Search All of the Math Forum:
Views expressed in these public forums are not endorsed by
NCTM or The Math Forum.


quasi
Posts:
11,785
Registered:
7/15/05


Re: Why reasoningaboutreasoning problems are flawed.
Posted:
Jan 26, 2013 10:21 AM


Paul wrote: > >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 deducible >without any reasoningaboutreasoning psychological logic, and >suppose that Y could only be deducible by appealing to the >failure of A and B to deduce X. > >Reasoningaboutreasoning 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 immediatededuction 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.
Puzzles typically have lots of implicit assumptions, and often this is by design, so as not to make the statement of the puzzle too unwieldy.
The issue you describe can easily be fixed by assuming, for example, that information and/or decisions are revealed only at integer times t = 0, 1, 2, 3 ... and all reasoning by participants is done during the time intevals n < t < n+1 between consecutive integer times.
quasi



