I don’t know if this interests anyone, but in a discussion, a person asserted that if one believes there is only one God, then he necessarily believes that there are no other gods. As a simple matter of Philosophy, this is not true as I can affirm and negate “There is one God” while never affirming or negating “There are more than one god”. I may be disposed to thinking there is but one God but not disposed to thinking there aren’t possibly more than one; which necessarily means I wouldn’t negate “There are more than one god.”
A person may intend that some propositions are mutually exclusive so that in believing one, the other must be rejected; such as believing a light is on in another room entails the belief the light is not also off at the same time. But although this sounds decisive and perfectly rational, people are not and they intuitively discard things like the “Law Of Non Contradiction” for very good, practical reasons that are perfectly natural. This is why there is a thing called “Doublethink” and why there is an epistemological philosophy of Dialetheism. It is perhaps true that a light is either on or off, but not true that our beliefs about the state of affairs with a light are binary.
Supposing I believe the light is actually in fact on, I may not be very committed to the belief; in other words, my certainty about it is very low (do note, certainty is Psychology, not Epistemology). Supposing whether or not the light is on is a very important state of affairs and knowing that state of affairs is vital, I may need to think out both possibilities. Were there some greater risk to “act as if” the light were on when it actually isn’t, then I ought to “act as if” it is not. That’s even if I happen to think the light is actually on.
Belief is a disposition to act and the above is simply one very common way one may approach some state of affairs, while it also shows or at least implies a very intimate tie to our psychologies.
For this idea I expressed about God that some may think is merely semantics, this is another direct example folks must agree with if they at all know maths. It represents what proponents of Dialetheism consider a “non trivial” example (while the example I just gave of binary contradiction is considered “trivial”).
1) I believe any number of the same sign produces a positive value when multiplied together.
2) I believe that all numbers have square roots.
By the count of the person disagreeing so far, we must discard one or both of these beliefs listed because asking for the square root of a negative number implies they both can’t be right.
Well, like any contradiction, they certainly can both be true … as Aquinas said, the smallest of distinctions moots all contradiction, and for this example, Bombelli mathematically resolved.
So again, if the claim is that a Monotheist must deny the verity of other states of affairs in opposition to Monotheism (such as there being many deity, or even no deity), that’s simply wrong.