For the case of denying science, I think that people sometimes get carried away. Science gives absolute answers, but only on a highly restricted set of questions. There is a discipline in not answering questions whose answer is unknown, and by extension, not asking questions whose answer is expected to be unobtainable. Many people cannot or won't accept this discipline, and prefer to complete their knowledge on the "big" questions with beliefs rather than leave some questions unanswered.

Which leaves a fascinating ancillary problem: where do the "big" questions come from and why won't they go away? I suspect that kids don't come up with these questions on their own, but rather absorb them and their "importance" from contact with adults, which leads to pressure to resolve them.

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$E(X_t|F_s) = X_s,\quad t > s$

 Why is it in someones interests to believe (say) that science is all a conspiracy.

Firstly, they enjoy the drama. Worrying that the world is going to end makes life more exciting than the day job.

Secondly it 'proves' that they're not really as stupid and powerless as science makes them feel.

Also, it's very rare for hardcore CT followers to be even slightly literate in basic science. Facts and paranoia look indistinguishable to them, because they don't have the background to tell them apart.

See this thread for a depressing example.

- Jake

Friends come and go. Enemies accumulate.