An apologetics aporia

1.) Reason can prove the Trinity free of logical contradiction.

2.) Whatever is proved free of contradiction is really possible.

3.) To prove that a necessary being is really possible proves it exists.

4.) The Trinity is a necessary being.

5.) The existence of the Trinity is a mystery that cannot be proven by reason.

Regardless of whether the Trinity exists or not #4 is true by definition and so I take it as given.

Possible responses:

A.) Take the unqualified affirmation of (1) as a truth of faith. While reason might be able to establish that it has proved the trinity free of all logical contradictions suggested so far, it cannot be sure it hasn’t missed one.

I reject this possibility since it destroys the very thing it tries to defend, sc. the reasonableness of apologetics. A reason that has to assume it’s missed some contradictions in something is one that cannot do its due diligence. True, “apologetics” is etymologically the defense of the faith, and in this sense is only a response, but the term clearly means more than this in actual practice.

B.) Take the logical space of metaphysically necessary beings as underdefined. While it is true that necessary truths must be either impossible or actual, the difference between mathematics and metaphysics is that the former domain is defined enough that we can specify the relevant possibilities while the latter is not. Ruling out contradictions can get us somewhere in mathematics while it can’t get us the same results in metaphysics. Reason must take the possibility of a Quaternity or Binity or Infinity as just as possible as a Trinity.

This account is false and possibly incoherent. How is the logical space of divine persons undefined? It’s one or not one, divided or undivided, etc. Either transcendental multiplicity is logically possible or it isn’t.

C.) Take freedom from contradiction as establishing agnosticism. To establish that something is not impossible leaves the mind undetermined as to its real existence. “Possibility” in this sense means “for all I can tell, it could be or not be so”. The contradictory of can’t be is might be, not can be. 

While Aristotle argues this, it’s hard to avoid the conviction that the previous sentence is obviously false. (N.B. The most persuasive critiques of the modal Ontological Argument confuse “can be” with “might be”: viz “saying “a necessary being is possible” and then “a necessary being can not be”, from which it’s non-existence is tehn rigorously proven, is an example of this).

While the principle that a little mistake in the beginning, etc. gets overused, it is very applicable here. One should decide at the beginning of his logic whether the contradictory of “can’t” is “might” or “can” or both.



  1. June 6, 2016 at 10:39 pm

    While I think the primary issue with the aporia is (2), I want to push your response (A) as perhaps stronger than you are suggesting. Your response would suffice if apologetics required demonstration; but it doesn’t seem to do so.

    • June 7, 2016 at 8:19 am

      I think the primary issue with the aporia is (2)

      Exactly. I’ve probably written twenty different posts about how I thought it was either false or impossible. The shift from mental to real being is something only God could do. But then I look at the premise on another day and it looks self-evident.

      Historically the problem of defining omnipotence led to some identity of the logical and the really possible. If the divine power extends to all things logically possible, then they’re really possible.

      Your response would suffice if apologetics required demonstration; but it doesn’t seem to do so.

      That paragraph had at least one major re-write and I’m still not happy with it. The weaker way of putting the claim is that all sorts of discourses are such that we have to allow that there might be some logical contradictions we haven’t noticed, but this doesn’t keep us from saying that we’ve really proved something. We treat the main contradictions, and if we do so without putting our finger on the scale then once we’ve disposed of a few objections we assume – we realize – that all others will fall in the same way. That said, we can also say that apologetics is reason so far as it has accepted certain things as revealed, and therefore as having a truth which, though it has no insight into, it has to preserve at all costs.

      I’m also bothered by the idea that if (A) is our account of mystery then it is only the mystery of any dialectical discourse. Biology or climate science or high-energy physics can never be certain that they’ve eliminated all possible contradictions either. Accounts of mystery demand more than this, but in doing so it is hard to keep them from running afoul of Davidson’s refutation of multiple conceptual schemes (i.e. God has one conceptual scheme and we have another). This might be the real aporia I’m gesturing at. Christian mystery demands multiple conceptual schemes, but Davidson seems to have shown there are no such things, at least for all those who conceptualize with language.

      • June 7, 2016 at 11:44 am

        I’ve always been inclined to think that Davidson’s argument founders on vagueness and approximations; one sees this particularly in his discussion of Kuhn and Feyerabend. Davidson takes incommensurability to be failure of intertranslatability, but it clearly is not — it’s imperfect intertranslatability. He does argue against partial non-intertranslatability later, but (1) his argument doesn’t seem to include approximate intertranslatability, but merely particular complete failures of intertranslatability and (2) methodology of interpretation doesn’t eliminate differences due to vagueness and approximation.

        On the other hand, mystery does seem to require much more than the fact that the truth identified by reason is something more than mere approximate truth, which is, as you quite rightly say, something found in any dialectical discourse.

        On omnipotence and real possibility, it’s true that they link up historically as you say. I’m inclined to think it’s a link too far. If God decides not to do something that he can do, it’s not really clear that it’s really possible. We tend to assume that the modal operators collapse here — If it could be really possible, it is really possible — but I’m not sure this is the case.

      • June 7, 2016 at 12:37 pm

        Do you think we could save Davidson’s point by positing a broader sense of translatability that includes commentary on terms, lexical entries to the original, meditation on original text, etc? True, if his argument against failure of translatability means we can capture every nuance in the original in a straight translation into the target language then his point is obviously wrong, but he might be assuming a broader sense of translation than that. To take a familiar example, “a translation” of John 1 might include not just the sentence in the target language but also a discourse on “arche” and “logos”.

      • June 7, 2016 at 1:47 pm

        I don’t think so, although in all honesty I haven’t thought about it in any sort of detail. In effect, the suggestion is that all one has to do to handle approximation and vagueness is to get more precise; but I think that human reason has some approximation and vagueness just built in.

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