Background and preliminaries

According to the doctrine of divine simplicity, as held by many mediaeval philosophers and theologians in Judaism, Christianity, and Islam, God is absolutely simple, lacking any sort of metaphysical complexity whatsoever; he has neither parts nor distinct intrinsic properties.Footnote ¹ There are different ways in which the doctrine of divine simplicity can be understood. A standard understanding of the doctrine, which can be called the property interpretation of divine simplicity (or more simply, the property interpretation), has it that God does possess intrinsic properties, such as omnipotence, omniscience, wisdom, etc., but all these properties are identical with each other, and with God himself. More generally:

In recent decades, however, the property interpretation has been forcefully challenged by several philosophers, most notably by Alvin Plantinga in his seminal work Does God Have a Nature? Perhaps the main difficulty with the property interpretation, initially introduced by Plantinga and further developed by Brower (Reference Brower2008 and Reference Brower, Flint and Rea2009) and others, is that the property interpretation would undermine what Brower calls ‘the traditional conception of properties (and substances)’. According to this conception, properties and substances belong to two ontologically distinct categories: properties (regardless of whether conceived as universals or as tropes) are exemplifiable entities, while substances cannot be exemplified by anything. It is not difficult to see that such a conception would render the property interpretation of divine simplicity seriously objectionable. One of the central tenets of traditional theism is that God is a person, at least in the broad sense of an entity capable of awareness, love, knowledge, and other characteristics constitutive for personhood. But persons are subsumed under the category of substances (namely, non-exemplifiable entities). Thus, given the traditional conception of properties, God cannot be identical with a property (namely, an exemplifiable entity), no matter whether we conceive of properties as universals or as tropes.Footnote ³

The alleged problem just mentioned with the property interpretation, which is sometimes called ‘the category problem’, eventually led some philosophers (Oppy (Reference Oppy2003); Bergman and Brower (Reference Bergman, Brower and Zimmerman2006); Brower (Reference Brower2008); Pruss (Reference Pruss and Kvanvig2008); Brower (Reference Brower, Flint and Rea2009)) to propose that divine simplicity is better understood in terms of truthmakers rather than properties. The general idea, which can be called the truthmaker interpretation of divine simplicity (or more simply, the truthmaker interpretation), comes in different forms. The core thesis, however, might be stated as follows:

As the above formulation makes clear, the truthmaker interpretation is not committed to God's being identical with a property, and thus is compatible with the traditional conception of properties.

Presumably, the truthmaker interpretation is the most promising suggestion so far proposed to make sense of divine simplicity. But I shall argue that it is faced with a real difficulty: given some plausible assumptions, it is at odds with what I shall call ‘the univocity thesis’, namely the plausible idea that there are ‘natural’ intrinsic predicates (such as ‘wise’, ‘just’, etc.) which apply with the same meaning to both God and created beings.Footnote ⁵ Moreover, I shall argue that the difficulty with the truthmaker interpretation cannot be remedied by abandoning the univocity thesis in favour of the Thomistic view that although no (natural) predicate univocally applies to God and creatures, some predicates can analogically apply to both. The conclusion which emerges is that the only way in which the advocate of the truthmaker interpretation can retain the idea that there are natural predicates which apply, either univocally or analogically, to both God and created beings is to opt for a wholesale radical nominalist position (with its own costs).Footnote ⁶ To begin with, let us first look at the truthmaker interpretation more closely.

The truthmaker interpretation of divine simplicity

According to advocates of the truthmaker interpretation, all that the traditional doctrine of divine simplicity requires is to identify God with his wisdom, his love, his omnipotence, etc. More generally, the doctrine involves nothing more than the following:

The crucial point, however, is that DS is itself silent about the metaphysical category to which God's F-ness belongs. Now, there are several options as to how to understand God's F-ness. A popular account is to identify God's F-ness with a property, F-ness, which God possesses. Obviously, this is tantamount to the property interpretation and would therefore inherit all of its alleged absurdities. Thus, to avoid identifying God with a property, the truthmaker interpretation recommends that DS be cashed out in terms of truthmakers rather than properties. Accordingly, the following truthmaker account of predication is suggested:

It is clear how TA leaves room for us to avoid identifying God with a property. According to DS, God is identical with his wisdom. Now, given TA, God's wisdom is to be understood as the truthmaker for ‘God is wise’, but such a truthmaker need not be identified with a property. Brower contends, in agreement with many contemporary philosophers, that the notion of a truthmaker should be partly understood in terms of a broadly logical necessitation:

Although TN only provides a necessary condition for a truthmaker, when an entity satisfies the condition it can be regarded as a candidate (perhaps even a strong candidate) for being a truthmaker (Brower (Reference Brower2008), 18; see also Bergman and Brower (Reference Bergman, Brower and Zimmerman2006), 380–381 and Brower (Reference Brower, Flint and Rea2009), 111). Consonant with these ideas, Brower plausibly argues that nothing in truthmaking theory rules out the possibility of a concrete individual serving as the truthmaker for all its true intrinsic essential predications. As an example, consider ‘Socrates is human’. The mere existence of Socrates necessitates the truth of ‘Socrates is a human’. Thus, Socrates himself can be regarded as the truthmaker for that truth. The same is the case for intrinsic predications of God, such as ‘God is wise’. Given the assumption that all true intrinsic predications of God are also essential predications,Footnote ¹⁰ it follows that God is essentially wise. But, if so, God can be regarded as the minimal truthmaker for ‘God is wise’. More generally, the truthmaker interpretation puts forward the following thesis:

Clearly, TA and TIP would provide advocates of the truthmaker interpretation with all they need: the conjunction of TA and TIP entails Truthmaker-DS, which I have introduced as the core idea of the truthmaker interpretation.

It is hard to disagree with Brower (Reference Brower2008) that the truthmaker interpretation ‘goes a considerable distance toward rendering the doctrine of divine simplicity coherent’. This interpretation, at least at first glance, can preserve the idea that God is identical with his wisdom, his justice, his love, etc., without getting into the absurdity of identifying God with a property. In fact, the truthmaker interpretation amounts, so to speak, to a kind of nominalism about divine attributes: God does not have any intrinsic properties at all (in the ontologically loaded sense of exemplifiables), and thus the question whether he is identical with his properties does not arise in the first place. Nevertheless, in the next two sections I shall argue that the truthmaker interpretation is confronted with a grave problem, as it tends to undermine the widespread assumption that there are natural predicates that are applicable, either univocally or (at least) analogically, to both God and some other beings. It seems that the only available way in which proponents of the truthmaker interpretation might preserve the above assumption is to opt for a wholesale radical nominalist position according to which not only God, but also mundane objects, lack any intrinsic property (in the ontologically loaded sense). Although this does not constitute a decisive rebuttal of the truthmaker interpretation, it does show that the truthmaker interpretation is far more constrained than it has been conceived so far.Footnote ¹²

The objective similarity argument

So far we have seen that Truthmaker-DS crucially hinges upon TIP. Nevertheless, I shall argue in the present section that given some plausible assumptions, TIP is incompatible with the univocity thesis. To set the stage for the argument (which might be called ‘the objective similarity argument’) let us very briefly rehearse two major motivations for positing properties, which are especially relevant to the present discussion: solving the one-over-many problem, and providing truthmakers for some truths. I will be more concerned with the relationships between these motivations than with their plausibility in their own right. Let us now begin with the first motivation, highlighting some ideas to be deployed in due course.

It is an undeniable fact that there are objective (that is, mind- and language-independent) similarities between particulars, and that these similarities are always relative to some respect. For example, human beings resemble each other in kind (or in their being human), and red things resemble each other in colour (or, in their being red). Furthermore, objective similarities can be inexact, as witnessed by the fact that 10 kg objects, for example, inexactly resemble 9 kg objects with respect to their mass. As illustrated by these examples, the respect relative to which two things objectively resemble each other can typically be specified in two different ways: sometimes it is specified by employing the very predicate that applies to the resembling objects – as, for example, in ‘a and b resemble each other in their both being red’.Footnote ¹³ But sometimes the relevant respect is specified in a more abstract way, as in ‘a and b resemble each other in colour’.

Now, it has been famously argued that objective similarities between particulars call for an explanation, and that the best explanation is obtained through positing a sui generis ontological category of properties. This broad idea comes in two versions: tropism and realism, whose proposed solutions for the one-over-many problem are well known.Footnote ¹⁴ In particular, according to tropism, (in)exact resemblance between two objects is explained by (in)exact resemblance between tropes they possess. Again, the resemblance between tropes themselves is always relative to a specific respect: two red tropes, for instance, resemble each other with respect to their kind (or, in their both being red tropes). Admittedly, it is constitutive of our very conception of resemblance that any resemblance, whether exact or inexact, holds only relative to a certain respect. Resemblance between tropes, if there are such entities, is no exception. At any rate, the one-over-many problem is not an unassailable motivation for positing properties. Radical nominalists take objective similarities between particulars as primitive: red things resemble each other because they are red. Nothing deeper is required.Footnote ¹⁵

Another major motivation for positing properties has to do with truthmaking considerations. Many philosophers, including Brower (Reference Brower2008 and Reference Brower, Flint and Rea2009) himself, have plausibly argued that at least some true subject-predicate sentences require truthmakers, and that we are obliged to posit properties to fulfil such a requirement. Consider, for example, a contingent truth like ‘Socrates is wise’. Since Socrates himself does not necessitate the truth in question, we need another entity to serve as its truthmaker. Two main options have usually been proposed to fulfil the role: (i) a fact (or a concrete state of affairs) which consists in Socrates’ instantiating the universal property of wisdom, and (ii) a non-transferable wisdom trope which is essentially dependent on Socrates.Footnote ¹⁶

So far we have seen that properties are supposed to play two different roles, each of which is alleged to provide a motivation for positing properties: explaining resemblances and providing truthmakers. Notice that these two motivations need not completely coincide with each other. One might be only motivated by the truthmaking consideration, and not by the one-over-many problem, to posit properties. For example, despite the fact that there is an objective similarity between human beings in their all being human, one might suggest, as Brower (Reference Brower, Flint and Rea2009, 12) seemingly does, that we need not posit such a universal property as humanity, nor a class of humanity tropes. For, according to the present suggestion, there is no need for such a property (or properties) in providing a truthmaker for truths like ‘Socrates is human’. This is in spite of the fact that Brower is quite willing to posit properties whenever they are required for truthmaking, as in the case of ‘Socrates is wise’.

Although the two roles just mentioned (explaining resemblances and providing truthmakers) are distinct, it seems that there is an intimate connection between them. To see this, suppose that both a and b are red, and that we have posited two colour tropes, t ₁ and t ₂, to play the role of truthmakers for ‘a is red’ and ‘b is red’, respectively. Given this, it would be entirely implausible to take the objective similarity between a and b with respect to their colour as a primitive unexplainable fact. If it is t ₁ and t ₂ which explain the truths that a is red and b is red, respectively, then any account of the colour similarity between a and b must essentially involve t ₁ and t ₂ as well (for example, the colour similarity between a and b can be explained by the fact that t ₁ resembles t ₂, as proposed by the standard tropist approach). Likewise, if we take the truthmaker for ‘a is red’ to be a fact consisting in a's exemplifying the universal property of redness (and similarly for ‘b is red’), then that universal property must be essentially invoked in our explanation for the colour similarity between a and b: they resemble each other with respect to their colour because they both instantiate the universal property of redness.Footnote ¹⁷ Generalizing this intuitive idea, we can arrive at the following thesis scheme, where ‘a’, ‘b’ and ‘F’ are to be replaced, inside and outside all quotation marks, by any two names and any predicate, respectively:

Notice that TSL does not require that any objective resemblance should be explained by positing properties. Rather, it is only committed to a weaker and intuitively plausible idea that when a property is already posited to play the role of truthmaking, it should also play an essential role in explaining the relevant objective similarities.Footnote ¹⁸

I am now in a position to present my main argument against the truthmaker interpretation, or more precisely, against its essential ingredient, TIP. The argument is rather indirect: I first take for granted three theses, namely TIP, the univocity thesis, and TN, and then argue that such a combination would result in an insuperable difficulty. But since both the univocity thesis and TN are not only highly plausible but also held by prominent advocates of the truthmaker interpretation,Footnote ¹⁹ it is TIP that should go, or so one might argue. Before proceeding further I must make a preliminary remark, which will be appealed to repeatedly in the argument. According to TIP, God himself, and not any property, is the truthmaker for the true intrinsic predications of God. This entails that God is not identical with any property whatsoever. Since if God were identical with a property, then that property would also be the truthmaker for those truths, contrary to what TIP requires.

Let us begin by saying a word about the univocity thesis. Admittedly, predicates like ‘wise’, ‘good’ and ‘just’ are natural predicates: they are not disjunctive, negative, or ‘grue’-like ones. Moreover, they seem to apply to God with the same meaning as to created beings – or, at least, there is a substantial overlap in meaning when they are (truly) used in these two domains. Notice that even partial overlap in meaning (or, partial univocity, to use Alston's terminology) between terms applicable to God and other beings is sufficient for the univocity thesis to hold. According to Alston (Reference Alston1989), although some predicates do not apply to God in exactly the same sense in which we use them in our ordinary language, we can subtract from the concept they express all items inconsistent with the divine nature, and finally end up with a concept that could be true of God, while retaining the core of the original one. The resultant new concept, then, could be expressed by a predicate which would apply, univocally this time, to both God and some other beings.Footnote ²⁰

Now, take ‘wise’, for example, which univocally applies to both God and another being, say, Socrates. According to TIP, the truthmaker for ‘God is wise’ is not a property, but God himself; whereas according to TN, the minimal truthmaker for ‘Socrates is wise’ cannot be Socrates himself, as he does not necessitate that truth. Thus, we are obliged to take its truthmaker to be either a wisdom trope possessed by Socrates or a fact constituted by Socrates’ exemplifying the universal property of wisdom. Parallel to these two alternatives, the argument would unfold in two parts. For the sake of simplicity, however, I will only be concerned with the tropist alternative, though the following remarks will apply, mutatis mutandis, to the realist alternative as well.

Suppose that t is the wisdom trope that makes ‘Socrates is wise’ true. Since ‘wise’ is a natural predicate which univocally applies to both God and Socrates, it follows that they (inexactly) resemble each other with respect to their both being wise. Now given TSL, we can conclude that t must play an essential role in explaining the objective similarity between God and Socrates in that respect. But it seems that there are only two options as to how t can play such a role. The first option is that the explanatory role t is supposed to play is analogous to typical cases where tropes are appealed to for explaining similarities: God possesses, just as Socrates does, a wisdom trope t*, and the resemblance between God and Socrates is to be explained in terms of resemblance between t and t*. Given the present dialectical context, however, this option must be rejected. For if t* is supposed to be distinct from God, then the first option would explicitly contradict the very idea of divine simplicity, as it would introduce a kind of metaphysical complexity in God. But if t* is taken to be identical with God, then the present option would clearly amount to God's being identical with a property, which is at odds with TIP (and also with the traditional conception of properties).Footnote ²¹

We are forced, therefore, to opt for the second option: God does not possess any trope, and the (inexact) similarity between God and Socrates should be explained in terms of an (inexact) similarity between t and God himself, not between t and a wisdom trope possessed by God. But, as pointed out, any resemblance whatsoever holds only relative to a certain respect. Thus, the second option would be admissible only if the two following conditions can be satisfied:

I shall argue, however, that these two conditions cannot be satisfied, and therefore the second option should be rejected as well. Let us begin with C1. There are several possible options as to the respect relative to which God and t resemble each other, only the last of which might be acceptable:

The first option is not even remotely acceptable, since no (creaturely) wisdom trope like t can be wise. Nor is the second option acceptable, since as we have seen, TIP has it that God cannot be a property. R3 has a better status; no doubt both God and t are truthmakers for ‘something is wise’. Let us abbreviate the predicate ‘is a truthmaker for “something is wise”’ as ‘T_wise’. The problem with R3, nevertheless, is that ‘T_wise’ is not a natural resemblance-conferring predicate, and consequently it is not the case that God and t resemble each other in their both being T_wise. I do not have a comprehensive theory as to when a composite predicate is natural, but I find the following thesis intuitively plausible.

For example, it is very odd to maintain that ‘. . . loves Socrates’ is natural while ‘. . . loves Plato’ is not: rather, we should say that either both or neither of the two predicates are natural. The idea behind NP might be stated as follows: whether or not a composite predicate is natural is a function of the naturalness/non-naturalness of its constituents (when the issue of naturalness is in principle applicable to the constituent in question) plus the way they are combined with each other. But the question of naturalness does not arise for singular terms; they are not the kind of expressions which might be (non-trivially) described as natural or non-natural, at least given the notion of naturalness at issue in the present context. Thus, the identity of singular terms contained in ‘F’ is irrelevant to whether it is natural or non-natural. That is, replacing those singular terms with other ones cannot affect the naturalness/non-naturalness of the resultant predicate.Footnote ²³

Turning to our case, to explore whether or not ‘T_wise’ is natural we should first examine the semantic function of the quotation embedded in ‘T_wise’. It seems that given any theory of quotations so far proposed, ‘T_wise’ can be shown to be non-natural. Because of space limitations I cannot go through the details, and shall rest content with presenting a very sketchy argument. Generally speaking, all theories of quotations treat them either as singular terms or else as definite descriptions, which designate (on both alternatives) quoted expressions.Footnote ²⁴ According to singular-terms theories, ‘T_wise’ should be taken as consisting in a two-place predicate (i.e. ‘. . .is a truthmaker for. . .’) saturated by a singular term (i.e. ‘something is wise’). Given this, NP has it that if ‘T_wise’ is a natural predicate then so would be all the predicates of the form ‘. . . is a truthmaker for “S”’ (where ‘S’ is to be replaced with any declarative sentence in English). But there are predicates of this form which are not natural. Consider for example ‘. . . is a truthmaker for “something is number-or-human”’ (let us abbreviate this as ‘T_{number−or−human}’). Both the number two and Socrates are T_{number−or−human}. But their both being T_{number−or−human} does not constitute an objective similarity between them. In this respect, ‘T_{number−or−human}’ is just like ‘is number-or-human’: just as the fact that two entities are number-or-human does not make them objectively similar to each other, neither does their both being T_{number−or−human}. I submit, therefore, that ‘T_{number−or−human}’ is not a natural predicate. Neither, then, would be ‘T_wise’.

A rather similar line of reasoning can be given if we opt for any variety of the definite-description theories of quotations. The main point is that such theories utilize descriptions which contain singular terms which refer to the quoted expressions or their parts. Consider, for example, the so-called ‘Description Theory of Quotation’ proposed by Geach (Reference Geach1972) and Quine (Reference Quine1960), among others. According to a version of this theory, ‘something is wise’ is to be read as ‘the expression which is constructed by concatenating ^┌something^┐, ^┌is^┐ and ^┌wise^┐ in this specific order’, where ‘^┌something^┐’ and the like are (unstructured) proper names which refer to the respective words. On this theory, therefore, ‘T_wise’ will be read ‘. . . is a truthmaker for the expression which is constructed by concatenating ^┌something^┐, ^┌is^┐ and ^┌wise^┐’. But NP implies that if ‘T_wise’ is natural then so would be the predicate which results from substituting ^┌wise^┐ by ^┌number-or-human^┐. But the resultant predicate, which is in fact ‘T_{number−or−human}’ introduced in the previous paragraph, is admittedly non-natural.Footnote ²⁵

I contend, therefore, that R3 is not acceptable.Footnote ²⁶ The next option, R4, is in the same spirit as R3, and as expected inherits its shortcoming. My discussion of R3 is applicable mutatis mutandis here, which I shall not repeat.Footnote ²⁷ As for R5, it should be rejected as well. According to this option, God and t resemble each other in their both being something's wisdom: God is God's wisdom and t is Socrates’ wisdom. As we may recall from the previous section, there are two main alternatives as how expressions of the form ‘a's F-ness’ should be interpreted. According to the property account, ‘a's F-ness’ refers to a property possessed by a. On this account, God's wisdom (if it exists) is a property and thus, it cannot be identical with God. According to the truthmaker account, TA, ‘a's F-ness’ refers to the truthmaker for ‘a is F’. Assuming this latter account, it is true that God is God's wisdom (God is the truthmaker for ‘God is wise’) and t is Socrates’ wisdom (t is the truthmaker for ‘Socrates is wise’). But the claim that God and t resemble each other in their both being something's wisdom will boil down to the claim that they resemble each other in their both being a truthmaker for a sentence of the form ‘x is wise’, which is what R4 states. But we have seen that R4 is not acceptable either.Footnote ²⁸

The only option which might have a chance of success is R6: God and t resemble each other in their both being concrete objects.Footnote ²⁹ The crucial problem, nevertheless, is that the second condition mentioned above, C2, cannot be satisfied here: such a similarity between God and t cannot explain the similarity between God and Socrates in their both being wise. The resemblance with respect to being concrete is too broad to be able to play the requisite explanatory role here. God not only resembles t in that they are both concrete objects, but also resembles other tropes possessed by Socrates, say a whiteness trope w, in that very respect. Now, if God-t resemblance in their both being concrete objects could explain God-Socrates resemblance in their both being wise, then, by parity, God-w resemblance in their both being concrete objects would have to be able to explain God-Socrates resemblance in their both being white. But the consequent of the conditional just mentioned does not hold, for the simple reason that God does not resemble Socrates in that they are both white, as he lacks any colour at all! To put the idea differently, when a fact explains another fact then the first one can be said to bring about (so to speak) the second one, at least given the notion of explanation employed in the present context. Now the problem is why God-t resemblance in their both being concrete objects can allegedly bring about God-Socrates resemblance in their both being wise, while God-w resemblance in their both being concrete objects cannot play an analogous role in bringing about God-Socrates resemblance in their both being white.

Thus far, we have seen that all the six options which might be proposed as to the respect in which God and t resemble each other are either false, or, alternatively, offer a kind of resemblance which cannot explain the similarity between God and Socrates in their both being wise. Perhaps there are analogous options in the vicinity, but I take it that they would be vulnerable to analogous problems. As far as I can see, there is no option which can satisfy both C1 and C2 mentioned above. We can conclude, therefore, that the resemblance between God and Socrates cannot be explained by a similarity between God and t.

Let us recap what we have arrived at so far. God and Socrates are objectively similar to each other in their both being wise. The truthmaker for ‘Socrates is wise’ is a wisdom trope Socrates possesses, t. Given TSL, therefore, t must play a substantial role in explaining the resemblance between God and Socrates. This cannot be done by positing a wisdom trope possessed by God, t*, which is to resemble t. For it would betray either TIP (if t* were identical with God), or the very idea of divine simplicity (if t* were distinct from God). The only remaining way in which t could play the requisite explanatory role is to resemble God himself. But then we will encounter a severe difficulty in specifying the respect relative to which God and t can resemble each other. The upshot is that TIP, the univocity thesis, and TN constitute an incompatible triad. But given the deep plausibility of both the univocity thesis and TN, TIP should be dismissed as seriously problematic.

As a matter of course, there are two possible options for proponents of the truthmaker interpretation to resist the pressure posed by the objective similarity argument. The first option is to give up the univocity thesis and go for a different stance towards divine predication. For example, they might be willing to embrace a Thomistic view according to which predicates like ‘wise’ can apply, at most, analogically to both God and created beings. I will explore the prospect of such a manoeuvre in the next section. The second option is to abandon TN in favour of a nominalism-friendly construal of truthmaking. The idea behind this latter option is that the truthmaker interpretation of divine simplicity has already been committed to a kind of nominalism regarding God's attributes, according to which he lacks any intrinsic property (in the ontologically loaded sense of ‘property’). Now, why should advocates of the truthmaker interpretation not take one step further and, by rejecting TN, opt for nominalism not only about God but also about other beings? For example, some have proposed a nominalism-friendly version of truthmaker theory according to which truthmakers need not necessitate the relevant truths.Footnote ³⁰ Thus, Socrates himself could be treated as the truthmaker for ‘Socrates is wise’. Given such an approach, although it might well be conceded that God and Socrates resemble each other in their both being wise, no property need be posited to play the role of truthmaker for ‘Socrates is wise’. Consequently, the objective similarity argument would not get off the ground, as the antecedent of TSL would not be satisfied.

I do not intend to decide here between TN and its nominalism-friendly rival. I merely want to make two short comments. Firstly, TN is not only highly intuitive, but also espoused by an overwhelming majority of truthmaker theorists, including prominent advocates of the truthmaker interpretation. Thus, rejecting TN is really a costly option, although one might eventually be willing to pay the cost to save TIP. Secondly, whether or not one endorses TN, an interesting result emerges from our preceding discussions: the only way to preserve TIP (without abandoning the univocity thesis) is to embrace wholesale radical nominalism. It is a familiar (and, in fact, trivial) idea that given wholesale radical nominalism, the category problem for the simplicity doctrine simply evaporates: when there is no property at all, we can retain God's simplicity without getting into the absurdity of identifying him with a property. But many philosophers have sought to defend the simplicity doctrine not by taking that easy step, as they have found wholesale radical nominalism utterly implausible. In particular, one interesting feature of the truthmaker interpretation is precisely that it tries to preserve the simplicity doctrine not by holding a thoroughgoing nominalist position, but only a restricted one, namely, nominalism about God's attributes. But it now turns out, thanks to the objective similarity argument, that the restricted nominalism does not work: nothing less than wholesale radical nominalism can preserve the conjunction of TIP and the univocity thesis.Footnote ³¹

A Thomistic way out?

Thus far we have seen that the truthmaker interpretation of divine simplicity can be proven to be incompatible with the conjunction of the univocity thesis and TN. Nevertheless, the proponent of the truthmaker interpretation might reply that the univocity thesis is by no means inevitable. In particular, s/he might be willing to give up the univocity thesis in favour of a Thomistic approach to theological predication. As is well known, Thomas Aquinas distinguished three manners in which a term could be used several times: univocal application (when the term is used with the same meaning), equivocal application (when it is used with different unrelated meanings), and analogical application (when it is used with different but related meanings). Aquinas rejects the wholesale God-creatures equivocation, mainly on the ground that it leads to a kind of unacceptable scepticism about God.Footnote ³² Moreover, he argues that while no predicate could be univocally applied to God and created beings, the so-called ‘pure perfection terms’ like ‘wise’, ‘good’ and ‘just’ can truly apply to both of them analogically.Footnote ³³ Now, the suggestion is that perhaps by opting for a Thomistic approach to divine predication, advocates of the truthmaker interpretation can gain two advantages at the same time: for one thing, they can neutralize the objective similarity argument, and for another, they can avoid the unfavourable consequence of the wholesale God-creatures equivocation, namely radical scepticism about God.Footnote ³⁴

We cannot explore whether such a manoeuvre is available for the advocate of the truthmaker interpretation before we determine how Aquinas's theory of theological predication should be understood. Unfortunately, however, there is a great controversy on this issue among Aquinas's contemporary commentators. Because of space limitations, then, my discussion shall be restricted: I will very briefly delineate the central tenets of what might be regarded as the ‘orthodox’ interpretation of Aquinas's theory of theological predication, without making any attempt to assess them either exegetically or philosophically. I will then examine whether advocates of the truthmaker interpretation could exploit Aquinas's theory (under the orthodox interpretation) to neutralize the objective similarity argument.Footnote ³⁵

Now, according to Aquinas's theory, ‘wise’ expresses different but related senses when it is truly predicated of God and Socrates. It might be convenient to introduce different terms parallel to these supposedly different senses; let us stipulate that ‘c-wise’ and ‘d-wise’ are synonymous with ‘wise’ when truly applied to Socrates and to God, respectively (‘c’ for ‘creatures’ and ‘d’ for ‘divine’). Moreover, ‘c-wisdom’ should be understood in a parallel way. We are all familiar with the sense expressed by ‘c-wise’. The crucial question is which sense ‘d-wise’ expresses, according to Aquinas's theory, and how this latter sense is related to the one expressed by ‘c-wise’. To answer this question we should look at Aquinas's general theory of causality, which constitutes the metaphysical basis for his theory of theological predication. Aquinas maintains that any perfection exemplified by creatures pre-exists in God, as their efficient cause, in a higher and more excellent way.Footnote ³⁶ Moreover, this would result in a kind of (inexact) resemblance or ‘likeness’ between God and creatures whose perfections pre-exist in him.Footnote ³⁷ Given all this, the meaning of ‘d-wise’ could be roughly characterized as follows:

Let us now turn to our main question: Can the objective similarity argument be neutralized by abandoning the univocity thesis in favour of Aquinas's theory of theological predication? I shall argue that this question should be answered in the negative. It seems that a generalized variation of the objective similarity argument can be constructed to show that TIP, TN, and Aquinas's theory of theological predication would constitute an incompatible triple.

To begin with, according to Aquinas's theory we can truly say that God is d-wise and Socrates is c-wise. Now given (A), it seems obvious that the mere fact that God is d-wise and Socrates is c-wise would constitute a kind of resemblance between God and Socrates. After all, God enjoys a perfection which somehow resembles the wisdom possessed by Socrates. Moreover, we have seen that Aquinas has explicitly conceded such a likeness between God and creatures. But if so, and given that any resemblance holds only relative to a specific respect, a question might arise as to the respect in which God and Socrates resemble each other. Were the univocity thesis not abandoned we could simply answer the question by saying that Socrates resembles God in that they both are wise. But since, under the present assumption, no natural predicate is univocally applicable to both God and Socrates the relevant respect should be specified in another way. One natural proposal is to characterize the relevant respect by using a pair of predicates rather than a single one: Socrates resembles God in that Socrates is c-wise and God is d-wise.

Although we do not normally use a pair of predicates to specify the respect relative to which a given resemblance holds, I take it to be completely cogent and even sometimes inevitable. To illustrate, consider a scenario in which a group of people use a language which is exactly like English except for the fact that it contains neither the word ‘red’ nor any of its synonyms, although it contains words for different shades of red, like ‘scarlet’ and ‘crimson’. Suppose that a speaker of this language perceives two objects, a and b, where one of them is scarlet and the other crimson. Arguably, he does recognize a kind of resemblance between a and b. But he cannot specify the respect of the given resemblance by saying ‘a resembles b in that both are red’. Instead, he can do the job by exploiting a pair of predicates: ‘a resembles b in that a is scarlet and b is crimson’. According to Aquinas, our language is as impoverished with respect to perfection terms as that imaginary language with respect to ‘red’: we do recognize that there is a resemblance between Socrates and God, but the respect of resemblance could not be specified by a single natural predicate.Footnote ³⁹

Now, the objective similarity between Socrates and God will pave the way for a generalized version of the objective similarity argument. To see this, notice that the very intuition underlying TSL would also support the following thesis, in which ‘a’, ‘b’, ‘F’ and ‘G’ are to be replaced, inside and outside all quotation marks, by any two names and any two predicates, respectively:

For example, suppose that a is scarlet and b is crimson. Clearly enough, there is an objective similarity between a and b in that a is scarlet and b is crimson, or equivalently, a's being scarlet and b's being crimson jointly constitute an objective similarity between a and b with respect to their colour. Suppose further that the truthmaker for ‘a is scarlet’ is a trope, r, possessed by a. Given all this, it seems utterly implausible to take the resemblance between a and b (in that a is scarlet and b is crimson) as a primitive unexplainable fact. Just as the truth of ‘a is scarlet’ is to be explained by r, it should also play an essential role in the explanation of the aforementioned resemblance between a and b. Standardly, that resemblance is explained by reference to the similarity between r and another colour trope possessed by b.

Equipped with GTSL, the steps of the generalized version of the objective similarity argument run much like the original version, and so they need not be reiterated in detail. Put briefly, Socrates resembles God in that the former is c-wise and the latter is d-wise. Moreover, given TN, the truthmaker for ‘Socrates is c-wise’ cannot be Socrates himself, but either a c-wisdom trope, t, possessed by Socrates, or a fact constituted by Socrates’ exemplifying the universal property of c-wisdom. For the sake of simplicity I am here presupposing the first option, though the argument will run, mutatis mutandis, given the realist alternative as well. Now, GTSL has it that t should play an essential role in explaining the aforementioned resemblance between Socrates and God. There are only two options as to how this can be done: (i) God-Socrates resemblance is to be explained by reference to a resemblance between t and a trope possessed by God. (ii) God-Socrates resemblance should be explained in terms of a resemblance between t and God himself, not a trope he has. But essentially similar remarks to those made in the original version of the argument can be repeated here to show that neither of these two options is viable for advocates of the truthmaker interpretation.

The upshot is that the objective similarity argument cannot be defused by switching from the univocity thesis to Aquinas's theory of theological predication, as both are incompatible, given TN, with the truthmaker interpretation. In fact, it is the objective similarity between God and Socrates that does the crucial job in the objective similarity argument, no matter whether ‘wise’ applies to them univocally or just analogically.