The original post was about analytic philosophy and, in particular, about how much intuitions should be trusted. This is a pretty interesting question when we are investigating hypotheses whose truth or falsity are subject to human intuitions. Therefore I find it natural to interpret the statement you were initially responding to, i.e.

And a claim that intuitions are uncorrelated with truth would be pretty hard to defend.

as refering to statements inside the domain of human intuitions. There is certainly no disagreement between us about the fact that human intuitions isn't applicable to all statements.

The googol amount of clauses was referred to as small if e.g. the number of clauses is randomly chosen as a natural number.

I understood that you sort of say that googol is small as compared to a (typical?) random natural number, but I am not sure what it exactly means. What is a typical random natural number? Do you have in mind some specific distribution whose mean is greater than googol? What would be a number which weren't small in comparison to random natural numbers?

(I have a feeling that my responses may appear somewhat obnoxious. If it is so, it's not intentional.)