Cognitive scientists have made many proposals for how the mind represents the world. Some argue that people reason by representing the world as images; others argue that people reason be representing the world as logical formulas. Those who advocate the existence of mental models reject these, and other, proposals. Mental models are not…

• …mental images. Mental images can’t contain abstract information — they can’t represent, say, the concept of negation. Likewise, images always depict a fixed perspective. Models don’t.
• …propositions, i.e., logical formulas. Propositions can’t be scanned to yield inferences — a proposition representing the spatial relation that the ball is on top of the table is a set of symbols such as: onTop(ball, table). This set of symbols can’t be scanned to yield the inference that the table is underneath the ball.
• …probability distributions. Each model represents a single possibility, whereas probability distributions represent an infinite number of possibilities at once.
• …3D physics simulations. Recently, scientists have hypothesized that mental simulations are similar to the simulations used in modern day physics engines. But, just like images, physics engines can’t directly represent negation and other abstract concepts, such as disjunction.
• …network representations. Networks — deep or shallow — can’t represent abstract concepts such as negation or disjunction, either; they can’t be scanned to yield inferences; and their structures are typically pre-specified. People, in contrast, continuously build, revise, and abandon 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 “diagram” that Peirce describes is a mental model of the world.

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 and to underlie explanation, but he thought that human reasoning was based on verbal rules. 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 similar to to architects’ models of buildings, to molecular biologists’ models of complex molecules, and to physicists’ diagrams of particle interactions.

Despite Craik’s insight, cognitive scientists took for granted that people reasoned based on the laws of symbolic logic until Phil Johnson-Laird published the book Mental Models in 1983. Johnson-Laird argued that the mind constructs mental models as a result of perception, imagination, knowledge, memory, and the comprehension of discourse. After Johnson-Laird developed the model theory, cognitive scientists began to 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.

The principal assumptions of the theory are:

1. 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.
2. 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.
3. 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.
4. 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.
5. 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.
6. 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.
7. 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 of mental models explains how people reason deductively, how they infer probabilities, how they make decisions, and how they reason recursively about about other people’s reasoning. The model theory explains:

• why some inferences are easy and other inferences are difficult;
• why people take longer to make some inferences than others;
• the sorts of heuristics people use to draw conclusions rapidly;
• the sorts of strategies people spontaneously adopt;
• how reasoners conclude that “nothing follows” from a set of statements;
• why some people are good at reasoning and others are bad at it

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.