Not trolling at all (and I don't think brokenhut was either), but genuinely think this is an important point.

I don't think you can learn anything about the physical universe using pure formal logic.

Being 'rational' to me means basing beliefs on evidence (including observation). Things you read in books, intuition and muscle memory are all kinds of evidence which may be more or less reliable.

Logic, mathematics and statistics can only be useful in helping to interpret that evidence well.