Two problems for Trinitarianism

There are two arguments that allegedly result in a contradiction for any orthodox Trinitarian view.Footnote ³ First, Trinitarians want to affirm the premises but not the conclusion of this argument:

1. 1. The Father is God.

2. 2. The Son is God.

3. 3. So, the Father is the Son.

To affirm the conclusion is to deny the distinctness of the Father from the Son. To deny the distinctness of the Father from the Son is to endorse a version of Modalism, the view that the Father, the Son, and the Holy Spirit are not distinct but are instead roles, functions, or guises of the same thing, just as Clark Kent and Superman are just the Kryptonian Kal-El in different guises or playing different roles.Footnote ⁴ Modalism was condemned at the First Council of Nicaea, and the aim of this article will be to maintain orthodox Trinitarianism, which requires denying 3.

The second alleged contradiction results from affirming the premises but denying the conclusion of this argument:Footnote ⁵

1. 4. The Father is a God.Footnote ⁶

2. 5. The Son is a God.

3. 6. The Holy Spirit is a God.

4. 7. The Father is not the Son.

5. 8. The Father is not the Holy Spirit.

6. 9. The Son is not the Holy Spirit.

7. 10. So, there are at least three Gods.Footnote ⁷

To accept the conclusion is to accept polytheism, the view that there is more than one God. To accept polytheism would be to deny monotheism, which is a central tenet of Christian Trinitarianism. Thus, to maintain orthodox Trinitarianism requires denying 10, which seems to be inconsistent with accepting 4–9.

How is the Trinitarian to respond? In what follows, I adhere to Thomas Aquinas's description of the Trinitarian's task: to provide a way to dispel contradictions rather than to understand the Trinity.Footnote ⁸ The goal of this article, then, will be to provide a strategy for how someone can affirm the premises but deny the conclusion of the above arguments without violating Trinitarian doctrine. The approach here does not involve an attempt to help the reader understand the nature of the Trinity, even by way of analogy; rather, the fact that there is a resolution to the apparent contradiction is taken on authority rather than through a positive understanding of the nature of the object(s) about which there is an apparent contradiction.Footnote ⁹ The strategy presented below is not without support, however; I argue that there is precedent for the strategy, provide a metaphysical picture that underlies the strategy, show that the strategy is arguably employed by Aquinas, and describe how the strategy is not beset with the same problems that extant strategies face. Although I believe the strategy here might be compatible with some extant views (with some modifications to those views), I do not here expound on that compatibility, except for some brief remarks in the notes.

Extant solutions to the above Trinitarian problems

The main extant strategies for solving the above problems can be categorized according to what those strategies understand the ‘is’ to signify in the first problem – the sense in which the Father is God and the sense in which the Son is God. In this section, I briefly describe these extant strategies and their problems in order to present a solution that is not susceptible to the same problems.

The first extant strategy is to take the ‘is’ in the first argument to be an ‘is’ of predication, a strategy that characterizes most Social Trinitarians.Footnote ¹⁰ According to this strategy, ‘The Father is God’, ‘The Son is a God’, and ‘The Holy Spirit is God’ are read as the Father, Son, and Holy Spirit sharing in the same divine nature, similar to how individual humans share a human nature.

This strategy solves the first problem. Just as Socrates is human and Aristotle is human, but Socrates is not Aristotle, so the Father is God and the Son is God but the Father is not the Son. The predication strategy, however, does not solve the second problem, according to which the Father is a God, the Son is a God, and the Father is not identical to the Son, so there seem to be at least two Gods. Carrying on the analogy from above, Socrates is a human, Aristotle is a human, and Socrates is not identical to Aristotle, so there are at least two humans. It is thus difficult to see how Social Trinitarians avoid polytheism – the most pressing problem for Social Trinitarianism.Footnote ¹¹ Social Trinitarians have responded to this charge to varying degrees of success; these strategies often include taking monotheism to be consistent with multiple Gods that are closely enough relatedFootnote ¹² or taking the divine persons not to be God but to be divine by participation in the one God, the Trinity.Footnote ¹³ The solution proposed below, however, does not maintain that there are three Gods in any sense. I take it that not affirming that there are Gods in any sense and thus being absolved of polytheism is a desideratum for an orthodox Trinitarian view.

The second extant strategy, Pure Relative Identity, holds that the lines of argumentation in the first problem are sortal-relative identity statements. To make a sortal-relative identity statement is to say that there is a sortal F in respect of which the relata are the same (for example, Cicero is the same person as Tully). The first premise of the first problem, ‘The Father is God’, should really be read, ‘The Father is the same God as God.’Footnote ¹⁴ Relative Identity views can be divided into pure and impure views. Pure Relative Identity, as described here, is the view that either

or

According to Pure Relative Identity, lines of argumentation in the first problem, if they are not ill-formed, must be relative identity statements.

What characterizes all Relative Identity theorists is the position that, possibly, x is the same F as y but x is not the same G as y. For example, I am the same person as I am, but perhaps I am not the same passenger as I am, because I may be counted by an airline as two different passengers.Footnote ¹⁶ For another example, two men are the same surman if they have the same surname; different men can be the same surman.Footnote ¹⁷ This enables Relative Identity theorists to say that, for example, the Father is the same God as the Son but the Father is not the same person as the Son.

If we restate the first problem according to Relative Identity logic, we have the following:Footnote ¹⁸

1. 1′. The Father is the same God as God.

2. 2′. The Son is the same God as God.

3. 3′. So, the Father is the same God as the Son.

3′ follows from 1′ and 2′, and the Trinitarian can accept all three premises. If we translate the lines of argumentation using a different sortal, person, the result is three falsehoods:

1. 1″. The Father is the same person as God.

2. 2″. The Son is the same person as God.

3. 3″. The Father is the same person as the Son.

So, by reducing the statements in the argument to Relative Identity statements, the Trinitarian is not forced into accepting an unorthodox conclusion that follows from true premises.

Pure Relative Identity can be used to respond to the second problem by taking predicates containing count-nouns like ‘is a God’ as reducible to Relative Identity statements. Thus, ‘is a God’ can be reduced to ‘is the same God as itself’. The second argument can then be translated into Relative Identity statements that the Trinitarian can accept:Footnote ¹⁹

1. 4′. The Father is the same God as the Father.

2. 5′. The Son is the same God as the Son.

3. 6′. The Holy Spirit is the same God as the Holy Spirit.

4. 7′. The Father is not the same person as the Son.

5. 8′. The Father is not the same person as the Holy Spirit.

6. 9′. The Son is not the same person as the Holy Spirit.

Using Relative Identity logic, it does not follow from 4′–9′ that there are at least three Gods; it only follows that there are at least three persons.

Although Pure Relative Identity can solve both of the above problems, the view has problems of its own. First, one might think the view conflicts with pre-theoretic and philosophical intuitions that there is absolute identity. It would be better if a view could solve the above problems Trinitarians face without holding that absolute identity statements are ill-formed or that all identity statements are reducible to relative identity statements.

Second, if Pure Relative Identity is true, there cannot be maximally general sortals like ‘thing’, ‘being’, or ‘entity’. To accept RI1, that all absolute identity statements are ill-formed, is to deny that there are maximally general sortals, but that comes at a cost. Maximally general sortals help us identify the things over which we can quantify with an existential quantifier, and it is what we count by when we want to count everything there is. If one accepts RI2, that all absolute identity statements are reducible to Relative Identity statements but holds that these statements include a maximally general sortal like ‘thing’, ‘being’, or ‘entity’, then Relative Identity does not solve the first problem. If each of 1–3 is read as an identity statement and the following principle holds:

then the affirmation of 1 and 2 but the denial of 3 creates a contradiction even in Relative Identity logic.Footnote ²⁰ The solution I propose below does not require commitment to RI1 or RI2 in order to address the alleged contradictions and, for that reason, avoids the above problems for Pure Relative Identity.

The final extant strategy discussed here is Impure Relative Identity, according to which there are true absolute identity statements, but there are also other ways of counting in a way that solves, or at least reduces the severity of, the two Trinitarian problems above. One such view is the Numerical Sameness Without Identity (NSWI) view, according to which one can count by either absolute identity or numerical sameness (or both).Footnote ²¹ To count by identity is to count objects that differ according to Leibniz's Law, whereas to count by numerical sameness is to count hylomorphic compounds by their shared matter (or, rather, what plays the role of matter). For example, one continuous chunk of marble can constitute a statue and a pillar. The statue and the pillar are distinct, because erosion can destroy the statue without destroying the pillar, but the statue and pillar are numerically the same because they share all the same matter.Footnote ²² According to proponents of NSWI, the divine nature plays the role of matter, and each divine person shares in that matter but also is distinguished from the other divine persons by another property – for example, being unbegotten, being begotten, and being spirated – each of which is distinct from the other. The Father, on this model, is a hylomorphic compound of the divine nature and being unbegotten, whereas the Son is a hylomorphic compound of the divine nature and being begotten, and so on. ‘God’, on this model, is an ambiguous name for whatever is constituted by the divine nature.

A Trinitarian proponent of NSWI can affirm the premises but deny the conclusion of the first problematic argument by affirming that the Father is identical to something that is named by ‘God’, as is the Son, and the Trinitarian proponent of NSWI can deny that the Father is identical to the Son because the Father is, in fact, distinct from the Son – the Father is unbegotten whereas the Son is not. Proponents of NSWI, while denying 3, still affirm that the Father is numerically the same as the Son; the Father and the Son share the same divine nature, which plays the role of matter.

A Trinitarian proponent of NSWI can also affirm 4–9 and the conclusion of the second problematic argument. The proponent of NSWI will need to affirm that there are three distinct entities that are each Gods, but NSWI allows the Trinitarian to reduce the severity of accepting 10 by asserting that each of the distinct beings that are Gods are numerically the same – they each are constituted by the same divine nature and so share what plays the role of matter.

The first problem for NSWI, as indicated in the paragraph on Social Trinitarianism, is that it would be a benefit to a Trinitarian view if it did not need to affirm in any way that there are three Gods. By affirming that in some way there are three Gods, a view has the appearance of polytheism. Hasker (Reference Hasker2010, 326–327) points out that if ‘God’ were an ambiguous name, we could provide subtext to disambiguate the three gods: God_F, God_S, and God_HS. Robert Koons (Reference Koons2018, 352) likewise states, ‘Thus, [for NSWI] the charge of tritheism seems inescapable, since each Person is divine in His own unique and incomparable way.’ To avoid the charge of polytheism, Hasker (Reference Hasker2010, Reference Hasker2019), who also endorses a constitution model of the Trinity, denies that ‘God’ is ambiguous and instead takes the ‘is’ in 1 and 2 to be an ‘is’ of constitution – the Father is constituted by God, and the Son is constituted by God. Hasker can then respond to the second problem by affirming that the Father and Son are constituted by the same, unique God. Aside from the (perhaps) problematic adherence to the view that the Father is not identical to God but is instead merely related to God in some way, Hasker's view and NSWI share a second problem: the godhead is very complex. According to NSWI, there are at least seven distinct entities in the godhead – the divine nature, being unbegotten, being begotten, being spirated, the Father, the Son, and the Holy Spirit – and it seems as if there are many entities in the godhead according to Hasker's view as well. Those views involve complex work in order to solve the Trinitarian problems. It is a benefit to a view not to have to postulate additional entities to solve such problems. The strategy I present below involves no such additional entities; in fact, the view is compatible with and (as will be shown in the section ‘Solving the second problem’) helped by the doctrine of divine simplicity, the view that there is no complexity in God whatsoever.Footnote ²³

In what follows, I propose a solution to the two problems above that allows a Trinitarian to remain orthodox by accepting the premises but denying the conclusion of the two problematic arguments above. The solution avoids affirming that there are three Gods in any sense, allows the Trinitarian to affirm that absolute identity statements are well-formed,Footnote ²⁴ does not require developing any new way of counting entities, and is compatible with (indeed, as will be shown, the view is helped by) the doctrine of divine simplicity.

Solving the first problem

In short, the strategy proposed here is to maintain that there are implicit opaque contexts in Trinitarian formulations. An opaque context is a linguistic context in which substituting co-referring terms does not guarantee the same truth value. That is, there is no guarantee of substitution salva veritate into an opaque context. Take, for example, the following argument:

1. a. Lois Lane knows: she is in love with Superman.

2. b. Clark Kent = Superman.

3. c. Lois Lane knows: she is in love with Clark Kent.

The context after ‘knows:’ in a. is opaque. Substituting a co-referring term (‘Clark Kent’) into that context in a. sometimes yields a different truth value – in this case, a. is true but c., in which the substitution is completed, is false. In the example above, the knowledge operator creates the opaque context that prevents the guarantee of substitutivity salva veritate.

The first problematic argument above also contains a substitution of co-referring terms: (‘the Son’ for ‘God’). Here is the argument again:

1. 1. The Father is identical to God.

2. 2. The Son is identical to God.

3. 3. So, the Father is identical to the Son.

According to premise 2 in this argument, ‘the Son’ and ‘God’ co-refer, and the problem is generated when ‘the Son’ is substituted for ‘God’ into premise 1 to guarantee the truth of 3, in which the substitution is completed.Footnote ²⁵ If, however, there is an opaque context that is substituted into in the first premise, then substitution into that context does not guarantee the truth of the conclusion. If there is such an opaque context, the Trinitarian can affirm the premises but deny the conclusion without contradiction, and so the problematic contradiction is resolved.

Of course, there is no textual indication in the argument itself that the first premise contains an opaque context. In the Lois Lane example, there is an explicit knowledge operator that indicates that there is an opaque context that ranges over the statement that succeeds it. Other examples of intensional operators, such as ‘believes’ or ‘feels’, are also not present in premise 1.Footnote ²⁶

There are views according to which a sentence functions in ways not made textually explicit, and discernment as to how the sentence functions is determined via context rather than explicit textual clues. For example, someone's statement, ‘There is nothing in the fridge’ is sometimes true even when there are shelves and crumbs in the fridge. One can explain the possibility that such claims are sometimes true by holding that there is an implicit quantifier that restricts the scope of the uttered statement to food items (assuming crumbs are not food items). So, there is precedent for believing that there are linguistic mechanisms present in the meaning of a sentence without explicit textual evidence.

There is also precedent for the view that there are implicit opaque contexts in sentences without textually explicit operators. According to Michael Della Rocca's interpretation of Spinoza, for example, Spinoza's views contain implicit opaque contexts.Footnote ²⁷ Della Rocca maintains that the following Spinozistic inference is invalid:

1. 14. My body causally interacts with mode of extension E.

2. 15. My body = my mind.

3. 16. So, my mind causally interacts with mode of extension E.

The argument is invalid, because although premise 15 contains an absolute identity statement, it cannot be used to substitute into 14 to guarantee the truth of 16. There is no explicit indication of an opaque context in 14. Instead, the fact that there is an opaque context in 14 is evidenced by the content of 14. According to Della Rocca, when there are descriptions or names that are described by a particular divine attribute such as (on Spinoza's view) extension, there is an opaque context that ranges over those descriptions/names. In 14, there is an opaque context preceding ‘causally interacts with mode of extension E’. In 14, ‘my body’ is in that context, and substitution of the co-referring term ‘my mind’ does not guarantee the same truth value for 16 as for 14.

If Della Rocca's interpretation of Spinoza is correct, Spinoza holds that there are implicit opaque contexts throughout Spinoza's work. That there are such contexts is discovered by realizing that Spinoza accepts the premises but not the conclusion in the argument containing 14–16 above, and through further analysis one can discover that there are such contexts present based on the content of the sentence.Footnote ²⁸

Similarly, Trinitarians can discover that there are implicit opaque contexts in Trinitarian formulations because Trinitarians believe on authority that they ought to hold to the premises but not the conclusion of the first problem (1–3) above.Footnote ²⁹ One could revise the absolute identity reading of the premises (which, as indicated in the section above, is problematic) or find ways to better understand the absolute identity reading. My view tries to do the latter, as does Della Rocca when interpreting Spinoza.

Although I have proposed that there are implicit opaque contexts in Trinitarian formulations – in premise 1 of the first problematic argument in particular – I have not yet provided an account of when these opaque contexts are created. I propose that they are created around a position in a sentence whenever the occupant of that position is (1) identified with either a divine person or some entity based on a divine person or (2) described by a feature that is based on a divine person.Footnote ³⁰ For example, according to (1), the contexts preceding ‘is the Father’, ‘is the Son’, and ‘is the Holy Spirit’ are all opaque, as are the contexts that follow ‘The Father is’, ‘The Son is’, and ‘The Holy Spirit is’, because all of the relevant contexts contain a position in a sentence in which the occupant is identified with a divine person. According to (2), the contexts preceding ‘is a being who begets’, ‘spirates’, and ‘proceeds from the Father’, are all opaque, because the relevant contexts contain a position in which the occupant is described by a feature that is based on a divine person. According to this proposal, ‘God’ in ‘The Father is God’ is in an opaque context, because it is preceded by ‘The Father is’, which according to (1) creates an opaque context. Thus, substitution of ‘the Son’ for the co-referring ‘God’ (according to premise 2) does not guarantee the truth of ‘The Father is the Son’. The first problematic argument, then, does not entail its conclusion, and the Trinitarian can accept the premises and deny the conclusion without contradiction. The first problem is thus solved.

The solution proposed here might appear ad hoc. To be clear, it is. As indicated above, the assumption here is that the task for the Trinitarian is to avoid contradiction; it is not to first understand the Trinity in order to explain how the arguments do or do not succeed. However, the ad hoc work is justified. If we have authoritative testimony that the arguments above fail and the solution is not beset with the same problems for extant views, then we have testimonial reasons (authoritative testimony that the problematic Trinitarian arguments fail) and explanatory reasons (that the solution I propose is not beset with the problems for extant views) to endorse the ad hoc solution.

One concern with the strategy just proposed is that it prevents making inferences that Trinitarians should be able to make. For example, suppose ‘P’ is the name of the omnipotent being. Trinitarians should be able to make the following valid inference:

1. 11. The Father is God.

2. 12. God is P.

3. 13. So, the Father is P.

If ‘The Father is’ creates an opaque context, then substituting ‘P’ for the co-referring ‘God’ does not guarantee the truth value of ‘The Father is P’. Trinitarians need a principled way of distinguishing the kinds of inferences made so that 1–3 is invalid but 11–13 is valid.

It is possible for there to be valid inferences even when substituting into opaque contexts. Some kinds of substitutions into opaque contexts can guarantee the truth value of the resulting sentence even if other kinds of substitutions do not guarantee the truth value of the resulting sentence. For example, even though the Lois Lane argument (a.–c. above) is not valid since co-referring terms cannot be substituted into the opaque context, if Lois Lane were to know that Clark Kent = Superman (and knowledge is closed under known entailment and Lois goes through the logical steps), it would follow that Lois Lane knows she is in love with Clark Kent. If the terms are known to co-refer, then the argument is valid.

So, substituting co-referring terms into an opaque context may, under some conditions, guarantee that the resulting sentence has the same truth value as the sentence substituted into. The context, however, is nevertheless opaque, because substituting co-referring terms into the context does not guarantee the truth value of the resulting statement under all conditions. What remains is to specify the conditions under which 3 does not follow from 1–2 but 13 does follow from 11–12 even though both inferences involve substituting co-referring terms into an opaque context.

I propose that the content of the relevant words/phrases can determine whether the terms are substitutable salva veritate into the opaque context created by phrases that satisfy (1) or (2) above, such as ‘The Father is . . .’ In what follows, I first divide descriptions/names into two different types based on their content, then I state conditions under which those types can be substituted salva veritate into opaque contexts generated by phrases that satisfy (1) or (2) above, and then I show how it allows 13 to follow from 11–12 but 3 not to follow from 1–2.

First, I propose dividing names/descriptions in Trinitarian statements into the following two types:

A PID is a description or name of God that has its basis in a divine person. For example, ‘The Father’, ‘The Son’, and ‘God's begotten’ are PIDs. A PUD is a description or name of God that does not have its basis in a divine person. For example, ‘The omnipotent being’ and ‘God’ are both PUDs; ‘The omnipotent being’ and ‘God’ have their basis in God as such rather than in a particular divine person.Footnote ³¹

Second, the conditions under which those types can be substituted salva veritate into opaque contexts generated by phrases that satisfy (1) or (2) are as follows: PIDs cannot be substituted salva veritate for PUDs into a sentence containing the relevant opaque context. On the other hand, PIDs can be substituted for PIDs salva veritate,Footnote ³² and PUDs can be substituted for PUDs salva veritate into the relevant opaque context.

In 11–13, since ‘God’ and ‘P’ are co-referring PUDs, substitution of one for the other into the opaque context created by ‘The Father is’ does guarantee that the resulting sentence will have the same truth value as the sentence substituted into. So, 13 follows from 11 and 12. On the other hand, in 1–3, since ‘God’ is a PUD and ‘The Son’ is a PID, substitution of ‘The Son’ for the co-referring ‘God’ into the opaque context created by ‘The Father is’ (in 1) does not guarantee that the resulting sentence, 3, will have the same truth value as the sentence substituted into, 1. So, if the proposal above is correct, 11–13 is valid, but the problematic argument 1–3 is invalid.

It is worth noting that according to Della Rocca's view of Spinoza, Spinoza can also make distinctions between kinds of names and descriptions that determine the conditions under which an opaque context can be substituted into salva veritate. First, to parallel what was said above, when there are descriptions or names that are described by a particular Spinozistic divine attribute, there is an opaque context that ranges over those descriptions/names. So, in 14, there is an opaque context preceding ‘causally interacts with mode of extension E’. In 14, ‘my body’ is in that context, and substitution of the co-referring term ‘my mind’ does not guarantee the same truth value for 16 as for 14.

1. 14. My body causally interacts with mode of extension E.

2. 15. My body = my mind.

3. 16. So, my mind causally interacts with mode of extension E.

There are, however, conditions such that if they are met, co-referring terms are substitutable salva veritate into the relevant Spinozistic opaque context. For example,

1. 17. The thing that has only four items causally preceding it causally interacts with mode of extension E.

2. 18. The thing that has only four items causally preceding it = the fifth being to have existed.

3. 19. So, the fifth being to have existed causally interacts with mode of extension E.

17–19 is valid even though it involves substituting into the same opaque context that is substituted into in 14–16. What is the difference that makes 14–16 invalid but 17–19 valid? The difference is determined by the content of the terms that are being substituted, though the difference is more complicated in Spinoza's case and does not exactly parallel the Trinitarian's distinctions. In the above Spinozistic arguments, there are EIDs – extension-involved descriptions or names – names or descriptions that have their basis in the Spinozistic divine attribute extension: ‘my body’, for example. There are also MIDs – mind-involved descriptions or names – names or descriptions that have their basis in the Spinozistic divine attribute mind: ‘my mind’, for example. There are also AUDs: names or descriptions that do not have their basis in a particular Spinozistic divine attribute, such as ‘the thing that has four items causally preceding it’ and ‘the fifth being to have existed’. MIDs cannot be substituted salva veritate for EIDs (and vice versa) into a sentence containing the relevant opaque context, but AUDs can be substituted salva veritate for AUDs into a sentence containing the relevant opaque context. Since the terms flanking the identity sign in 15 are an EID and MID, respectively, one term cannot be substituted for the other salva veritate to make 14–16 valid. However, since the terms flanking the identity sign in 18 are both AUDs, substituting one for the other into the relevant opaque context does make 17–19 valid. According to Della Rocca's Spinoza, the inference from 17 and 18 to 19 is valid in a way similar to how I propose that the inference from 11 and 12 to 13 is valid, even though the substitution in each of those arguments is into an opaque context. Plausibly, then, according to Della Rocca's Spinoza, if two terms, both of which do not have their basis in a Spinozistic attribute, flank an identity sign, one term can be substituted for the other salva veritate even into the relevant opaque context. Likewise, according to my proposed strategy, if two terms, both of which do not have their basis in a divine person, flank an identity sign, one term can be substituted for the other salva veritate even into the relevant opaque context.

One might be concerned that the strategy presented in this section entails denying either classical inference rules or the transitivity of identity. However, what has been said above is compatible with classical inference rules and the transitivity of identity, both of which are able to be maintained while holding that substitution of co-referring terms into opaque contexts does not guarantee the same truth value of the resulting sentence as the sentence substituted into.Footnote ³³ The strategy developed here is merely meant to help discover where those opaque contexts are when they are not textually explicit and to discover what can be substituted into those contexts salva veritate.

To be clear, I do not advocate adopting a strategy similar to the one given above whenever one wishes to resolve an alleged contradiction that occurs via substituting co-referring terms. Trinitarians have a strong reason to believe that the above strategy succeeds; they believe that the above problems can be resolved on the basis of divinely authoritative testimony. Further, one might have good reasons to believe that absolute identity statements are well-formed, that they are not reducible to relative identity statements, and that one should not endorse a view that affirms that in some way there are three Gods. These reasons provide support for the above strategy, whereas one might not have reasons that strong to endorse the strategy whenever one wants to avoid a contraction that occurs via substitution.

Thus ends the proposed semantic strategy for how to avoid the alleged contradictions. However, one might want more than a semantic strategy for how to resolve the alleged contradictions; one might want to know what it is about the Trinity that would provide metaphysical support for the semantic strategy. In the following section I sketch a brief metaphysical picture to underlie the semantic strategy, though, to be clear, the metaphysical picture is insufficient for understanding the Trinity. In the process of sketching the metaphysical picture, I use the writings of Aquinas, who I believe can be interpreted as employing both the metaphysics described below and the semantic strategy described above.

Metaphysical and historical support

In this section, I provide a metaphysical picture of why the opaque contexts are created in the way I have proposed they are created, with the aim of developing a metaphysical account that is compatible with divine simplicity, throughout citing Aquinas as a plausible employer of the metaphysical picture and the accompanying semantic strategy. The historical work will be very brief; I will leave it to another project to provide more extensive historical support.

The metaphysical picture begins with the view that some divine entities, features, or activities have their basis or ground in one divine person but not in another. We can then make the connection between this grounding picture and the linguistics. We can do so by maintaining that if a description or name of God designates something that either has a ground in one divine person but not another or which is identical to the divine person that provides such a ground, then that description/name cannot be substituted salva veritate into any context that requires a name or description not to have its basis/ground in that particular divine person. When, for example, Trinitarians try to substitute ‘the Son’ into the context after ‘The Father is’, they are substituting a name of God (‘the Son’) that designates a divine person that is the basis or ground for some features (e.g. being begotten, proceeding only from the Father) that do not have a ground in another divine person. They are substituting this name into a context (after ‘The Father is’) that requires a name or description not to have its basis in a divine person other than the Father. The grounds are misaligned upon substitution, and therefore the resulting sentence is not guaranteed to have the same truth value as the sentence substituted into.

The same picture can be given for Della Rocca's Spinoza, according to whom some descriptions (e.g. ‘my body’) describe something that has its basis or ground in a Spinozistic divine attribute (e.g. extension), and substituting a co-referring term (e.g. ‘my mind’) that describes something that has its basis or ground in a different Spinozistic divine attribute (e.g. mind) does not result in a sentence with the same truth value as the sentence substituted into.

The idea is that there are certain entities that have a basis or ground that in some way restrict the kinds of inferences one can make about those entities. In some cases, if co-referring terms indicate certain kinds of different bases or grounds, even if those terms co-refer, we cannot expect that substituting one of those terms for its co-referent into contexts that require a particular basis or ground will preserve truth value.

To get more specific about how the picture supports the substitutivity rules given above, first note that an opaque context is created in Trinitarian statements that include a divine person-involved description or name – a PID – (per (1) and (2) above). Per (1) and (2) above, it is a PID that creates the opaque context. For example, ‘The Father is’, a PID, creates an opaque context that contains ‘God’ in premise 1. According to the metaphysical proposal here, that is because a term that occupies the opaque context (‘God’ in premise 1) refers to or describes an entity that is required to have a basis or ground compatible with the divine person whose description/name (PID) creates that opaque context (‘The Father’ in premise 1). If one substitutes into that opaque context a co-referring term (e.g. ‘the Son’) that refers to or describes an entity that has a basis or ground in a different divine person, then one should not expect the substitution to preserve truth value. Suppose one substitutes a PUD for a co-referring PUD or a PID for a co-referring PID into an opaque context that requires a particular basis or ground for what is referred to or described by the term that occupies that opaque context. If one makes that kind of substitution, one should not expect a change in basis or ground from what is substituted into that context. Suppose, however, that one substitutes a PID for a co-referring PUD into an opaque context that requires a basis or ground not to be in some other divine person. One might thus expect there to be a mismatch between the basis or ground indicated by what is substituted into that context and the basis or ground that is required by what creates the opaque context. Since there can be such a mismatch, one should not expect truth value to be preserved by substituting.Footnote ³⁴

There is historical support for the view that some divine objects, attributes, or activities have their basis or ground in one divine person but not in another. According to Aquinas, even though all divine persons are identical to God, divine persons provide the basis for opposing a feature or activity to another divine person. The activity generating the Son, for example, is based on the Father, and so the Father provides a basis for generating the Son not to be attributed to other divine persons. Aquinas thus holds that generating the Son is not truly predicated of the Son or the Holy Spirit.

The issue is a bit more complicated than that presented in the previous paragraph. According to Aquinas, to be a person is to be a distinct individual of a rational nature. (See De Pot. IX.4 ans.) The distinctness part of that definition is fundamentally relational and, in a way, opposed to another. Aquinas holds that such a definition of divine persons adds nothing to God as such except for distinction, or relation. Aquinas thus holds that divine persons are reducible to what he calls ‘internal divine relations’ (‘. . . “divine person” signifies a relation as subsistent’, ST I.29.4 ans.), and the divine relations are distinguished from each other only because each divine relation is the basis for an opposition to the other divine relations: ‘The real distinction among the divine relations consists of nothing other than relational opposition’ (ST I.30.2 ans.). So, the divine persons provide the basis (viz. internal divine relations) for opposition to other divine persons.

To generalize the metaphysical picture proposed in this section, if a divine person R provides the basis for opposing a feature to a divine person S, S cannot be identical to R, nor can any feature based on S be truly predicated of R, and vice versa. If we were to allow a PID to substitute for a PUD into an opaque context created by a PID, we would sometimes get the result that two terms or phrases, each signifying opposition to the other, signify the same thing, which is impossible. So, PIDs cannot substitute for PUDs salva veritate into opaque contexts created by PIDs. God as such, however, does not provide the basis for opposing a feature to any divine person. If a feature is based on God, then that feature is truly predicated of each of the divine persons, and vice versa. Hence, a PUD can be substituted for a co-referring PUD salva veritate into opaque contexts created by PIDs.

This picture can be summarized in the following passages from Aquinas's On the Power of God (square brackets indicate my gloss) in which Aquinas states that divine persons are distinct from other divine persons because they provide a basis or ground, which Aquinas calls a ‘property’, for opposing other divine persons; they do not provide a basis that opposes God as such.

So, there is something about the personhood of each divine person that includes a property that distinguishes that person from other persons. To be clear, Aquinas does not think there are properties in God due to his adherence to divine simplicity, according to which there is no property/subject distinction in God. The property referenced by Aquinas is most likely an internal divine relation (or relative property) that is identical to God and which is thus the basis or ground for distinguishing one person from another. (See De Pot. IX.5 obj. 16.) According to Aquinas, God, which is signified by a PUD, does not provide a basis or ground for opposition to divine persons, whereas divine persons, which are signified by PIDs, do provide grounds for such an opposition.

The above view allows Aquinas to make the following statement:

One upshot for the view proposed here is that there only needs to be one way of counting. We do not have to count by sortals or distinguish counting by identity from counting by numerical sameness. Instead, when we count divine entities, we always count by absolute identity. The result of our counting, however, will differ according to how we begin the count. If we start with God, we get one entity. God is identical to the Father, the Son, and the Holy Spirit, and God as such does not provide any grounds for opposition to any of them. If we start with any divine person, however, we get three entities. Supposing we start with the Father: the Son is identical to God, and the Father provides a basis for opposition to the Son, so the Father is not identical with the Son. Mutatis mutandis for the Father providing a basis for opposition to the Holy Spirit and the Son providing a basis for opposition to the Holy Spirit. Since the Father provides a basis that opposes the Son and the Holy Spirit, and since the Son provides a basis that opposes the Holy Spirit, the three are not identical to any other, and the result of the count is three entities. There is one way to count, but what matters is where you start. If you start with a person, you get three, and if you start with God, you get one.

The above counting view is also supported by Aquinas, who says that there is only one God (no plurality) if you do not begin by counting relations (persons) in God. However, if you count relations (persons), there is a plurality, because they are predicated with respect to something else, viz. what they oppose:

So, according to the previous passage, if we begin by counting with God and not divine persons, we get one entity due to God's sheer simplicity. However, if we count beginning with persons, we get a plurality – more than one – because they provide grounds that oppose other divine persons.

The preceding should help us understand some passages in Aquinas more clearly. For example, Aquinas answers an objection that goes like this: the Son does not have the same power the Father does, because the Father can generate but the Son cannot. Aquinas is thus addressing the following parallel inferences that one might think are valid:

Argument 1:

1. i. The Father is God.

2. ii. God is the omnipotent being.

3. iii. So, the Father is the omnipotent being.

4. iv. The omnipotent being can generate.

5. v. So, the Father can generate.

Argument 2:

1. i. The Son is God.

2. ii. God is the omnipotent being.

3. iii. So, the Son is the omnipotent being.

4. iv. The omnipotent being can generate.

5. v. So, the Son can generate.

Aquinas's response mirrors the strategy proposed in the sections above – the inference from step iii. to iv. does not entail v. in each argument, because iii. contains a PID (‘the Father’, ‘the Son’) and a PUD (‘is the omnipotent being), and iii. is being used to substitute a PID (‘the Father’, ‘the Son’) for the PUD (‘is the omnipotent being’) into the opaque context created by ‘can generate’ in iv. The result (v.) will not be guaranteed to have the same truth value as the sentence substituted into (iv.) and so both arguments are therefore invalid. Even if iii. is true – the Son is the omnipotent being – and iv. is true – The omnipotent being can generate – v. might be false – it does not follow that the Son can generate. Here are Aquinas's words:

In the preceding, I hope to have provided an underlying metaphysical picture (with historical support from Aquinas) for why the opaque contexts are generated in the way that solves the first problem for Trinitarianism. The second problem remains, however, to which I turn in the next section.

Solving the second problem

Again, here is the second problematic argument for Trinitarians:

1. 4. The Father is a God.

2. 5. The Son is a God.

3. 6. The Holy Spirit is a God.

4. 7. The Father is not the Son.

5. 8. The Son is not the Holy Spirit.

6. 9. The Father is not the Holy Spirit.

7. 10. So, there are at least three Gods.

The strategy I have proposed above does not yet get Trinitarians out of this alleged contradiction, because the argument does not, on the face of it, require any substitutions.

There is, however, a way to apply the strategy I have proposed above even to this argument in a way that allows us to replace the predicates in 4–6 with a name and an identity sign. To do that, we can adopt the doctrine of divine simplicity. To show how the doctrine of divine simplicity allows us to replace the predicates in 4–6 with a name and an identity relation, we should first look to the formulation of the doctrine. The doctrine of divine simplicity is the view that ‘there is no ontological composition in God of any sort, whether of matter and form, or of essence and accident, or of this attribute and that attribute considered as ontologically distinct’ (Pruss (Reference Pruss and Kvanvig2008), 150). God is identical to any intrinsic, non-relational property that is truly predicated of God;Footnote ³⁶ there is no composition in God at all. So, if God has any non-relational attributes essentially, God's having that attribute is identical to God. Aquinas, who endorses divine simplicity, also endorses the view that God's attributes are identical to God:

Some contemporary writers make similar statements about divine simplicity. Bergmann and Brower (Reference Bergmann, Brower and Zimmerman2006, 31), write, ‘[T]o say that God is identical with his goodness is just to say that God is identical with God.’ Since God is identical with God, God is thus identical with God's goodness.

So, according to the doctrine of divine simplicity, to have an intrinsic and non-relational property such as being a God just is to be identical to God (where God is an individual, not a property). 4–6 are equivalent to 4ʺ-6ʺ:

1. 4ʺ. The Father = God.

2. 5ʺ. The Son = God.

3. 6ʺ. The Holy Spirit = God.

If we combine 4ʺ–6ʺ with 7–9 above, the conclusion that follows is

1. 10ʹ. f = g & s = g & h = g & f ≠ s & f ≠ h & s ≠ h

10ʹ, when translated, does not entail that there are three Gods, so Trinitarians can affirm the conclusion without accepting any kind of polytheism. The second problem is thus solved.

Accepting 10′ might seem like it entails a contradiction, and it would be contradictory if all the relevant contexts were transparent. But, as I have proposed above, they are not. Substitutions that would create a contradiction from 10′ do not occur salva veritate. For example, an argument that would allegedly show a contradiction could run as follows:

1. d. The Father = God.

2. e. The Son = God.

3. f. The Father = The Son (d. & e.)

4. g. The Father ≠ The Son.

5. h. The Father = The Son & The Father ≠ The Son (f. & g.)

According to the strategy I have proposed above, f. does not follow from d. and e., because the inference requires substituting a PID (‘The Son’) for a PUD (‘God’) into an opaque context in d. created by ‘The Father =’.

It is worth noting that divine simplicity helps the Trinitarian solve the above problems given the strategy proposed above. This should be surprising; divine simplicity is thought to be trouble for the doctrine of the Trinity. In fact, given how Social Trinitarianism and NSWI require complexity inherent in the godhead, it is difficult to maintain divine simplicity. If one is inclined to accept divine simplicity already, that might provide reason to incline towards the strategy proposed above. If not and one finds the strategy proposed above attractive, that might provide reason to incline one towards accepting divine simplicity.