Limits to Logical Analysis in Doctrinal Debates

Limits to Logical Analysis in Doctrinal Debates

Only a handful of critics go beyond merely asserting the charge of incoherence of the Trinity and provide logical arguments to support their claim of incoherence.

In general, a logical demonstration of incoherence may include the following steps: Given propositions P and Q, one may demonstrate a contradiction between these two propositions by positing another proposition R (which is presumably true) such that Q and R taken together will lead to a fresh proposition S which clearly contradicts P. Conversely, one may claim that P and Q are coherent if S is evidently coherent with P. For examples of such an exercise, I refer to my earlier articles

In any case, the task of logical demonstration is not so straightforward. Note that we assume that the propositions are clear and unambiguous. For example, we assume that the particular statement P or Q adequately and accurately and precisely represents essential aspects of God. But the fact is, we do not have any clear account of human nature that has gained consensus, let alone an account of divine nature. In reality, propositions P and Q are read differently (though implicitly) by different protagonists in logical debates.

We should be honest and admit that the terms used in logical demonstration are essentially contestable. Given the essentially contestable nature of the logical terms, a modest expectation of logical proof is in order. Agreement is more likely be achieve if the objective is to demonstrate the coherence of the Trinity and Incarnation at the formal rather than material level.

Logic can only demonstrate that you are logical, that is, logical with the initial premises. We sometimes quip in a debate, “You are indeed logical, but your premise is wrong.” That is to say, logical coherence pertains to coherence with a suitably defined body of propositions. That being the case, we need more empirical or conceptual data to help ascertain both the logical coherence and truth claim of any proposition. To give an example, William Craig suggested the triangle as an analogy of the Trinity in his debate with Shabbir Ally: one shape, with three angles each being a part of the whole. Ally’s rebuttal was that each angle is not itself the triangle.

Craig responded,

I want to simply say let’s assume the Christian doctrine of the Trinity is what it is, and the question is: is that rational to hold to? And all, Shabir actually could say here was that in a triangle each angle was not a triangle, but according to the doctrine of the Trinity, each person is God. This is simply based on a misunderstanding by Shabir. The ‘is’ in the statement ‘Jesus is God’ is not an ‘is’ of identity. It’s not like saying ‘Cicero is Tully,’ where those are simply two different names of the same person – an ‘is’ of identity. Rather, this is an ‘is’ of predication. It’s like saying ‘the couch is red’. You don’t mean that the couch is a color; you mean that the couch has the property of being red. Similarly, when you say ‘Jesus is God, the Father is God, the [Holy Ghost] is God,’ that is to say that they are all divine – they all share attributes of deity. This is not an ‘is’ of identity, and unless you understand that, you’re bound to be confused. So, it is simply not the case that according to the classic doctrine of the Trinity that the Godhead as a whole is identical to any one of the three persons. It is very much like a triangle, where you have one entity comprising of [sic] three angles, or one entity comprising of [sic] three persons. And if that is the doctrine, then I ask you what is rationally objectionable about that? That is the doctrine I believe, and I see nothing irrational about it.

My view is that Craig is successful here in acquitting the Trinity/Incarnation from the charge of incoherence at the formal level. However, some critics may charge Craig for committing the fallacy of equivocation. But the charge of equivocation is unfair. I have noted that we need to bring in empirical or conceptual data to move the discussion further. Bringing in new data is unavoidable and even though this may be misread as equivocation.

Bringing in new data also means shifting the discussion to another (perhaps more comprehensive) framework. It seems that truth claims for any doctrine can be made at different levels and therefore the test of coherence has to be formulated to match the truth claim at different levels.

Note the following examples for different levels of coherence:
1) The theorem that two parallel lines meet at infinity is coherent with Euclidean axioms and geometry but not with Riemannian axioms and geometry.

2) Someone is a coherent speaker given his good grammar.

3) The Manifesto of the People’s Party offers a coherent set of economic policy

4) The multi-headed monster Hydra from Greek mythology is a coherent concept based on the criterion of functional unity exemplified by Siamese Twins.

Logicians since the twentieth century are aware that any sufficiently complex set of truth claims cannot be cannot be limited to simple logical analysis. I have in mind the the implications of Kurt Godel’s Incompleteness Theorem. Godel’s theorem proved two things:
1) If axiomatic set theory is consistent, there exist theorems which can neither be proved nor disproved.
2) There is no constructive procedure which will prove axiomatic set to be consistent.

I quote from Michael Polanyi, Personal Knowledge, pp. 259-260:

Within any deductive system which includes mathematic (such as for example the system of Principia Mathematica) it is possible to construct formulae – i.e. sentences – which are demonstrably undecidable within that system, and that such a sentence – the famous Godelian sentence – may say of itself that it is undecidable within the system. We can then go further by informally matching the sentence with the situation on which it bears, that is, with the demonstration of its own undecidability. We shall now find that what the sentence says is true and decide accordingly to assert it in that sense. Thus asserted, the sentence represents an additional axiom, which is independent of the axioms from which the unasserted sentence was derived.

Polanyi concludes, “This process reveals both that any formal system (of sufficient richness) is necessarily incomplete and that our personal judgment can reliably add new axioms to it.

Perhaps it is unavoidable that we go beyond abstract logical analysis and provide ‘thick descriptions’ of doctrines (to borrow from the anthropological discussion of Clifford Geertz) in order to demonstrate (not so much as to prove as to display) the coherence of any doctrine.

In this regard, the logical analysis deployed by Craig may be too restrictive. One may also judge that he should not have separated too sharply the ‘is’ of identity and the ‘is’ of predication. Of course, it is unfair to expect too much from his presentation given in the limited context of a formal debate. In that regard he provided a sharp and adequate response to Ally’s objection. But it should never be forgotten that the categories of ‘person’ (identity) and ‘nature’ (predication) were precisely formulated by Christian theologians to negotiate the extreme position of unqualified, strict ‘identity’ and mere predication to explain the Trinity/Incarnation.

I will dwell more on the language of predication later. In the next entry I juxtapose together two thinkers – Al Ghazali (who opposes the Trinity) and William Craig (who defends the Trinity) to compare how they appeal to analogical language and ‘thick description’ to reconcile diversity and functional unity (coherence).


  1. EJ says:


  2. CP says:

    Dr. Ng,

    You may already be aware of Denis Giron’s (an agnostic) defense of the coherence of the Trinity at the following URL:

    I’m posting it here for the benefit of readers who do not.