What are mental models?
Mental models are psychological representations of real, hypothetical, or imaginary situations. They were first postulated by the American philosopher Charles Sanders Peirce, who postulated (1896) that reasoning is a process by which a human
“examines the state of things asserted in the premisses, forms a diagram of that state of things, perceives in the parts of the diagram relations not explicitly mentioned in the premisses, satisfies itself by mental experiments upon the diagram that these relations would always subsist, or at least would do so in a certain proportion of cases, and concludes their necessary, or probable, truth.”
The Scottish psychologist Kenneth Craik (1943) proposed a similar idea; he believed that the mind constructs “small-scale models” of reality that it uses to anticipate events, to reason, and to underlie explanation. Like pictures in Wittgenstein’s (1922) “picture” theory of the meaning of language, mental models have a structure that corresponds to the structure of what they represent. They are accordingly akin to architects’ models of buildings, to molecular biologists’ models of complex molecules, and to physicists’ diagrams of particle interactions.
Since Craik’s insight, cognitive scientists have argued that the mind constructs mental models as a result of perception, imagination and knowledge, and the comprehension of discourse. They study how children develop such models, how to design artifacts and computer systems for which it is easy to acquire a model, how a model of one domain may serve as analogy for another domain, and how models engender thoughts, inferences, and feelings.
How we reason
The theory of mental models rests on simple principles, and it extends in a natural way to inferring probabilities, to decision making, and to recursive reasoning about other people’s reasoning. We can summarize the theory in terms of its principal predictions, which have all been corroborated experimentally. According to the model theory, everyday reasoning depends on the simulation of events in mental models (e.g., Johnson-Laird, 2006). The principal assumptions of the theory are:
- Each model represents a possibility. Its structure corresponds to the structure of the world, but it has symbols for negation, probability, believability, and so on. Models that are kinematic or dynamic unfold in time to represent sequences of events.
- Models are iconic insofar as possible, that is, their parts and relations correspond to those of the situations that they represent. They underlie visual images, but they also represent abstractions, and so they can represent the extensions of all sorts of relations. They can also be supplemented by symbolic elements to represent, for example, negation.
- Models explain deduction, induction, and explanation. In a valid deduction, the conclusion holds for all models of the premises. In an induction, knowledge eliminates models of possibilities, and so the conclusion goes beyond the information given. In an abduction, knowledge introduces new concepts in order to yield an explanation.
- The theory gives a ‘dual process’ account of reasoning. System 1 constructs initial models of premises and is restricted in computational power, i.e., it cannot carry out recursive inferences. System 2 can follow up the consequences of consequences recursively, and therefore search for counterexamples, where a counterexample is a model of the premises in which the conclusion does not hold.
- The greater the number of alternative models needed, the harder it is: we take longer and are more likely to err, especially by overlooking a possibility. In the simulation of a sequence of events, the later in the sequence that a critical event occurs, the longer it will take us to make the inference about it.
- The principle of truth: mental models represent only what is true, and accordingly they predict the occurrence of systematic and compelling fallacies if inferences depend on what is false. An analogous principle applies to the representation of what is possible rather than impossible, to what is permissible rather than impermissible, and to other similar contrasts.
- The meanings of terms such as ‘if’ can be modulated by content and knowledge. For example, our geographical knowledge modulates the disjunction: Jay is in Stockholm or he is in Sweden. Unlike most disjunctions, this one yields a definite conclusion: Jay is in Sweden.
The theory accounts for the informality of arguments in science and daily life, whereas logic is notoriously of little help in analyzing them. If people base such arguments on mental models, then there is no reason to suppose that they will lay them out like the steps of a formal proof. The theory of mental models, however, is not a paragon. It is radically incomplete; and it is likely to have problems and deficiencies. Proponents of rule theories have accused it of every conceivable shortcoming from blatant falsehood to untestability. It postulates that human reasoners can in principle see the force of counterexamples, and indeed people are able to construct them — a competence that is beyond the power of formal rule theories to explain. The model theory may well be overturned by counterexamples predicted by a superior theory. In which case, it will at least have had the virtue of accounting for its own demise.