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...the encounter of an immovable object with an irresistible force...
Reread me Caledonian - this is a problem with logic; not a problem with language. You had no problem expressing it verbally, so it's not the kind of thing I'm talking about.
In response to
Disputing Definitions
Is this a problem with logic or a linguistic expression of a paradox?
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I do know why I trust my intuitions as much as I do. My intuitions are partly the result of natural selection and so I can expect that they can be trusted for the purposes of surviving and reproducing. In domains that closely resemble the environment where this selection process took place I trust my intuition more, in domains that do not resemble that environment I trust my intuition less.
Black box or not, the fact that we are here is good evidence that they (our intuitions) work (on net).
So then anything that has evolved may be relied upon for survival? It is impossible to rationalize faith in an irrational cognitive process. In the book Blink, the author asserts that many instances of intuition are just extremely rapid rational thoughts, possibly at a sub-conscious level.