I just finished reading the graphic novel Logicomix: An Epic Search for Truth. It is based on the biography of Bertrand Russell and his quest to derive all of mathematics using logic, e.g., to prove that one plus one equals two.
A recurrent theme in the book is that there is a tendency in logicians towards madness. A friend once told me the same about philosophers. Certainly logic and philosophy are related fields.
The book leaves it open as to the direction of the cause-effect relationship of this madness-logician correlation. Does delving into logic drive you mad or does being a bit mad drive you to logic? I suspect it is more of the latter.
Schizophrenia was cited as one of the main causes of madness that plagued the logicians and their family members. Schizophrenia is characterized by auditory hallucinations, i.e., hearing voices in your head. Rather than being able to determine the true nature of reality based on their own objective observations, schizophrenics have to deal with the possibility that their internal demons, of the sort proposed by Decartes, might be fooling their senses. In this situation, what can you truly know, other than that I am?
A respite from this uncertainty might be the alluring potential of deduction. Certainly much knowledge of the unseen can be deduced from the induced as is common in the sciences. And perhaps even the non-existence of the seen, or heard, can be deduced if the facts and logic merit.