Recently, Nathan criticized Bar-Hillel and Falk's analysis of some classical probability puzzles on the grounds that they wrongheadedly applied mathematics to the solving of problems suffering from “ambiguous informalities”. Nathan's prescription for solving such problems boils down to assuring in advance that they are uniquely and formally soluble—though he says little about how this is to be done. Unfortunately, in real life problems seldom show concern as to whether their naturally occurring formulation is or is not ambiguous, does or does (...) not allow for unique formalization, etc. One step towards dealing with such problems intelligently is to recognize certain common cognitive pitfalls to which solvers seem vulnerable. This is discussed in the context of some examples, along with some empirical results. (shrink)

Rutherford criticizes the way some people have analyzed the 2-children problem, claiming that slight nuances in the problem’s formulation can change the correct answer. However, his own data demonstrate that even when there is a unique correct answer, participants give intuitive answers that differ from it systematically — replicating the data reported by those he criticizes. Thus, his critique reduces to an admonition to use care in formulating and analyzing this brainteaser — which is always a good idea — but (...) contributes little what is known, analytically or empirically, about the 2-children problem. (shrink)

Recently, Nathan (1986) criticized Bar-Hillel and Falk's (1982) analysis of some classical probability puzzles on the grounds that they wrongheadedly applied mathematics to the solving of problems suffering from "ambiguous informalities". Nathan's prescription for solving such problems boils down to assuring in advance that they are uniquely and formally soluble--though he says little about how this is to be done. Unfortunately, in real life problems seldom show concern as to whether their naturally occurring formulation is or is not ambiguous, does (...) or does not allow for unique formalization, etc. One step towards dealing with such problems intelligently is to recognize certain common cognitive pitfalls to which solvers seem vulnerable. This is discussed in the context of some examples, along with some empirical results. (shrink)