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I think I see what you mean. I would probably describe it not as a difference in the properties of axioms/assumptions themselves, but rather a difference in the way they are used and manipulated, a difference in the context.
I do not recall a realization similar to yours, however, perhaps because thinking in counterfactuals and following the chain of consequences comes easy to me. "Sure, let's assume A, it will lead to B, B will cause C, C is likely to trigger D which, in turn, will force F. Now you have F and is that what you expected when you wanted A?" -- this kind of structure is typical for my arguments.
But yes, I understand what you mean by blocks in empty space.
I don't think this is really the same skill as following counterfactuals and logical chains and judging internal consistency. Maybe the "parallel postulate" counterfactual was a bad example.
It's more the difference between
"Logic allows you to determine what the implications of assumptions are, and that's useful when you want to figure out which arguments and suppositions are valid" (This is where your example about counterfactuals and logical chains comes in) [1]
and
"Axioms construct / pin down universes. Our own universe is (hope... (read more)