It's "If I can imagine it, it's logically possible", right?
So, it may be the case that something is logically possible and that I can't imagine it. OK?
Yes. That was my primary worry not wanting to link human imagination too closely with logical possibility. There might be no end of logical possibilities that no human being can possibly conceive of. We might simply lack the cognitive powers. We might not have evolved in conditions where those logical possibilities exist. (black holes, the big bang, higher dimensions, heaven, who knows what...)
Obviously cockroaches can't conceive of mathematical physics. They simply lack the cognitive powers. So might there be beings elsewhere in the universe that stand in the same relation to us that we stand to the cockroach? And might there be fundamental aspects of reality whose understanding requires their sort of cognitive powers? (That example is from Albert Einstein.)
So I think that it's hubris to imagine that logic is somehow coextensive with human imagination. If that wasn't what you wanted to suggest, then we would be that much closer to agreement.
We both seem to agree that inability to imagine something does
not justify the conclusion that it's illogical.
That still leaves us with "
If I can imagine it, it's logically possible". I'm not entirely convinced of that one either.
Dreams are an obvious counterexample. Dreams are often illogical yet we still succeed in dreaming them. Psychotic delusions are a similar sort of waking state counterexample.
So "
If I can imagine it, it's logically possible" might have to be modified to become "
If I can imagine it in a logical manner, then it's logically possible". That change may or may not render it circular.
And I'm also still troubled by the idea of collapsing a psychological criterion (our ability to imagine something) with what I take to be a more ontological matter (whether or not something is logically possible).
The idea of logic seems a bit ambiguous. It seems to me to have both a psychological sense (how we think and reason) and an ontological sense (the underlying structure of how reality behaves that we try to capture in physics, mathematics and logic). Trying to invent a psychological criterion (our ability to imagine) to serve as a criterion for the ontological sense seems to me to confuse the two. That's my worry. Maybe I'm wrong.
Certainly that's how we typically operate in our everyday reasoning process. Thinking about things is the only way that we have to understand or explain anything. But I don't see what can justify any necessary isomorphism of the psychological and ontological senses.
Our reasoning may function more as a heuristic. It may not be optimal and it may not always be correct. (I'm sounding very much like Hume there.)