We must analyze what logical reasoning is. Inductive reasoning is not
logical reasoning. Logical reasoning is, in essence, operations on propositions of language. As such they are part of language and does not transcend it.
The crucial point is that it does not make sense to doubt a logical argument
. Logic is determined by the correct usage of logical connectives, such as "and", "or", "not", etc...
Logic is simply the way we treat propositions.
I don't mean that, say, inductive reasoning is wrong, but I do mean that it is not logical.