The idea of monotheism can be put in different ways, and sometimes other ideas can be mistaken for monotheism. A more abstract approach, for example, would not necessarily say there is only one God, but only that there is no more than one God. This way of putting things is amenable to those who think there is something conceptually wrong with polytheism: it’s a confusion, an incoherence, a category error, and so forth. This idea can be called ‘anti-polytheism’ and can be expressed in predicate logic as follows:

Anti-polytheism: ∀x∀y[(Dx & Dy) -> y = x]

AP states that for any x and for any y, if x is divine, and y is divine, then x is identical to y. In other words, there is no more than one divine thing.

But, this is something even an atheist could agree with because 0 Gods is no more than 1.

So, some may wish to clarify that there is in fact only one God. If they just want to assert such at this level of generality, without specifying who or which God it is, they will want to say:

Abstract Monotheism: ∃x∀y[Dx & (Dy -> y = x)]

In other words, AM says there is some x, such that for all y, x is in fact divine, and if anything is divine, it is identical to x. If they want to pick out the God they have in mind and express a more creedal form of monotheism, they can use the same formula, but replace the variable ‘x’ with the specific constant for their God–say, ‘h’ for ‘YHWH’.

Creedal Monotheism: ∃h∀y[Dh & (Dy -> y = h)]

Failing to keep these ideas distinct could result in confused responses and reactions that jeopardize one’s connection to truth. You might still end up hitting a target, but it won’t be the one you were aiming at.

What I find interesting about analyzing the preceding positions in these logical terms is that it makes it clear that each takes it for granted that purported Gods would belong to the same domain of discourse: that’s how they can all be ranged over at the same time.

That is, there is one overarching domain of discourse, and of the things in there, if any of them are divine, then they are identical.

But, what if there was no single domain of discourse in which any two Gods were contained? At least, contained in some relevant respect, say, as First Principle?

That is, what if we treated a plurality of purported Gods as Gods, entertaining their transcendence, and did not assume from the outset that a polytheism at this level is false?

Something to consider.

Cheers!