Lomax wrote:BiV implies that the everyday propositions we take to be logically true (such as 2 + 2 = 4) are by that token necessarily true…

Agreed, the truths of math/logic are NOT 'man-made'; nor reliant upon the existence of man.

We have no 'means' to refute math/logic. Any attempt to invalidate only invalidates our own invalidation.

The (non changing) truths of math/logic are much more certain than the (constantly changing) 'man-made' truths of science. -- Logic/math is our best means of ascertaining truths. There is no higher authority.

RJG wrote:The primary purpose of logic in philosophical discussions it to identify and rule out the logical impossibilities and contradictions. If "married bachelors" are 'logically impossible', then any continued debate, assertions, and posturing of such should cease (...one would think, right?).

Lomax wrote:...RJG says that the primary purpose of logic is to identify and discard logical impossibilities (my italics). That would render it somewhat trivial - we might as well say that the purpose of Scientology is to rule out Scientological impossibilities. Presumably what RJG means is that the purpose of logic is to rule out impossibilities - in which case we need some explanation as to how it does so, as opposed to merely ruling out inconceivabilities.

Are "inconceivabilities" the same as "logical impossibilties"??

One's inability to see (conceive of) something, seems to be quite different than one's ability to see a 'contradiction'.

Lomax wrote:Firstly, we (humans, philosophers, scientists, sense-makers) don't all agree which logic is the correct one (or even if there is only one) - metalogicians differ about whether higher-order logics should be allowed, whether fuzzy logics should be allowed, which axioms to choose in the construction of a mathematical logic, and so on. Hilbert systems differ from other logics in the way they prioritise axiom schema over rules for inference, for example.

"X = not-X" is a logical impossibility in "everyone's" logic!

Other logical impossibilities include 'before / after', and 'greater than / less than' relationships. If A>B is true, then A<B is also a logical impossibility.