Introduction
A theory of properties provides an answer to the question of how two distinct things can share the same feature, e.g. how Fido and Lassie are both dogs. A systematic metaphysics without a theory of properties is surely incomplete since it leaves the problem of universals unanswered. On the other hand, for most classical theists, God's aseity and sovereignty are not negotiable. If there were anything distinct from God but dependent for its existence not on God, it would undermine God's aseity and sovereignty. Combining the foregoing two ideas, one of the theistic metaphysicians’ tasks is to offer a solution to the problem of universals which does not posit any entities incompatible with God's aseity and sovereignty.
Leftow's theist concept-nominalism, henceforth TCN, is proposed as such a theory.Footnote 1 Since the topic of this article is TCN itself, I will not conduct a survey of various theistic theories of properties.Footnote 2 Instead, I focus on the question of whether TCN is successful in answering a notorious problem in the literature on properties, i.e. the regress problem. Before the main body of this article, I would like to add two provisos for the following discussion. First, I assume that God's aseity and sovereignty are incompatible with any putative entity whose existence is independent of God.Footnote 3 The exegetical problem about these two doctrines is not my concern.Footnote 4 In this article, I take the traditional interpretation for granted. That is, I assume that one necessary condition for the success of TCN is that it does not presuppose the existence of any entity or object independent of God.
Second, I assume that divine predications are somehow different from non-divine predications. In order to avoid the well-known bootstrapping objection, divine predications need a separate treatment different from TCN.Footnote 5 In other words, TCN, in the present context, should be understood as a theory which only deals with the sameness of type of non-divine predications, e.g. that the predicate ‘is a dog’ occurs twice in ‘Fido is a dog’ and ‘Lassie is a dog’.Footnote 6 Therefore, the examination of TCN will concentrate on how it handles the regress problem for non-divine predications. Following the previous point, I assume a truth-making theory of divine predication.Footnote 7 Precisely, I hold that God Himself serves as the truth-maker of all divine intrinsic predications,Footnote 8 like ‘God is omnipotent’ and ‘God is omniscient’.Footnote 9 This is the best theory of divine predication I know. However, it is not essential to the following discussion. My points will not be affected by adopting a different theory of divine predication as long as it is not contradictory to TCN.
The structure of this article is as follows. In the next section, I summarize TCN by illustrating what its ontology is and how its theory works. In the third section, the regress problem is recast within the framework of TCN. In the fourth section, I present my solution to this problem. In the final section, several objections to my solution are addressed and replied.
Theist concept-nominalism: its ontology and theory
As noted, a theistic metaphysician should provide a theory of properties which is compatible with God's aseity and sovereignty. To check whether TCN satisfies this requirement, we have to take a look at its ontology. Despite its misleading name, TCN does not presuppose the existence of any kind of concepts. Instead, Leftow writes:
I suggest then that in the final analysis, the ontology behind talk of divine concepts is in terms of divine mental events . . . So on my view, the reality behind talk of God forming a concept is that He produces an event with a particular causal role. (Leftow (Reference Leftow2012), 303 & 315)
Therefore, the ontology of TCN includes no divine concepts but God's mental events. Since God's mental events are concrete particulars produced by God and having causal powers, they can and do depend on God. Thus, their existence will not undermine God's aseity and sovereignty.
The opponents might object that some of God's mental events, e.g. God's thinking of what it is to be a cat, require universals to explain or individuate their contents. If so, TCN will have to presuppose something, i.e. universals, which seem incompatible with God's aseity and sovereignty. In reply, Leftow argue:
But we need not think that some entity gave the cat-event its content. We could treat being contentful, and contentful one way rather than another, as a primitive fact about mental events. Many ontologies involve entities not made to be as they are by other entities . . . Realists say that cathood makes cats cats, but nothing makes cathood cathood: it just is as it as. So it is not clear what special fact about the cat-event would make it require to be made as it is by cathood. If we bring the attribute into the story of God's mental content, the story goes this way: a particular event encodes what it is to be a cat because it grasps cathood. Ignoring the questions of what this means and how it is done, we can ask simply: why does it do so? Well, it just does. That is just the event's nature, as a brute fact; that is where explanation stops. All there is to the event is the grasping and the content grasped; the content grasped makes it the event it is; to be that event is to be the grasping of that content, period. Without the attribute, the story goes: a particular event encodes what it is to be a cat. Why? It just does. That is its nature, as a brute fact; that is where explanation stops. All there is to the event is God's thinking and its being contentful in a particular way; the way it is contentful makes it the event it is; to be that event is to be an event contentful that way, period; and ‘way’ is not ontologically commissive. Either way, explanation stops at a brute fact about the nature of a mental event. Why is the one resting point any better than the other? (ibid., 311)
Here, Leftow proposes a sort of adverbialism with regard to mental content in which God's mental events can be contentful one way or another without appeal to universals or any God-independent entities.
After making the ontology of TCN explicit, let us turn to the question of how its theory deals with the problem of universals. The prototypical concept-nominalism says that an object a is F just in case that a falls under the concept F.Footnote 10 The proponents of TCN cannot take the same route since, according to TCN, there are really no concepts. However, among God's mental events, there are divine representations which take the place of divine concepts. Leftow articulates this idea as follows:
I suggest that the primary causal role of the events behind creature-concept-talk is to provide ‘objects’ for evaluation, preference, intention, and so on . . . I suggest that every divine representation—henceforth DR—of candidate creaturely items or states of affairs actually plays this role: every DR is an object of some attitude . . . God forms the DR dog. (ibid., 315)
So the question becomes what role divine representations play in explaining how two distinct things can have the same feature. In an early work, Leftow writes: ‘Fido is a dog not because of what he resembles but because this is what God made him to be, in accord with His concept dog. This is the deepest account of it’ (Leftow (Reference Leftow and Zimmerman2006), 346). Later, he rephrases the deepest account in terms of God's mental events and causal links among them:
I alter Augustine: I parse divine concepts away . . . What makes something a cat on my account is its dependence not on a divine concept but on certain bits of God's mental life. These are just primitively events with a particular causal role in God's mental economy, such that when appropriately involved in the execution of a divine intention, cats result. (Leftow (Reference Leftow2011), 73)
Generally speaking, on TCN, an object a is F because the existence of a is jointly brought about or caused by (i) God's mental event E 1 which is the divine representation of F and (ii) God's mental event E 2 which is His intention to conserve or create a according to the divine representation of F.Footnote 11 Thus understood, TCN offers an answer to the problem of universals. Why are Fido and Lassie both dogs? It is because they are both caused by the same divine representation of dog. Generally speaking, two distinct objects a and b are both F in virtue of there being a common cause, i.e. the divine representation of F, of the existence of a and the existence of b.
In sum, on TCN, there are only concrete particulars, including God, events, and non-divine creatures like dogs, none of which pose a challenge to God's aseity and sovereignty. On the other hand, in place of Platonic universals, divine representations (as concrete events) play the main role in explaining how distinct things can have the same feature. The foregoing paragraphs are merely a brief summary of TCN, but it suffices for our present purpose. In the next section, I turn to a notorious problem for theories of properties, i.e. the regress problem, and see why it is a thorny challenge to TCN.
Regress problem
To being with, it will be useful to focus on Platonism with regard to properties for a while. Platonism says that an object a is F just in case that (i) there exists a Platonic universal Fness, and (ii) the object a exemplifies the Platonic universal Fness. Now we can ask why a exemplifies Fness. It is natural for a Platonist to say that it is because there exists a Platonic relation exemplification such that a and Fness jointly exemplify the Platonic relation exemplification. Again, if we ask further why a and Fness exemplify exemplification, the answer will be that a, Fness, and exemplification jointly exemplify exemplification. Since we can repeat more questions ad infinitum, the enquiry seems to lead to a vicious regress in which the explanation is never completed.
The regress problem is not a patent only for Platonism. Class nominalism says that a is F just in case that a is a member of a natural class C F which only contains F things. By the same reasoning, we can ask why a is a member of the class C F. According to class nominalism, it is because the ordered pair <a, C F> is a member of a natural class C F+1 which only contains ordered pairs of members and their classes. Here the membership relation appears again between <a, C F> and C F+1. Therefore, we can ask for new explanations repeatedly and then get the regress problem for class nominalism. Similarly, the regress problem(s) for other theories of properties can be produced in parallel ways by asking how predications involving resemblance, falling-under, compresence, and so on can be explained further.
Some might argue that the alleged regress problem is a pseudo one because two kinds of explanatory problems are confused. Lewis complains:
I fear that the problem does not remain rightly understood. Early in Universals it undergoes an unfortunate double transformation. In the course of a few pages (Universals, I, pp. 11–16) the legitimate demand for an account of Moorean facts of apparent sameness of type turns into a demand for an analysis of predication in general. The analysandum becomes the schema ‘a has the property F’. (Lewis (Reference Lewis1983), 352)Footnote 12
His idea is that the problem of universals only asks why two distinct objects a and b can be both F. At this point, the sameness of type between a's being F and b's being F is a Moorean fact in need of an account. However, a general analysis of predication asks for something more: further explanation of the explanantia for the sameness of type between distinct objects. However, are the explanantia, e.g. that a exemplifies Fness or that a is a member of C F, also facts which need further explanation? It is not so obvious. At any rate, once we take the demand on, there seems to be no way to escape the regress problem. Lewis thus concludes: ‘Doing away with all unanalysed predication is an unattainable aim, and so an unreasonable aim’ (ibid., 353). For Lewis, in order to answer the problem of universals, Platonists (and other nominalists) only need to explain why two distinct things have the same feature. Every explanation must stop somewhere. Since the notions of exemplification, membership, compresence, falling-under, and so on are not pre-philosophical ones, the sameness of type between the predications about them does not call for further explanation. Therefore, no further analyses need to be given.
Lewis's strategy might work for the aforementioned theories of properties. However, the regress problem cannot be dismissed as easily for TCN. Recall that on TCN, two distinct objects a and b are both F only if a's existing, call it E a, and b's existing, call it E b, are both (partially) caused by God's mental event E F, which is the divine representation of F. Is it legitimate to ask further why they are both caused by E F? Now there are two possibilities. If the answer is yes, then according to TCN, the explanation might go as follows: the event of E F’s causing Ea and the event of E F’s causing Eb are both caused by God's mental event E causation, which is the divine representation of causation. Now, in this further explanation, the notion of causality is invoked again. Thus, we do not get an informative explanation of causal claims at any rate.
On the other hand, if we do not ask why E a and E b are both caused by E F, there will be another problem: if there is no Platonic entity as the causal relation or any qualified substitute for it, it is hard to see how it is guaranteed that one event causes another.Footnote 13 Now suppose that Fido is white. According to TCN, Fido is white only if the existence of Fido, call it E Fido, is caused by God's mental event E white, which is the divine representation of white. Since it is possible that E Fido occurs and E white occurs while E white does not cause E Fido, the mere existence of E Fido and E white does not suffice to make E white cause E Fido. (Just consider a possible world in which God still has the mental event E white but conserves or creates Fido according to another mental event E black which is the divine representation of black. That is, He makes Fido black.) If so, then we are not even sure that E Fido is caused by E white rather than E black. The rejection of the causal relation invites different permutations. This undermines the core idea of TCN, i.e. that two distinct objects a and b are both F because E a and E b are both caused by E F, since, given the possibility of permutations, there is no reason to say that they are not caused by some other divine representation E G. Again, if this is not solved, TCN will never get off the ground.
We have seen how the regress problem poses a challenge to TCN. Then, is there any way out? Leftow once wrote: ‘Here other sorts of nominalist seem to have an edge: as long as they do not lurch over into realism or tropism, they are free to mix and match different sorts of nominalist account’ (Leftow (Reference Leftow and Zimmerman2006), 346). Thus, perhaps we can combine TCN and another sort of nominalism and leave all and only causal claims to the latter. I myself do not endorse this option for two reasons. First, as a referee of this article has pointed out to me, TCN would not be so attractive when some other nominalism also enters the scene.Footnote 14 Second, even if the combination of TCN and another sort of nominalism could be overall better than any other full-blooded nominalism, it would still be threatened by the permutation problem raised in the previous passage. Thus, it would be better for the proponents of TCN to find a solution free from it.
In this section, I present the regress problem for TCN. We have seen that the replies given by Lewis and Leftow are not satisfactory. In the next section, I propose my own reply called the ‘truth-making solution’ to the regress problem.
Truth-making solution
The way I put the permutation problem may remind one of a harder regress problem to Platonism or any form of realism with regard to universals, i.e. Bradley's regress. Recall that Platonism posits the universal Fness to explain why a is F. However, the mere existence of a and Fness cannot explain why a is F. It is possible that a exists and Fness exists while a is not F. (Consider a possible world in which a is not F but b is F.) Therefore, Platonism needs to posit another relation exemplification to relate them. This is the reason why it says that a is F because a exemplifies Fness. However, if exemplification can do the explanatory work, it must be something real. But again, the mere existence of a, Fness, and exemplification cannot explain why a is F. It is possible that a, Fness, and exemplification exist while a does not exemplify Fness. (Consider a possible world in which a does not exemplify Fness but b exemplifies Fness.) So, a, Fness, and exemplification must be related by a further relation(s), and so on, ad infinitum.
The Bradley's regress pushes us to answer the question of the existence of what kinds of entities can guarantee the truths of a certain predication. As we have seen, the mere existence of a particular and a universal does not entail that the particular has the universal. Something more is needed. Armstrong, a diehard fan of universals, believes that the moral here is that realists should posit, in additional to universals, the so-called states of affairs, or facts.Footnote 15 For instance, suppose that a is F. Although the mere existence of a and the universal Fness is not sufficient for the truth, the existence of the state of affairs a's being F does guarantee that a is F because it is impossible that this state of affairs exists but a is not F. Therefore, Bradley's regress, or more generally, the problem of universals, calls for an explanation indicating what makes a predication true, or in a more famous terminology, a truth-making explanation rather than conceptual analysis of predications.Footnote 16
So, what exactly is a truth-maker? On a prevalent view, an entity E is a truth-maker of a true predication P if and only if E necessitates P’s being true or that E exists entails that P is true.Footnote 17 The definition is inadequate because it renders all necessary truths being made true by everything. Since our present concern is to answer the problem of universals instead of spelling out a complete theory of truth-makers, we may leave necessary truths aside at this stage. This definition suffices for our purpose now because most truths related to the problem of universals are contingent.Footnote 18
Let us come back to TCN. Suppose that Fido is white. Now we are looking for the truth-maker of the predication that Fido is white. Although I have kept mentioning only divine representations as (partial) causes of the existence of objects, the full account given by TCN is as follows: Fido is white because E Fido is jointly caused by (i) E white and (ii) God's mental event of His intending or willing to conserve or create Fido according to E white. There are two of God's mental events on the scene: (i) His divine representation of white and (ii) His intention to conserve or create Fido according to it. We have noticed that the mere existence of E Fido and E white cannot make the causal claim that E white causes E Fido true, and therefore cannot make the predication that Fido is white true. However, note another event on the scene, i.e. God's intention to conserve or create Fido according to E white. This event undoubtedly makes the following claim true: ‘God intends or wills to conserve or create Fido according to E white.’ Furthermore, this truth and another truth that God is omnipotent jointly entail that Fido is white since it is impossible that an omnipotent God wills so but it turns out otherwise. In other words, the truth-maker of ‘God intends or wills to conserve or create Fido according to E white’ in conjunction with the truth-maker of ‘God is omnipotent’ can guarantee the truth of the predication that Fido is white. Given the second assumption made in the first section, the truth-maker of ‘God is omnipotent’ is God Himself. Therefore, the truth-maker of the predication that Fido is white is (i) E white, (ii) God's intention to conserve or create Fido according to E white, and (iii) God Himself.Footnote 19 The existence of these three things can explain why Fido is white.
Now in this explanation, the truth of the predication that Fido is white is explained or analysed in terms of no causal claim but God and His certain mental events. Therefore, the regress problem does not occur at all. However, one might wonder whether the causal claims, e.g. that E dog causes E Fido, still play any role at all. My answer is that they do not really explain anything. What does the explanatory work is the truth-makers. In fact, the truths of causal claims are just epiphenomena supervening on truth-makers, e.g. the truth that E dog causes E Fido supervenes on the existence of (i) God, (ii) E dog, and (iii) God's intention to create or conserve Fido according to E dog.Footnote 20 Given the existence of relevant truth-makers, the truths of corresponding causal claims follow. Hence, there is no need to posit any Platonic entities to back the truths of causal claims.
In sum, on the one hand, it is widely agreed now that to give a theory of properties, or to answer the problem of universals, is nothing more than to provide truth-makers of the truths of predications. On the other hand, I have argued that TCN has its own resources to do so. This is, I suggest, how the regress problem for TCN can be solved.
Objections to the truth-making solution
In the previous section, we have seen that according to the truth-making solution, the truth-maker of a predication that a is F is (i) God, (ii) God's divine representation of F, (iii) God's intention to create or conserve a according to His divine representation of F. In this section, I deal with four objections to this truth-making solution. I hope that our understanding of it will be deepened by replying to these objections.
First, some opponents might claim that the truth-maker must be closely related to its truth. For instance, John's funeral also necessitates that John is dead. But it is absurd to claim that the funeral is the truth-maker of the predication that John is dead. Intuitively, the very truth is about John's death instead of his funeral. Likewise, although the existence of (i) E dog, (ii) God's intention to conserve or create Fido according to E dog, and (iii) God can necessitate the truth of the predication that Fido is a dog, they seem not what the truth is directly about. The opponents might then object that only the state of affairs Fido's being a dog or the trope Fido's doghood are eligible to be the truth-maker of the true predication that Fido is a dog.
Smith raises the foregoing objection (though in a different context) and suggests that truth-makers should be defined in terms of the notion of projection.Footnote 21 Roughly speaking, the projection of a true predication is the fusion of all things to which the terms occurring in that predication refer. Thus, he proposes the following definition: an entity E is a truth-maker of a true predication P if and only if E necessitates that E is a part of the projection of P. Since John's funeral is not referred by any term occurring in the predication that John is dead, John's funeral is not a part of its projection. According to Smith's definition, John's funeral will not be classified as a truth-maker of the predication that John is dead. Likewise, for him, God's mental events and Himself are not the truth-maker of the predication that Fido is a dog since they are not referred by terms occurring in it.
However, I cannot see why God's mental events are not parts of the projection of the predication that a is F. In fact, what an abstract term refers to depends on which theory of properties is true. On Platonism, the predicate ‘F’ or its nominalized term ‘Fness’ refers to a Platonic universal. For class nominalists, it refers to a class of particulars. If trope theory is true, its reference will be a trope. Similarly, nothing prevents the proponents of TCN from holding that it refers to some mental event(s) of God. Excluding God's mental events from the projection of a predication simply begs the question.Footnote 22
Also, it is not clear why the state of affair Fido's being a dog or the trope Fido's doghood can be the truth-maker of the predication that Fido is a dog but God and His mental events cannot. On the contrary, for classical theists, since God is the most fundamental thing, all or nearly all non-divine entities depend for their existence on God.Footnote 23 Thus, on classical theism, it is God and His creative activity rather than other putative non-divine entities which constitute the ultimate explanation of the truths of predications. There is no good reason (for classical theists) to accept that God and His mental events cannot serve as the truth-maker of the predication that Fido is a dog.
The second objection arises from the case of free actions. Suppose that both Suzy and John freely X where ‘X’ stands for a basic action, e.g. raising one's left hand. According to the truth-making solution, ‘Suzy Xs’ and ‘John Xs’ are true because God intends to create or conserve them according to the divine representation of X. If free actions here are understood in a compatibilist sense, then God and His mental events will have no difficulty in making their actions free. This can be done if God also lets them have the proper mental state when they perform the very action. However, if their free actions are libertarian, then it seems that God and His mental events cannot be the truth-makers of these predications. On the one hand, since a truth-maker is something which can guarantee the truth of a predication, its existence has to necessitate the predication's being true. On the other hand, a (libertarianly) free action, by definition, is not necessitated by anything external to the agent. Therefore, the truth-makers of true predications about libertarianly free actions cannot be God and His mental events.
Here we run into something very similar to the theological fatalist argument in which God's foreknowledge and His omniscience necessitate one's action in the future. In the present case, God's foreknowledge and omniscience are replaced respectively by His creative will and omnipotence. A typical reply to the theological fatalist argument comes from Ockhamism. Ockhamists distinguish between hard and soft facts about the past. Hard facts are facts wholly about the past while soft facts are in part about the future. For instance, Trump's being elected 1 year and 1 month before I type this sentence is a fact about the past but someone, i.e. the author of this article, has the power to bring about its non-occurrence. If I were not to type it, then this fact would not occur. Ockhamists call this kind of facts soft facts. Now the Ockhamist solution to the theological fatalist argument is that since God's foreknowledge is a soft fact, its occurrence is compatible with one's power to do otherwise. If one were to do something contrary to the content of God's foreknowledge, its content would be different. Therefore, one's free action will not be necessitated by God's foreknowledge. Regardless of the success or failure of Ockhamism, the proponents of the truth-making solution might attempt to make a similar move. For example, they might argue that since God's will or intention is a soft fact (or event), one's free action is not necessitated by it (and God Himself). However, this reply does not work because if God's will or intention is soft, it means that its content would change if one were to do otherwise. This seems plainly contradictory to the meaning of ‘creative intention’. Unlike God's foreknowledge, God's creative or conservational intention is by no means determined by one's free action.
My own preferred reply is that God's intentions are only parts of the truth-makers of predications about actions. To be more precise, on my view, God's intention does not necessitate that John Xs. Rather, it only confers the power or disposition to X on John. This is why it cannot make the predication that John Xs true alone. Rather, the predication that John Xs is made true by the existence of God, the divine representation E x, God's intention(s), and John's own intention all together. Among these, what makes the disposition to X manifest is John's own free intention to X. But, we should note that God's divine representation and His intention(s) are still indispensable because they (i) bestow the power to X on John and (ii) provide a suitable environment or opportunity for him to exercise that power. Without them, John's intention alone does not suffice to make the predication true. Perhaps it is proper to say that the truths of this kind of predications are explained in terms of the cooperation of God and human agents.
Another objection is that since the idea of truth-making has its own difficulty, it cannot be invoked to aid TCN in answering the problem of universals. A theory of truth-makers does not merely explain positive truths about properties. Besides the truths with which we concern ourselves in the present context, there are other kinds of truths like negative truths, i.e. truths of the forms ‘a is not F’ or ‘there is no F’, and universal truths, i.e. truths of the form ‘all Fs are Gs’. Presumably, a satisfactory theory of truth-makers should also provide explanations of these truths, or else it will be unclear why positive singular truths need any explanation or truth-maker at all if these truths do not. However, it is highly disputed what their putative explanations or truth-makers should be and whether they are ontologically acceptable.
Armstrong posits a totality state of affairs which is a higher-order state of affairs consisting of the aggregate of (i) all first-order state of affairs, (ii) the totalling relation, and (iii) the property of being a first-order state of affairs. The existence of the totality state of affairs guarantees that there is no more first-order state of affairs other than those included in the aggregate. Armstrong holds that this totality state of affairs can serve as the truth-maker of all general truths and negative truths.Footnote 24 Some object that the truth-makers of general truths and negative truths should be more fine-grained.Footnote 25 For instance, the subject matter of the general truth that all ravens are black is ravens, so its truth-maker should be different from the truth-maker of the general truth that all humans are mortal, whose subject matter is humans. Likewise, the truth-maker of the negative truth that Fido is not a cat seems to be different from the one of the negative truth that Fido is not white since it is intuitive that what makes Fido not a cat is different from what makes Fido not white.
To avoid positing controversial entities like negative facts or totality states of affairs, Bigelow proposes the following principle ‘truth supervenes on being’: if something is true then it would not be possible for it to be false unless either certain things were to exist which don't, or else certain things had not existed which do.Footnote 26 Roughly speaking, the principle allows that some propositions might be true in virtue of the absence of something rather than the existence of something. For instance, the negative claim that Fido is not white is true because there does not exist the possible truth-maker of the positive claim that Fido is white, and if it were to exist, the negative claim would be false. Similarly, the general truth that all ravens are black is true because there exists no counterexample, e.g. a white raven, to it. However, this modified truth-making explanation is problematic too since general truths and negative truths are still explained in terms of other negative existential truths of the form ‘there is no entity E such that if E were to exist, the general/negative truth would be false’.Footnote 27 On pain of infinite regress, these negative existential truths cannot be explained in the same way. Therefore, some negative truths are left unexplained after all.
Man's extremity is God's opportunity. In dealing with this problem, a theistic theory of truth-makers exhibits its advantage. On TCN, the truth-makers of positive truths are God and His mental events (as concrete particulars). One merit of a theistic theory of truth-makers is that for negative truths and general truths, there is no need to posit different kinds of truth-makers, e.g. negative facts or totality states of affairs. Negative truths and general truths are also made true by God and His mental events. For instance, the truth-maker of the negative claim that Fido is not a cat is (i) God, (ii) E cat, and (iii) His intention to create or conserve Fido not according to E cat; the truth-maker of the negative existential claim that there is no unicorn is (i) God, (ii) E unicorn, and (iii) His intention to not create anything according to E unicorn; the truth-maker of the general claim that all ravens are black is (i) God, (ii) E raven, (iii) E black, and (iv) His intention to not create or conserve anything according to E raven but not according to E black.Footnote 28 All these entities are concrete particulars. Neither do we posit any dubious or ad hoc entities (like Armstrong), nor do we leave any negative truths unexplained (like Bigelow). Therefore, I conclude that a theistic theory of truth-makers is free from this objection.
The final objection is about the truths of truth-making claims. The opponents might argue that the truth-making solution also has its own version of the regress problem. Consider the following explanation: (i) God, (ii) Edog, and (iii) His intention to create or converse Fido according to Edog make the claim that Fido is a dog true. Call the propositionFootnote 29 expressing this explanation P 1. Since P 1 is true, the opponents might ask what makes it true. Suppose that E 1 is its truth-maker. Let P 2 be the proposition that E 1 makes P 1 true. Obviously, this truth-making explanation is true too. Thus, we can further ask what makes P 2 true, and so on, ad infinitum.
This is not a problem for TCN only. If truth-makers are Armstrongian states of affairs, we can ask what makes the claim that the state of affairs Fido's being a dog is the truth-maker of the truth that Fido is a dog true. Armstrong's own reply is that since it is impossible that the state of affairs Fido's being a dog exists but does not make the claim that Fido is a dog true, the same state of affairs (perhaps in conjunction with the truth-bearer, be it a proposition or what have you) can serve as the truth-maker of the truth-making claim.Footnote 30 Likewise, it is impossible that God and His mental events exist but do not make the claim that Fido is a dog true. Therefore, we may say that they are the truth-maker of other truth-making claims. As Armstrong says, there are many truth-making explanations if you like, but only one truth-maker.Footnote 31
However, the foregoing reply will not be quite satisfactory if the idea of ‘explanation’ is taken seriously. Even if the state of affairs Fido's being a dog does explain why Fido is a dog, it is still unclear why the same state of affairs also explains why it makes the claim that Fido is a dog true. Explanations are deemed to be informative. The state of affairs Fido's being a dog does not seem to provide any further information about the infinitely many truth-making claims.
Again, this is a problem, I think, for all metaphysicians. Generally speaking, this is a question of what grounds/explains facts about what grounds/explains what. Explanations themselves either stand in need of explanation or not. If not, then this will be good news for the proponents of TCN since we do not need to explain the truths of truth-making claims. Thus, there is no regress problem. On the other hand, if explanations stand in need of explanation, then we need to appeal to some further fact(s) to explain them. Some philosophers believe that it is the essence or real definition of the grounded fact, or explanandum, which explains the whole explanation.Footnote 32 If this line of thought is applied to the case of states of affairs, we can say that the essence of the proposition explains why the state of affairs makes the claim that Fido is a dog true. At this point, one may ask what explains why the proposition's essence is as it is. If facts about essences have further explanation, then the problem will remain. If they do not, then we will need to live with lots of unexplained facts about essences of propositions, among other things. Therefore, the essentialist approach requires us to accept many brute facts about essences into our theory.
However, it is not always a bad thing to be unexplained. For instance, classical theists are happy to accept that facts about God's existence and essence are unexplained.Footnote 33 Hence, it will be helpful if we can explain the truths of truth-making claims in terms of these unexplained but theologically acceptable facts. For example, it may be the case that God's essence is such that for any proposition P, if God were to will P, then God and His relevant mental events would make P true. If this, or some similar story, is true, then the truth of truth-making claims can be explained without generating any vicious regress. Here, theistic essentialists have an edge over their secular fellows because they do not need to accept too many brute facts, and the only price, i.e. taking facts about God's essence as primitive or unexplained, is something which they, as classical theists, have already paid.
By considering these four objections, I think that it has been made clear that the truth-making solution is defensible. If immanent realists, e.g. Armstrong, and trope theorists, e.g. Smith, are justified in answering the problem of universals by providing truth-makers of certain true predications, there is no reason why the proponents of TCN cannot do the same trick. On the contrary, my replies to the last two objections have indicated that TCN is more appealing than other non-theistic theories because it works better when we take the explanation of negative/general truths and the explanation of explanatory claims into consideration. I hope that this shows that TCN is not only a coherent but also a competitive theory of properties.
