Date: Jan 26, 2013 9:46 AM
Author: Paul
Subject: Why reasoning-about-reasoning problems are flawed.

In what was probably an overly long post, I tried to explain why a genre of maths problems is flawed and I didn't get any responses, so I'm trying again with a shorter post.
In this type of problem, there may be two participants A and B where A and B are in the same position. There are two possible scenarios X and Y, and A and B try to deduce whether scenario X or Y pertains.
Suppose that if X pertains, this would be readily deductible without any reasoning-about-reasoning psychological logic, and suppose that Y could only be deducible by appealing to the failure of A and B to deduce X.
Reasoning-about-reasoning problems claim that A should reason "If X were true,
B would be able to deduce it." Similarly B should reason "If X were true, A would be able to deduce it."
A then appeals to the lack of a deduction from B. B appeals to the lack of a deduction from A. This lack in deduction is used to deduce that X does not hold and that Y is therefore true.

I regard this entire type of problem as being nonsensical, due its failure to make explicit the assumptions the solver should make about the reasoning process.

The poser of this genre of puzzle assumes that if X were true, A and B could deduce it immediately. Since the participants have this immediate-deduction facility, why should they not be similarly immediate in following the intended solution to deduce Y? If they only deduce Y after (for example) 5 minutes, then (unless more conditions are given) a contradiction could be said to arise from the fact that the problem wasn't solved (by A and B) in four minutes.

Paul Epstein