Boolean algebra was fist described in a book on philosophy. It's not something different than the study of whether an argument is logical or not, it's a tool that was developed as part of a methodology to analyze if an argument is logical or not.
wrt x and ~x, can a statement about a quantum state be both true and false at the same time? Depending on how you interpret quantum mechanics it may well be. What philosophy and modern logic have to say about this I'm not sure.
If you are talking about the 1850's book by George Boole, then Boole lived at a time when many mathematicians and early scientists still thought of themselves as philosophers.
I don't think anyone here is dismissing the mathematical work which those people did (I wont bother to name them all, because they are rightly famous, all the way from the time of Euclid through people like Leibniz and right up to 1900 with people like Einstein and Minkowski).
But maths is now really a separate subject from philosophy. And it was really a separate subject even then, eg iirc Galileo described himself as a philosopher, astronomer and mathematician.
We are not complaining about philosophy just for the sake of it. Nor just because we want to give credit to what has become “science”. But more because philosophers today, and people on the internet, often want philosophy to take the credit for what science has achieved, and that's just not acceptable.
According to most of the pro-philosophy posts here, people also want philosophy to take the credit for advising and guiding people in all sorts of other subjects/fields too. I think most of us are less concerned about that. Though perhaps we should be concerned because there does not seem to be any genuine basis for why philosophy should be claiming credit there either.
I could answer your question about about quantum states of particle/fields, but given what has happened here, I am not going to bother wasting my time (because I don't think you actually want to know, except as a way of creating more endless philosophically inspired acrimonious arguments).