Robust monotheism

Jews, Muslims, and Christians agree that the number of gods is one. Indeed, before the incarnation (which, according to christianFootnote ¹ theology, is the special, enfleshed revelation of God, including God's triune nature), all in the traditional monotheistic family agreed with the core traditional monotheistic thesis (TM, for traditional monotheism):

What standard christian theology involves is that, given the incarnation, the full truth of TM is in fact expressed via a necessary equivalence (for triune god):

Muslims, Jews and Christians agree on the left-hand side of TG but only Christians accept TG and its critical right-hand side.

How is christian theism robustly monotheistic? My answer points not only to TG but also to trinitarian identity (more on which below): any robust monotheist should accept that God isn't defined by some notion of divinity; rather, any notion of divinity worthy of robust monotheism must entail identity to God. That constraint, on my view, is necessary for robust monotheism. But that constraint also serves to accentuate the target logical problem.

The logical problem and its solution in nuce

A central question lingers: since each of Father, Son, and Spirit is divine, and divinity, from above, entails identity to God (as reflected in the Athanasian Creed), the resulting theology is one in which

1. 1. it's true that Father is identical to God;

2. 2. it's true that Son is identical to God;

3. 3. it's true that Spirit is identical to God;

yet also

1. 4. it's false that Father is identical to Son;

2. 5. it's false that Son is identical to Spirit;

3. 6. it's false that Spirit is identical to Father.

But, then, whatever the given identity relation – call it trinitarian identity – happens to be in the foregoing axioms (doctrines, creedal statements), it is apparently non-transitive (in the sense that the trinitarian identity of a and b, together with the trinitarian identity of b and c, fails to entail the trinitarian identity of a and c).

The so-called logical problem of the trinity is an identity problem: precisely identify trinitarian identity – the relation of identity such that all of (1)–(6) are true without equivocation of ‘is’ or new-fangled semantics for names involved. By way of solution, Divine Contradiction responds to the given logical problem by precisely defining the target relation and explaining (rather than merely declaring) the failure of transitivity – an explanation that critically involves contradictions true of God. In particular, the non-transitivity of trinitarian identity arises in virtue of contradictions in divine reality. Were it not for such contradictions, the given identity relation would be transitive. In other words, contradictions that are true of God explain the non-transitivity of trinitarian identity – a non-transitivity clearly exhibited in standard trinitarian axioms above. (Spelling out the explanation involves spelling out trinitarian identity, which is too much for this précis but is done leisurely in the central chapter 3 of the target book.)

Gluts, gaps, and logical consequence (i.e. logic)

The reader, trained in the standard (so-called classical) account of logical consequence, may be wondering how on earth (or even heaven) any of this can make logical sense. The question is important; it receives full answers in chapter 2 of each target work – namely, Divine Contradiction and The Contradictory Christ. The basic idea is straightforward: the standard account of logical consequence, as we know it, is a rather new account arising from the project of recording the entailment (the ‘logical’) behaviour of sparse logical vocabulary (e.g. ‘it is false that’, ‘it is true that’, ‘. . . and . . .’, ‘either . . . or . . .’, and ‘all objects are such that . . .’ and ‘some object or other is such that . . .’) in true mathematical theories. The result of the project: so-called classical logic, which gets things right as far as the given project goes. But logical consequence governs the behaviour of the logical vocabulary in all true theories, not just true mathematical ones. Does the standard account, which was aimed only at mathematical theories, generalize to all true theories? There are many, many, many reasons to think that the answer is negative. (I can't rehearse them here given space limitations.) If, as I and many others think, the standard account does not generalize to all true theories, and hence is simply an important restriction of the full account of logical consequence, how does the full account go? The answer, again, is in chapter 2 of each target work. But an important point is that the full account and the restricted (classical-logic) one agree on the truth and falsity conditions (‘the meanings’) of logical vocabulary; they differ only in that the latter (i.e. classical-logic) account restricts the space of logical possibilities afforded by the meanings of the given vocabulary. For present purposes: the full account involves gluts (sentences that are true and false) and gaps (sentences that are neither true nor false); the restricted, classical-logic account proscribes those possibilities. (And, of course, there are other accounts that also agree on the truth and falsity conditions of the logical vocabulary but allow only gluts but not gaps, and some that allow gaps but no gluts, and so on.) For present purposes: the take-home point is that the correct account of logical consequence, of which the so-called classical-logic account is a restriction, is perfectly compatible with the contradictions in true theology just as it is with their absence in true mathematics.

Virtues of the contradictory account

The book advances seven virtues of the contradictory account. The virtues, in short, are:

1. 1. unified solution: the ‘logical problem’ of both apparent contradictions – the incarnation and trinity – are of a kind (viz. divine contradiction);

2. 2. simplicity: there is a striking explanatory simplicity in the account;

3. 3. no need for ‘analogical’ or metaphorical gesturing at the contradictions;

4. 4. standard (leibnizian) recipe for identity relations;

5. 5. no positing of unmarked equivocations in fundamental, central axioms;

6. 6. neutrality: the account is neutral on metaphysics and epistemology;

7. 7. mystery: the account opens up a novel understanding of traditional trinitarian mystery.

While each virtue is substantial the first one is especially notable. Both christology and trinitarian theory confront the same logical problem which is called just that – namely, ‘the logical problem’ (one concerning the incarnation, the other the trinity). The problem is conspicuous contradiction on the very surface of the various theological axioms. Many christian theologians have urged that theology proceed in a Christ-driven fashion, the idea, just on the theoretical level (versus the level of humble, pious practice), being that much of specifically christian theology is from the special enfleshed revelation, including the triune nature of God. As a result, it is theoretically prudent to let facts of Christ – the remit of true christology – guide trinitarian theory and systematic theology more generally. But, then, it is at least prima facie compelling to think that the conspicuous contradictions confronting both the incarnation and trinity enjoy a common explanation. Some theorists (e.g. so-called pure relative identity theorists, and so-called epistemic-mystery theorists) have done just that: offered unified accounts. The contradictory account offered in Divine Contradiction is unified with the account in The Contradictory Christ. In short, the apparent contradictions involved are explained by the reality of divine contradiction.

Measuring the contradictory account vis-à-vis salient others

The promises of the contradictory account may be measured against alternative accounts, all of which, at the time of writing, are driven by the quest to ‘consistentize’ God – to avoid a contradictory account of divine reality. Chapter 6 of Divine Contradiction marches through the salient alternatives within the same basic project constraints (e.g. constrained by Chalcedon 451, by Athanasian Creed, and more). The chapter argues that the main avenues of unified accounts (e.g. pure relative-identity accounts and epistemic-mystery accounts) come up wanting against the contradictory account. Moreover, extant impure relative-identity accounts (a technical term that doesn't carry any value connotations with respect to impurity) are provably inconsistent or critically incomplete (e.g. with respect to semantics). While each such would-be non-contradictory account ushers in important ideas, each of them, as things stand, also come up short when measured against the contradictory account – or so the book argues.

Some concrete novel contributions in nuce

The contradictory account is a novel account of the trinity (and incarnation); however, even if one rejects the conclusions (for reasons I would very much like to know), Divine Contradiction makes a significant number of novel contributions to work on the target ‘logical’ problem. Some of the notable contributions, beyond the principal account, are:

• • clearly distinguishing the logical problem of the trinity from the so-called 3-1-ness problem (which is a counting convention problem – the problem of specifying the counting convention associated with the given identity relation);

• • clearly spelling out the standard (leibnizian) recipe for identity relations, in general;

• • clearly spelling out trinitarian identity as one of the identity relations arising from the standard leibnizian recipe;

• • clearly spelling out the standard and very general counting convention for any identity relation;

• • clearly spelling out the trinitarian counting convention (e.g. 3 divine persons, 1 crucified divine person, 2 unbegotten divine persons, etc.) as one of the conventions arising from the standard and general counting convention applied to trinitarian identity (so defined);

• • clearly spelling out a promising account of divine simplicity in terms of entailing identity to God;

• • clearly showing that at least some prominent ‘solutions’ to the target logical problem are either significantly underdeveloped (at critical points) or are in fact contradictory.

Reflecting on the contributions above suggests that Divine Contradiction does a lot, and it does. If nothing else, I hope that the contributions stimulate advances on each issue. There are undoubtedly many important advances to make on the target problem(s).

I believe that the contradictory account of divine reality is the most promising direction for christian theology. May further work either confirm or clearly refute the account.