Interesting discussion but I suspect an important distinction may be required between logic and probability theory. Logic is a special case of probability theory where values are restricted to only 0 and 1, that is to 0% and 100% probability. Within logic you may arrive at certain conclusions but generally within probability theory conclusions are not certain but rather assigned a degree of plausibility.

If logic provides, in some contexts, a valid method of reasoning then conclusions arrived at will be either 0% or 100% true. Denying that 100% confidence is ever rational seems to be equivalent to denying that logic ever applies to anything.

It is certainly true that many phenomena are better described by probability than by logic but can we deny logic any validity. I understand mathematical proofs as being within the realm of logic where things may often be determined as being either true or false. For instance Euclid is credited with first proving that there is no largest prime. I believe most mathematicians accept this as a true statement and that most would agree that 53 is easily proven to be prime.