It may help to distinguish the following questions.
1. Is there a clear scriptural basis for the doctrine of the Trinity?
2. Is the doctrine, as formulated in the Athanasian creed and related canonical documents, true?
3. Is it possible for human reason, unaided by divine revelation, to know the doctrine to be true?
4. Is the doctrine of the Trinity possibly true?
5. Is the doctrine thinkable (conceivable) without contradiction?
I have little to say about the exegetical (1) since it is beyond my competence as a philosopher. I cannot pronounce upon (2), either for or against, until I have decided (4) and (5). The same goes for the epistemological question, (3). My present interest is in (4) and (5), which are logically prior to the first three, with (5) being logically prior to (4).
(4) and (5) are distinct questions. An affirmative answer to (5) does not entail an affirmative answer to (4). This is because conceivability is no sure guide to real (extramental) possibility. Of the two questions, (5) comes first in the order of inquiry: if we cannot think the Trinity without contradiction, how could we advance to the further question of whether it is really possible?
(5) is the question at the center of my interest.
It is difficult to get some people to appreciate the force and importance of (5) because they are dogmatists who accept the Trinity doctrine as true simply because they were brought up to believe it, or because it is something their church teaches. Since they accept it as true, no question of its logical coherence arises for them. And so they think that anyone who questions the doctrine must not understand it. To 'set the objector straight' they then repeat the very verbal formulas the logical coherence of which is in question. "What's the problem? There is one God in three divine Persons!" They think that if they only repeat the formulas often enough, then the objector will 'get it.' But it is they who do not get it, since they do not understand the logical problems to which the doctrinal formulations give rise.
Or the adherent may think that the objector is merely 'attacking' or polemicizing against his faith; it doesn't occur to the adherent that there are people whose love of truth is so strong that they will not accept claims without examination. Now if one examines the creedal formulations, one will see that the gist of the Trinity doctrine is as follows:
1. Monotheism: There is exactly one God.
2. Divinity of Persons: The Father is God; the Son is God; the Holy Ghost is God.
3. Distinctness of Persons: The Father is not the Son; and the Holy Ghost is not the Father or the Son.
The problem is to show how these propositions are logically consistent, that is, how they can all be true, but without falling into heresy. If you cannot see the problem, you are not paying attention, or you lack intelligence, or your thought-processes are being distorted by ideological commitments. Whatever you think of Brower and Rea's solution to the problem, their exposition of it is very clear and I recommend it to you. My reason for not accepting their solution is here.
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