Posted: May 17, 2012 8:54 pm
amkerman wrote:
Because classical logic's singular terms must denote existing things (when, as usual, ‘∃’ is read as “there exists”), classical logic is unreliable in application to statements containing singular terms whose referents either do not exist or are not known to. Consider, for example, the true statement:

(S) We detect no motion of the earth relative to the ether,
using ‘the ether’ as a singular term for the light-bearing medium posited by nineteenth century physicists. The reason why (S) is true is that, as we now know, the ether does not exist. According to classical logic, however, (S) is false, because it implies the existence of the ether. Free logic allows such statements to be true despite the non-referring singular term. Indeed, it allows even statements of the form ~∃x x=t (e.g., “the ether does not exist”) to be true, though in classical logic, which presumes that t refers to an object in the quantificational domain, they are self-contradictory.

Which hopefully illucidates why shrunks premise 1 is self contradictory in terms of classical logic.

No it doesn't, because it's not.

Simply explained, that example is unlike this example:-
"If God exists, he is a square circle."

Because there is no assumption of the existence of either god, or square circles.

Now, rather than editing in links to your earlier posts, can you please give a straightforward answer, what logic are you claiming your working from? Is it free logic as I see you've pasted that in to 2 of those posts?