Ockham’s solution to the Trinity problem

In the fifth chapter of the third book of his monumental Summa Logicae, Ockham presents an interesting solution to the problem of the Trinity. He says that the following syllogism is not valid:

Every divine essence is the Father
The Son is a divine essence
Therefore, the Son is the Father

Why not? Surely it is valid by the rule of dici de omni that Ockham frequently applies to arguments. According to this rule, a universal proposition denotes that the predicate is truly affirmed or denied of anything of which the subject is predicated. Thus “every divine essence is the Father” denotes that of whatever ‘divine essence’ is predicated, so also ‘the Father’ is predicated. Since the minor premisses states that ‘divine essence’ is predicated of the son, it follows (by this rule) that ‘the Father’ is also predicated of the Son. So the conclusion “the Son is the Father” apparently follows. Why, then, does he now say that it does not follow?

Ockham answers that the proposition “every divine essence is the Father” does not denote that the predicate is truly affirmed or denied of anything of which the subject is predicated. And so the argument above is not governed by dici de omni, and so it does not have to be valid.

We can only know when such an argument holds, or when not, from sacred scripture, or from the determination of the church. If scripture, or the church, states that the premisses of such an argument are true and the conclusion false, we can be sure that the argument is not governed by ordinary logical laws. He notes also that such an argument is always valid in the physical or ‘created’ world. For “in the world of created things it is impossible that something one in number, simple and singular, really be several things, really distinct” (inter creaturas impossibile est quod una res numero, simplex et singularis, sit realiter plures res distinctae realiter).