Predication (Oxford 2006), p. 29.  They could be demonstrators.  And unless some of them have very long arms, there is no way that any one of them could satisfy the predicate, 'is surrounding the building.'  So it is obvious that (1) cannot be analyzed in terms of 'Al is surrounding the building & Bill is surrounding the building & Carl is surrounding the building & . . . .'  It cannot be analyzed in the way one could analyze 'They are demonstrators.'  The latter is susceptible of a distributive reading; (1) is not.  For example, 'Al is a demonstrator & Bill is a demonstrator & Carl is a demonstrator & . . . .'  So although 'They are demonstrators' is a plural predication, it is not an irreducibly plural predication.  It reduces to a conjunction of singular predications.

Continue reading “Irreducibly Plural Predication: ‘They are Surrounding the Building’”

The Hatfields and the McCoys

Whether or not it is true, the following  has a clear sense:

1. The Hatfields outnumber the McCoys.

(1) says that the number of Hatfields is strictly greater than the number of McCoys.  It obviously does not say, of each Hatfield, that he outnumbers some McCoy.  If Gomer is a Hatfield and Goober a McCoy, it is nonsense to say of Gomer that he outnumbers Goober. The Hatfields 'collectively' outnumber the McCoys. 

It therefore seems that there must be something in addition to the individual Hatfields (Gomer, Jethro, Jed, et al.) and something in addition to the individual McCoys (Goober, Phineas, Prudence, et al.) that serve as logical subjects of number predicates.  In

2. The Hatfields are 100 strong

it cannot be any individual Hatfield that is 100 strong.  This suggests that there must be some one single entity, distinct but not wholly distinct from the individual Hatfields, and having them as members, that is the logical subject or bearer of the predicate '100 strong.'

So here is a challenge to William the nominalist.  Provide analyses of (1) and (2) that make it unnecessary to posit a collective entity (whether set, mereological sum, or whatever) in addition to individual Hatfields and McCoys.

Nominalists and realists alike agree that one must not "multiply entities beyond necessity."   Entia non sunt multiplicanda praeter necessitatem!  The question, of course, hinges on what's necessary for explanatory purposes.  So the challenge for William the nominalist is to provide analyses of (1) and (2) that capture the sense of the analysanda and obviate the felt need to posit entities in addition to concrete particulars.

Now if such analyses could be provided, it would not follow that there are no 'collective entities.'  But a reason for positing them would have been removed.

I Need to Study Plural Predication

Here is a beautiful aphorism from Nicolás Gómez Dávila (1913-1994), in Escolios a un Texto Implicito (1977), II, 80, tr. Gilleland: 

Stupid ideas are immortal. Each new generation invents them anew.

Clearly this does not mean:

1. Each stupid idea is immortal and is invented by each new generation anew.

So we try:

2. The set of stupid ideas is immortal in the sense that every new generation invents some stupid idea or other.

(2) is much closer to the intended meaning. The idea is that there are always stupid ideas around, not that any one stupid idea is always around. (2) seems to capture this notion. But (2) presents its own puzzles. A set is a collection, and a collection is not the mere manifold of its members: it is "a further entity over and above them" as Michael Potter puts it in Set Theory and its Philosophy (Oxford 2004, p. 22).

Potter speaks of collections versus fusions. The distinction emerges starkly when we consider that there is a distinction between a singleton collection and its member, but no distinction between a 'singleton' fusion and its member. Thus Quine is distinct from {Quine}, the set consisting of Quine and nothing else. But there is no distinction between Quine and the sum or fusion, (Quine). {Quine}, unlike Quine, has a member; but neither (Quine) nor Quine have members. A second difference is that, while it makes sense to speak of a set with no members, the celebrated null set, it makes no sense to speak of a null fusion. The set consisting of nothing, the null set { } is something; the fusion of nothing is nothing.

Getting back to stupid ideas, what I want to say is that 'stupid ideas are immortal' can be understood neither along the lines of (1) nor along the lines of (2). The generality expressed is quite obviously not distributive, but it is not quite collective either. We are not expressing the idea that there is some one entity "over and above" its members to which immortality is being ascribed. 'Stupid ideas' seems to pick out a fusion; but if a fusion is a pure manifold, how can it be picked out?  

The puzzle is that immortality is not being predicated of each stupid idea, but it is also not being predicated of some one item distinct from stupid ideas which has them as members, whether this one item be a mathematical set or a mereological sum.

We know what we mean when we say that stupid ideas are immortal, but we cannot make it precise, or at least I can't make it precise given my present level of logical acumen.

So rather than contribute any stupid ideas of my own, I will go to the library and check out Thomas McKay's Plural Predication.  

 

Richard Gaskin on the Unity of the Proposition

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

Predicates and Properties

We are warming up to an examination of deflationary theories of truth according to which truth is either not a property or not a metaphysically substantive property.  (I oppose deflationary theories of truth just as I oppose deflationary theories of existence.) But first some clarification of 'predicate' and 'property.'

1. I begin by resisting the traditional conflation of predicates and properties, a conflation in evidence when we hear a philosopher claim that "existence is not a predicate."  That claim makes no sense unless a predicate is a property.  After all, 'existence,' as an abstract substantive, is not grammattically tuited to occupy predicate position.  If, however, a predicate is a bit of language used to express a property, then the claim should be that " '. . . exists' is not a predicate."  That's in order, as is "Existence is not a property."  As expressing properties, predicates are distinct from properties.  Predicates are linguistic while properties are extralinguistic.

To be a bit more precise, predicates (whether types or tokens) are tied to particular languages whereas the properties they express are not so tied.  Thus schwarz is tied to German in the way black is tied to English, but the property of being black is tied to neither.  Equally, the property of being disyllabic is tied to no one language even though it is a property that only linguistic items can have.  Thus 'Boston' but not Boston is disyllabic.

2. Some of you will question whether there are properties distinct from predicates.  Question away.  But just realize that in order to raise this very question you must first have distinguished predicates and properties.  You must already have made the distinction 'at the level of intension' if not 'at the level of extension.'  For you cannot maintain that there are no properties distinct from predicates unless you understand the term 'property' just as you cannot maintain that there are no unicorns distinct from horses unless you understand the term 'unicorn.'

3. By my lights, you are a very foolish philosopher if you deny properties, but not if you deny universals.  If you deny universals you are merely mistaken.  So let's be clear that 'property' and 'universal' are not to be used interchangeably.  It is a substantive question whether properties are universals or particulars (as trope theorists maintain).  Universals I define as repeatable entities, particulars as unrepeatable entities.

4. The predicate/property distinction under our belts, we need to note three views on their relation.

5. One view is that  no predicate expresses a property.  I rejected this view in #3.  To put it bluntly, there is a real world out there, and the things in it have properties whether or not there are any languages and language-users. Some of our predicates succeed more or less in expressing some of these properties.

6. A second view is that every predicate expresses or denotes a property.  The idea is that for every predicate 'P' there is a property P corresponding to 'P.'  But then, given that 'exists' and 'true' are predicates, it would follow straightaway that existence and truth are properties.  And that seems too easy.  Deflationists, after all, deny for reasons that cannot simply be dismissed that truth is a property.  They cannot be refuted by pointing out that 'true' is a predicate of English.  The following equivalence is undeniable but also not formulable unless 'true'  is a predicate:

'Grass is green' is true iff grass is green.

The deflationist will take an equivalence like this to show that 'true' is a dispensable predicate and therefore one that does not pick out a property.  (On Quine's disquotationalism, for example, 'is true' is a device of disquotation: it merely undoes the semantic ascent displayed on the LHS of the biconditional.)  We should therefore be uneasy about the view that every predicate expresses or denotes a property.  The existence of a predicate does not show the existence of a corresponding property.  A predicate need not predicate a property.  It should not be a matter of terminological fallout that wherever there is a predicate there is a property.

7.  Determined to maintain  that every predicate expresses or denotes a property, a deflationist  could of course hold that existence and truth are properties, but not metaphysically substantive properties.  A deflationist could argue like this:

Every predicate expresses a property

'True' is a predicate

Ergo: Truth is a property, but not a substantive one.

But he could also argue like this:

Every genuine predicate expresses a substantive property

Truth is not a substantive property

Ergo: 'True' is not a genuine predicate.

8.  A third view about the predicate-property relation has it that some predicates pick out properties and some don't.  I suggest this is how we should use 'predicate.'  It then becomes a matter of investigation, not of terminology, whether or not there is a property for a given predicate.

The Truthmaker Theory of Predication and Divine Simplicity

In this post I first try to get clear about the truthmaker theory of predication proposed by Michael Bergmann and Jeffrey E. Brower in their A Theistic Argument Against Platonism.  I then try to understand how it solves a certain problem in the doctrine of divine simplicity (DDS). Finally, I raise a question about the authors' solution.

The truthmaker theory of predication is a rival to the following theory of predication which, with a little inaccuracy, we can label 'Platonistic' so as to have a handy label:


P: The truth of all true predications, or at least of all true predications of the form "a is F", is to be explained in terms of a subject and an exemplifiable (however exemplifiables are themselves to be conceived). (p. 7)

This post will not address the authors' impressive theistic argument  against P.  For present purposes we can assume that it is sound the better to evaluate the alternative which  Bergmann and Brower put  as follows:



P*: The truth of all 

true predications, or at least of all true predications of the form "a is F", is to be explained in terms of truthmakers. (p. 25)

To appreciate how the two theories differ, consider the proposition expressed by the true essential predication, 'God is divine.'  The Platonistic theory explains the truth of this proposition in terms of the subject God and the exemplifiable, the property of being divine.  The proposition is true because the subject exemplifies the property.  By contrast, the truthmaker theory of predication explains the proposition's truth in terms of its truthmaker.  Three questions:  What is a truthmaker?  What is the truthmaker of the proposition *God is divine*?  What exactly is the difference between P and P*? The authors offer the following as a "partial analysis" of the notion of a truthmaker:

TM: If an entity E is a truthmaker for a predication P, then 'E exists' entails the truth expressed by P. (p. 22)

From TM and the fact that 'God is divine' is an essential predication it can be inferred that the truthmaker of this truth is God himself.  For 'God exists' entails the truth expressed by 'God is divine.'  This is because there is no possible world in which God exists and the proposition in question is not true.  Thus God himself suffices as truthmaker for 'God is divine,' and there is no need for an exemplifiable entity or a concrete state of affairs (the subject's exemplifying of the exemplifiable entity.) This allows us to appreciate the difference between the Platonistic and the truthmaker theories of predication.  The first, but not the second, requires that the explanation of a truth's being true invoke a subject and an exemplifiable.  On the truthmaker theory it is not the case that every predication is such that its explanation requires the positing of a subject and an exemplifiable.  The subjects of all essential predications of the form a is F suffice as truthmakers of the propositions expressed by these predications.

In the case of such accidental predications as 'Tom is tired,' the truthmaker cannot be Tom by himself, as the authors appreciate. (p. 26)  Neither Tom nor Tom's existence nor *Tom exists* necessitates the truth of 'Tom is tired.'  On one approach, the truthmaker of true accidental predications is a concrete state of affairs.  On another, the truthmaker is a trope.  I think it follows that P is a special case of P*.  I don't find the authors stating this but it seems to be a clear implication of what they do say.  According to the truthmaker theory of predication, the truth of every true affirmative monadic predication, whether essential or accidental, is explained by a truthmaker, an entity which can belong to any ontological category.  The Platonistic theory is the special case in which the truthmaker either is or involves an exemplifiable.  (A special case of this is the case in which the truthmaker is a concrete state of affairs.)  The truthmaker theory is more general because it allows for truthmakers that neither are nor involve exemplifiables.

Application to Divine Simplicity

One of the entailments of the doctrine of divine simplicity (DDS) is that there is no distinction between God and his attributes.  Thus God is (identical to) his goodness, his power, etc.  We have discussed the motivation for this doctrine in earlier posts.  But how could an individual be identical to its attributes or properties? If God is identical to one of his properties, such as the property of being divine, then it follows that he is a property or exemplifiable — which is absurd.  It is absurd because God is a person and persons are not exemplifiable entities.  But if the truthmaker theory of predication is correct, then there is a way to make coherent sense of the notion that God is identical to his nature, goodness, power, wisdom, and other such attributes.

Consider 'God is his omnipotence.'  If the abstract singular term 'God's omnipotence' is taken to refer to a property, then we get the unacceptable consequence that God is identical to a property.  Proponents of the truthmaker theory of predication, however, can maintain that the referents of abstract singular terms are truthmakers.  Accordingly, 'God's omnipotence'  and 'God's divinity' refer respectively to the truthmakers of 'God is omnipotent' and 'God is divine' respectively.  Because both of these predications are essential, the truthmaker of both is God himself.  To say that God is identical to his omnipotence is to say that the referent of 'God' is identical to the referent of 'God's omnipotence.'  And that amounts to the unproblematic claim that God is identical to God.

A Question

The authors have shown us a way to demonstrate the coherence of 'God is identical to his divinity'  assuming we are prepared to accept P* and TM.   But I wonder whether their demonstration 'proves too much.'  Consider the parallel but presumably incoherent  'Socrates is identical to his humanity.'  We now must ask whether the strategy that works in the case of God also works in the case of Socrates.  If it does, then the radical difference between God and creature, which is part of the motivation for DDS, will not have been  properly accommodated.

The authors will grant that Socrates is truthmaker enough for (the propositions expressed by) all essential predications about him.  Thus Socrates himself makes true 'Socrates is human' by TM.  Because they hold P* they will grant that no exemplifiable need  be invoked to explain 'Socrates is human.'  We needn't say that this is true because Socrates exemplifies the property of being human; we can say that it is true because 'Socrates' and 'Socrates humanity' have the same referent, namely Socrates. But then does it not follow that Socrates is ontologically simple, at least in respect of such essential predicates as 'human,' 'rational,' and the like?  Does it not follow that Socrates is identical to his humanity, his rationality, animality, etc.?  Rhetorical questions aside, I am arguing as follows:

a. Socrates  is the truthmaker of 'Socrates is human' and like essential predications.  (From TM)

b. Socrates is the referent of both 'Socrates' and 'Socrates' humanity.' (From P*)  Therefore:

c. Socrates is identical to Socrates' humanity. (From b) 

But we surely do not want to say that Socrates is identical to his humanity, rationality, etc.  which would imply that his humanity, rationality,etc. are identical to one another.  Socrates, unlike God, is a metaphysically composite being.  So something appears to have gone wrong.  The Bergmann-Brower approach appears to 'prove too much.'  Their approach seems to imply what is false, namely, that both God and Socrates are ontologically simple  in respect of their essential attributes.

Scholastic Realism and Predication

This post continues our explorations in the philosophy of The School. What is a scholastic realist? John Peterson (Introduction to Scholastic Realism, Peter Lang, 1999, p. 6) defines a scholastic realist as follows:

S is a scholastic realist =df i) S is a moderate realist and ii) S believes that universals exist in some transcendent mind, i.e., the mind of God.

A moderate realist is defined like this:

S is a moderate realist =df i) S denies that universals exist transcendently and ii) S affirms that universals exist immanently both in matter and minds.

Peterson A universal exists transcendently just in case it exists "independently of matter and mind." One who holds that universals exist independently of matter and mind is a Platonic or extreme realist. A moderate realist who is not a scholastic realist Peterson describes as an Aristotelian realist. Such a philosopher is a moderate realist who "denies that universals exist in some transcendent mind."   In sum, and interpreting a bit:

Platonic or extreme  realist:  maintains that there are universals and that they can exist transcendently, i.e., unexemplified (uninstantiatied) and so apart from matter and mind.

Moderate realist:  denies that there are any transcendent universals and maintains that universals exist only immanently in minds and in matter.

Scholastic realist: moderate realist who believes that there is a transcendent mind in which universals exist.

Aristotelian realist:  moderate realist who denies that there is a transcendent mind in which universals exist.

Continue reading “Scholastic Realism and Predication”

Divine Simplicity and Truthmakers: Notes on Brower

1. One of the entailments of the doctrine of divine simplicity (DDS) is that God is identical to: God's omniscience, God's omnipotence, and in general God's X-ness, where 'X' ranges over the divine attributes.  And it is easy to see that if God = God's F-ness, and God = God's G-ness, then (by transitivity of identity) God's F-ness = God's G-ness.  I suggest that we use 'divine attribute' to refer to those properties of God that are both essential and intrinsic.  The problem, of course, is to make sense of these identities given the fact that, prima facie, they do not make sense.  The pattern is the same as with Trinity and Incarnation.  These doctrines imply identities which, on the face of it, beggar understanding.  It thus falls to the philosopher of religion to try to render coherent that which, on the face of it, is incoherent.

2. One of the questions that arise when we try to make sense of DDS concerns which category of entity such phrases as 'God's omniscience' pick out.  One possibility is that such phrases pick out properties, whether universal (multiply exemplifiable) properties or particular (not multiply exemplifiable) properties, also known as tropes. But this leads to trouble as Brower points out.  For if God is identical either to omniscience or to his omniscience, then God is identical to a property — which sounds absurd: how can God, a person, be a property?  Properties are predicable entities, but God is an individual and so not predicable.  Properties are exemplifiable entities (whether multiply or non-multiply); but God is an individual and so not exemplifiable.  Properties are abstract (causally inert)  whereas God is concrete (causally active/passive).  No property is a person, but God is a person.  No property creates or knows or loves.  These are some hastily sketched reasons for thinking that God cannot be identical to his properties.

3. Jeffrey E. Brower forwards an interesting proposal.  He suggests that such phrases as 'God's nature,' 'God's goodness' and 'God's power' refer to "entities of a broadly functional type — namely, truthmakers." (Simplicity and Aseity, sec. 2)  The idea is that 'God's omniscience' refers to the trruthmaker of 'God is omniscient' or perhaps to the truthmaker of the proposition expressed by 'God is omniscient.'  If (Fregean) propositions are the primary truthbearers, then (tokenings of) declarative sentences that express such propositions can be said to be secondary truthbearers.  I trust that it is clear that truthbearers and truthmakers are not to be confused.  One key difference is that while some truthbearers are are false, no truthmaker is false.  Truth and falsity are properties of certain representations (propositions, declarative sentences, beliefs, judgments, etc.)  whereas truthmakers are the ontological grounds of some true truthbearers.  If I understand Brower's view, it is not only that truthmakers are neither true nor false — every TM theorist will hold this — but also that truthmakers are not at all proposition-like.  By contrast, I follow D. M. Arstrong in holding that truthmakers must have a proposition-like structure.  But more on this in a moment.

4. Roughly, a truthmaker is whatever plays a certain role or performs a certain function; it is whatever makes true a true truthbearer.  The 'truthmaker intuition' — which I share with Brower — is that a sentence such as 'Tom is blogging' cannot just be true; there is need of some worldly entity to 'make' it true, to serve as the ontological ground of its truth, to 'verify' it in an ontological, not epistemological, sense of this term.  To say that some or all truthbearers need truthmakers is not yet to specify which sort of entity plays the truthmaker role.  Among philosophers who accept the need for truthmakers there is disagreement about the ontological category to which they belong. 

 Brower says rather incautiously that the functional characterization of truthmakers "places no restriction on the specific nature or ontological category to which a truthmaker can belong." (sec 2.1)  That can't be right.  Surely there are some restrictions.  For one thing, a truthmaker cannot be a Fregean proposition for the simple reason that such items are among the items made true by truthmakers.  And the same goes for declarative sentences, beliefs, and judgments.  My belief that the cat is asleep is either true or false and as such is a truthbearer.  It is in need of a truthmaker but is not itself one.  Of course, the fact of my believing that the cat is asleep can serve as truthmaker for the sentence ' BV now believes that the cat is asleep'  if concrete facts are admitted as truthmakers – but that is something else again.  So not just anything can be a truthmaker.  Charitably interpreted, what Brower is telling us is that TM theorists are allowed some ontological latitude when it comes to specifying which category of entity is fit to play the truthmaker role. 

5. Let us note that if a true Fregean proposition p entails a Fregean proposition q, then one could say that the first 'makes true' the second.  And so one could speak of the first as a 'truthmaker' of the second.  But this is not what is meant  by 'truthmaking' in these discussions despite the fact that p broadly logically necessitates q.   What is intended is a relation of broadly logical necessitation that connects a nonpropositional entity (but on some theories a proposition-like entity) to a propositional entity, or more precisely, to an entity that can serves as the bearer or vehicle of a truth-value.  As I see it, the entailment relation and the truthmaking relation are species of broadly logical necessitation; but truthmaking is not entailment.  Entailment will never get you 'outside the circle of propositions'; but that is exactly what truthmaking is supposed to do.  A truthmaker is an ontological, not propositional or representational truth-ground.  Philosophers who are attracted to truthmakers typically have a realist sense that certain of our representations need to be anchored in reality.

Brower sees it a little differently.  He would agree with me that entailment and truthmaking cannot be identical, but he thinks of it as "a form of broadly logical necessitation or entailment" and says that entailment is necessary but not sufficient for truthmaking. (Sec. 2.1)  So Brower seems to be maintaining that while there is more to truthmaking than entailment, every truthmaker entails the truth it makes true.  But this makes little or no sense.  Entailment is a relation defined on propositions.  If x entails y, then you can be sure that x and y are propositions or at least proposition-like entities, whether these be sentences or judgments or beliefs or even concrete states of affairs such as the fact of (not the fact that) Peter's being tired, which concrete fact contains Peter himself as constituent, warts and all.  But for Brower, as we will see in a moment, concrete individuals such as Socrates, entities that are neither propositions nor proposition-like, can serve as truthmakers.  As far as I can see, it makes no sense to say that Socrates entails a proposition.  It makes no sense because entailment is defined in terms of truth, and no individual can be true or false.  To say that p entails q is to say that it is impossible that p be true and q false.  Since it makes no sense to say of an individual that it is true, it makes no sense to say of an individual that it entails a proposition.  So truthmaking cannot be a type or species of entailment if individuals are truthmakers.

6.  But setting aside for the moment the above worry, if it makes sense to say that God is the truthmaker of 'God is omniscient,' and if 'God's omniscience' refers to this truthmaker, then it will be clear how God can be identical to God's omniscience.  For then 'God is identical to his omniscience' is no more problematic than 'God is God.' It will also be clear how God's omniscience can be identical to God's omnipotence. 

7.  But can it really be this easy to show that DDS is coherent? Although I agree with Brower that some truthbearers need truthmakers, I don't see how truthmakers could be ontologically structureless individuals or 'blobs' as opposed to 'layer-cakes' in Armstrong's terminology.  By 'ontologically structureless' I mean lacking in propositional or proposition-like structure.  Consider the following true intrinsic essential predicative sentences: 'Socrates is human,' 'Socrates is an animal,' Socrates is a material object,' 'Socrates exists,' and 'Socrates is self-identical.'  (It is not obvious that 'Socrates exists' is an essential predication inasmuch as Socrates exists contingently, but let's not enter into this thorny thicket just now.)

Brower's claim is that in each of these cases (which parallel the true intrinsic essential predications of divine attributes) the truthmaker is the concrete individual Socrates himself.  Thus Socrates is the truthmaker of 'Socrates is human' just as God is the truthmaker of 'God is omniscient.'  Unfortunately, no individual lacking propositional or proposition-like structure can serve as a truthmaker as I argued in #5 above.  Just as it makes no sense to say that Socrates is true, it makes no sense to say that Socrates entails the proposition expressed by 'Socrates is human.' 

There is more to say, but tomorrow's another day.  Time to punch the clock.