Marilyn Adams gives the most sober and convincing account of Scotist univocity:
For his part, Scotus returns to the notion that Aristotelian science is a system of propositions organized into sound deductive syllogisms. A syllogism–e.g., ‘all A’s are B’s; all B’s are C’s; therefore all A’s are C’s’–can be valid only if the middle term ‘B’ is taken univocally in both premisses. Otherwise, there is a fallacy of four terms. Scotus concludes that metaphysics can furnish sound cosmological arguments from finite beings to infinite being, only if there is some concept of being that applies univocally to God and creatures.
As Richard Cross points out, this is for Scotus a semantic thesis. As Stephen D. Dumont emphasizes, Scotus’ concept of univocity is very thin, requiring only as much sameness of meaning as it would take to avoid the fallacy of four terms. Aquinas advances cosmological arguments using metaphysical principles. How–Cross asks–could Aquinas deny that the concept ‘being’ deployed in them is univocal in Scotus’ sense?
I’m not convinced. First, being cannot be the middle term of a cosmological argument since it shows up in the conclusion. The whole point is to prove that a god exists, after all. But I’ll leave that aside since it seems that the argument could still be made if there were an equivocation between, say, the major term in the premises and the conclusion. But I deny this is is the case precisely because of the sort of logical inference involved in a cosmological argument.
A cosmological argument is one that posits God as the proper cause of some created effect. Specifically, it identifies something as a secondary or instrumental cause, the primary cause of which is something that everyone considers divine. Thus, the basic form of the argument is
A is a secondary or instrumental cause to B (which all call a god/divine)
therefore, B exists.
This form is exactly the same as
A plays music (say, a lute)
A is a secondary or instrumental cause to B (lutists)
Therefore, B plays music.
But, as pointed out a few days ago, there’s no sense in which “plays music” is univocal, since it does not specify a multiplicity of things falling in one group, even as used logically in the argument. Say that A, M, X and P are every thing that “plays music” in the sense of premise 1. B is not a fifth item in that list, and, indeed, so far as we are speaking of primary and secondary causes, we know it must not show up on the list.
Briefly: “plays music” is equivocal between the premise and conclusion, but the conclusion is still follows from the nature of how we speak about instrumental or secondary causes. For the same reason, ‘exists’ must be used equivocally in the premises and conclusion of a cosmological argument, but the conclusion still follows logically from the premises, because of the nature of the causal inference one is drawing.