"logical possibilities" is a grammatically correct and usable phrase in written English.
It refers to the various options or potential outcomes that make sense in a given situation. Example: In order to solve the mystery, the detective considered all logical possibilities of who could have committed the crime.
In addition, on the standard model of the relation between these kinds of modalities the logical possibilities are the most inclusive; they include any proposition that sheer logic leaves open, no matter how otherwise impossible it might be.
"Pack for the logical possibilities," Ms. Foster instructed.
I realized that there were only two logical possibilities.
There are only two logical possibilities, both of them sad.
One is that these devices are highly effective, despite the logical possibilities for bypassing them.
Determined to uncover the mechanism of the paramutation, the researchers tested and ruled out a number of logical possibilities, such as DNA or histone methylation.
After all, on Field's account, in order to avoid the platonist commitment to models or proofs, the concept of logical consequence is understood in terms of the primitive modal concept of logical possibility: A follows logically from B as long as the conjunction of B and the negation of A is impossible, that is, ¬◊(B ∧ ¬A).
Although some such methods undoubtedly belong to everyone's normal unarticulated conceptual repertoire, it is not clear that they are defined or even definable widely enough to enable philosophers to make satisfactory sense of a quantified logic of logical necessity and logical possibility.
In this respect, logicians' prospects have been enhanced by the development of a semantical theory of modal logic, both in the narrower sense of modal logic, which is restricted to logical necessity and logical possibility, and in the wider sense, in which all concepts that exhibit similar logical behaviour are included.
One reason to accept (b) is that metaphysical possibility and necessity, as defined as truth in some possible world and truth in all possible worlds may itself reduce either to logical possibility and necessity or physical possibility and necessity.
If you mean someone who agrees that logically there could be a god, but who doesn't think that the logical possibility is terribly likely, or at least not something that should keep us awake at night, then I guess a lot of us are atheists.
