I asked on MathSE What are the various respects under which a logic can deviate from classical logic, thus being “ non-classical”? and received one short answer. So, I'm interested in responses from Philosophy SE, too.
In what ways can a logic deviate from classical logic? I think one can find rather easily a list (though maybe incomplete) of non-classical logics. But it seems more difficult to find a presentation of the field that exhibits in a systematic fashion under which respects a logic can be non-classical.
The aspects I can think of are the following:
- Type of objects over which quantifiers range --> first-order/ second-order logic
- Validity of "ex falso" or not --> paraconsistent logics
- Use of modal operators, or not --> modal logics
- Finite or infinite number of premises --> compactness maybe?
There is an attempt at such a presentation in Theodore Sider's book Logic For Philosophy, but I'd be much interested in other references.
Note: I'm not asking for an absolutely complete list of points of departure from classical logic; I suppose it would be too long. Rather, what interests me is the systematicity of the presentation.