Four experiments examined the strategies that individuals develop in sentential reasoning. They led to the discovery of five different strategies. According to the theory proposed in the paper, each of the strategies depends on component tactics, which all normal adults possess, and which are based on mental models. Reasoners vary their use of tactics in ways that are not deterministic. This variation leads different individuals to assemble different strategies, which include the construction of incremental diagram corresponding to mental models, and (...) the pursuit of the consequences of a single model step by step. Moreover, the difficulty of a problem (i.e. the number of mental models required by the premises) predisposes reasoners towards certain strategies. Likewise, the sentential connectives in the premises also bias reasoners towards certain strategies, e.g., conditional premises tend to elicit reasoning step by step whereas disjunctive premises tend to elicit incremental diagrams. (shrink)
We report three experimental studies of reasoning with double conditionals, i.e. problems based on premises of the form: If A then B. If B then C. where A, B, and C, describe everyday events. We manipulated both the logical structure of the problems, using all four possible arrangements (or ''figures" of their constituents, A, B, and C, and the believability of the two salient conditional conclusions that might follow from them, i.e. If A then C , or If C then (...) A . The experiments showed that with figures for which there was a valid conclusion, the participants more often, and more rapidly, drew the valid conclusion when it was believable than when it was unbelievable. With figures for which there were no valid conclusions, the participants tended to draw whichever of the two conclusions was believable. These results were predicted by the theory that reasoning depends on constructing mental models of the premises. (shrink)
We set out a doctrine about truth for the statements of mathematics?a doctrine which we think is a worthy competitor to realist views in the philosophy of mathematics?and argue that this doctrine, which we shall call ?mathematical relativism?, withstands objections better than do other non-realist accounts.