The problem: if X is said of many, we have Xes. i.e. if “cat” is said of many, we have cats, if “flower” is said of many, we have flowers. The truth seems analytic: what is said of many is plural. What else could “plural” mean?
But (on trinitarian theory) “God” is said of many, and we do not have Gods. An offence, its seems, against grammar and self-evident truths.
Response 1: We avoid “Gods” because it is an expression used by our opponents, and we sometimes need to avoid expressions used by our opponents.
Response 2: The use of the plural never indicates a real plurality in what is said of many. In saying we have three “cats” we don’t mean to indicate that we have three feline natures. We don’t have three gods with Father, Son and Ghost because we don’t even have three men with Tom, Dick and Harry. The plural is only in the mode of signification and not in either the logical or real order.
Response 3: “God” is the name of an operation, not of a nature, just as “projectile” is the name of anything that is thrown (an operation), unlike “granite”, which is the name of a sort of nature. All names that appear to be said of God’s nature are either negations, or relations to creatures without showing us God as he is in himself. And thus when we say the trinity is “one God” we mean nothing but he is one undivided operation performed by three persons.
Response 4: Only what is circumscribed can be enumerated. Gold coins might be added up, but gold (the element) cannot be. Gold differs from golden things by not being numerable. But “God” names a nature which cannot be known since it is not circumscribed.
Response 5: Words denoting cause are not the same as words denoting nature. But persons are multiplied by causal relations (or what Western thought would call “principles” and not “causes”- ed). Therefore diversity of persons does not require diversity of nature.