Deductive Reasoning

Psychological investigations of deductive reasoning focus on inferences drawn from premises conveying operators such as if, and, or, and not, and quantifier terms such as all and some. Formal logic typically is usedtheories to determine which deductive inferences are valid. People routinely draw many valid inferences, but often accept others that are fallacious, and psychological research needs to account for both. Some researchers, such as Jonathan Evans, have focused on task features that influence fallacious inferences, proposing biases and heuristics in reasoning. This approach, however, does not explain the valid inferences that people make, nor the intuitions about the validity of such inferences.

Researchers such as Patricia Cheng, Keith Holyoak, and Leda Cosmides have focused on the role of content in making inferences, and certain types of content can both discourage some common fallacies and encourage some valid inferences. This approach, however, does not explain a wide set of valid inferences made with content outside of those described in these theories. Other researchers, such as David Over, Mike Oaksford, and Nick Chater, have proposed Bayesian inferential processes, in which knowledge about problem content guides computations about probabilities. These do not explain inferences that are made from premises with abstract content.

Two research paradigms address deductive inferences across all sorts of content: mental-logic theories and mental-models theories. Two mental-logic theories have been proposed, one by Lance Rips and another by Martin Braine and David O'Brien. These theories propose sets of inference schemas and procedures for implementing the schemas. Many reasoning errors are explained by limitations in the reasoning procedures. Braine and O'Brien proposed a universally available direct-reasoning routine that applies the inference schemas whenever the requisite propositions are considered simultaneously. For example, when premises of the form p or q and not p are in working memory conjointly, a schema infers q, and when premises of the form if p then q and p are considered conjointly, another schema infers q. Considerable evidence shows that people apply such schemas automatically and effortlessly whenever the premise information is available both in laboratory problems and in stories. Reasoning strategies that go beyond the basic program are not universal and require effort, and problems that require such strategies are solved far less and often lead to fallacious inferences. Another source of reasoning error addressed by the mental-logic approach is found in pragmatic inferences. For [Page 236]example, if p then q can invite one to infer if not p then not q, which is not deductively valid.

Philip Johnson-Laird and Ruth Byrne have proposed a mental-models theory in which people construct analogical representations of premise information. Because working memory has limited capacity, people tend to construct only minimal representations, although a completely logical representation usually would require more complete models. For example, given the premises if p then q and p, one can construct the following incomplete models:

where the models for the two premises and then for their combination are separated by semicolons. A conclusion will be based on the final model, which would support a conclusion of p and q, although no one states this conclusion, saying instead only q. Models theorists explain this by arguing that because p is a categorical premise, its inclusion in a conclusion would violate pragmatic constraints.

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