Mental models: Rationality, representation and process

approach, is incorporated in a number of texts as the systematic formal search for a counterexample as a system of formal rules. As we would all expect, the difficulty of the search increases when disjunctions of possible models are involved, and as I and most logicians would expect, the difficulty also increases when existential quantifiers are present. These particular sets of rules were chosen as much for formal goals as for psychological ease, so I am not arguing that they are exactly the right representation of ordinary deductions, but I do believe that J-L & B have not presented a conclusive case against formal rule systems generally. The second argument is the alleged suppressibility of modus ponens. Given a premise "If she meets her friend, Mary will go to the play" and "Mary meets her friend" the consequent will be deduced by modus ponens by most deducers. However, J-L & B have found that if they also present a second premise, "If Mary has enough money, she will go to the play," that reasoners will not draw the conclusion that Mary goes to the play given that she meets her friend. The authors conclude that modus ponens has been "suppressed" and thus is not a mental rule. Perhaps, given the second premise, subjects mentally rewrite the first premise as "If Mary meets her friend and she has enough money, she will go to the play," in which case modus ponens is not suppressed but is inapplicable. The third argument is related to the issue concerning existential quantification. J-L & B's argument that existential quantification is no harder than universal seems to have two bases one a conceptual analysis and the other an experimental one. On page 136 they give an example of a derivation using universal quantifiers, noting that a comparable problem with existentials "differs only in that the existential quantifier, 'some', in the second premise has to be existentially instantiated, and so the quantifier restored at the end of the derivation is also existential. There is no principled way in which the derivations for the two sorts of problems can be made to differ in length." There is no recognition that existential instantiation in many systems requires a new subproof, and that in others it requires flagging a variable or in other ways giving special status to the formula in question. (In fact, in the universal derivation there is no mention of the necessary restriction on universal generalization.) This raises doubts in my mind whether J-L & B have a sufficient grasp of what is involved in formal existential inferences. J-L & B's experimental evidence involves two pairs of sentences. The first sentence of each is "None of the painters is related to any of the musicians," while the second sentences are, respectively: