Some Questions About the Trinity Distinguished
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, 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.
(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.
The problem, to put it schematically, is to prove the consistency of the following set of propositions:
a) P1 is numerically distinct from P2.
b) P2 is numerically distinct from P3.
c) P1 is numerically distinct from P3.
d) P1 is G.
e) P2 is G.
f) P3 is G.
If the 'is' in the last three propositions is the 'is' of identity, then a contradiction is easily derivable. (Verify this for yourself.)
This suggests that the solution must lie in the direction of reinterpreting the 'is' as it occurs in the last three propositions. Say what you want about Bill Clinton, he rendered a great service to philosophical logic by insisting that much depends on what the meaning of 'is' is. And he saved his hide to boot!
Reading the 'is' as the 'is' of predication won't cut it, as I have already argued in more than one post. Are there any other possibilities?