Johnson-Laird gives an overview an account of mental models that originally is derived from Kenneth Craik. Craik’s use of models was originally directed towards an account of explanation. The review Johnson-Laird gives is to find a mechanism for formalizing meaning in language that explains cognition. The formulation is strongly tied in the notion of computation, and models are represented as computationally formalizable. This puts Johnson-Laird at odds with proponents of embodiment, but his theory nonetheless gives a formal strategy for forming and understanding mental models.
The prologue introduces a set of questions which is good for characterizing the investigation. Here are a couple of them (p. ix):
- Why is it that we cannot think everything at once but are forced to have one thought after another? Our memories exist together, yet we cannot call them to mind all at once, but only one at a time.
- Why are there silences when we think aloud? Aren’t we thinking at those moments, or are we unable to put our thoughts into words? It seems unlikely that thoughts should be grossly intermittent, so what barrier prevents them from being articulated?
- What happens when we understand a sentence? We are aware of understanding it, and are more aware of having failed to do so. Why can’t we follow the mental processes of comprehension as we can follow the action of tying a shoelace?
The concept of mental models derives from Craik. Johnson-Laird notes Weizenbaum’s ELIZA, but claims that it is not a simulation, but rather a dissimulation. It does not have a process of thought, but conjures thought instead. This distinction raises the contrasting idea that ELIZA matches and responds to the interactor’s model, rather than having a model of its own.
The Nature of Explanation
Most theories of cognition consist of description, and lack are not formal (in the sense of algorithmic). Johnson-Laird asks what the criteria is for a definition of cognition. This criteria, he explains, should describe theory in the form of an effective procedure. Theory must be in the form of an algorithm. This should not be a limitation in what exists in the world, but rather, what constitutes a theory that describes the world.
Later in the chapter, there is an extensive discussion of Turing machines, and explaining their universality. He is very impressed by and fascinated with the capacity for Turing machines to do any computation, and furthermore represent each other. If theories are algorithms, then they must be computable. That assertion is the claim of functionalism, to which Johnson-Laird ascribes.
The Doctrine of Mental Logic
Models are intended to replace the doctrine of mental logic, which is the propositional model of cognition. Propositional logic is a fallacious as a model for cognition because of the many logical mistakes that people make on a daily baisis. If our brains worked according to mental propositional logic, then we would be able to more readily correctly answer certain logical problems, which is clearly not the case. Johnson-Laird is not attempting to argue against logic, but rather, that there are multiple kinds of logic.
The logical problem demonstrated is case where the subjects are shown a set of cards with the symbols: [E, K, 4, 7], and told that every card has a number on one side, and a letter on the other. The subject given the generalization, “If a card has a vowel on one side then it has an even number on the other side.” The subject is then asked what cards to turn over to find out whether the generalization is true or false. (p. 30)
These simple logic problems are strongly affected by context. Context affects inference. Changing context in logical problems leads to variable results in whether people can solve the problem correctly. Certain formulations of equivalent problems are frequently solved correctly, while other formulations are frequently solved incorrectly. Familiarity generally helps performance. This argument surfaces when making the connection to embodiment and associative reasoning.
The conclusion of this section presents 6 bullet points (p. 39):
- People make fallacious inferences.
- Which logic is found in the mind?
- How is logic formulated in the mind?
- How does logic arise in the mind? (development)
- Deduction depends on the content of the premises. When an individual is familiar with (or has a model of) a situation, they are more likely to reason about it correctly.
- “People follow extra-logical heuristics in making inferences. They appear to be guided by the principle of maintaining the semantic content of the premises but expressing it with greater linguistic economy.” That is, when presented with propositions p and not-p or q, they are likely to conclude q, instead of p and q.
Theories of the Syllogism
Propositional logic is psychologically flawed. A more accurate logic occurs in syllogisms. Syllogisms are first order declarations: All X are Y, or some X are Y, no X are Y, etc. Johson-Laird puts forth several goals for a theory of reasoning (p. 65-66), and will later deduce that syllogisms satisfy these goals.
- “A descriptively adequate theory must account for the evaluation of conclusions, the relative difficulty of different inferences, and the systematic errors and biases that occur in drawing spontaneous conclusions.”
- “The theory should explain the differences in inferential ability from one individual to another.”
- “The theory should be extensible in a natural way to related varieties of inference rather than apply solely to a narrow class of deductions.”
- “The theory should explain how children acquire the ability to make valid inferences.”
- “The theory must allow that people are capable of making valid inferences, that is, they are potentially rational.”
- “The theory should shed some light on why formal logic was invented and how it was developed.”
- “The theory should ideally have practical applications to the teaching of reasoning skills.”
How to Reason Syllogistically
In giving a description for how people might reason using syllogisms, Johnson-Laird gives an example of how syllogisms might be visualized by an individual. The syllogism is of the form, “All the artists are beekeepers, and all the beekeepers are chemists.” A way to visualise syllogisms without using a Euler circle or Venn diagram is to imagine a tableau of actors who play the parts of artists, beekeepers, and chemists. Thus, there would be artist-beekeeper-chemists, beekeeper-chemists, and a lone chemist. (p. 94) The metaphor of the tableau is useful for representing mental representations of the situation, but more telling is the use of the troupe of actors who enact these roles. This representation covertly emphasizes the cultural and embodied manner by which the syllogism is understood.
Going a step further, though. Johnson-Laird produces an algorithm for how to reason syllogistically. However, syllogistic logic is still not a complete representation of the logic that humans follow when reasoning, because we still make reasoning mistakes in complex syllogistic problems, for example: “Some B are A, no C are B” yields incorrect conclusions in almost all cases. (p. 74)
Inference and Mental Models
The key to this chapter is how to reason without rules of inference. Both propositional and syllogistic logic define rules for drawing inferences, but they do not line up to natural everyday reason. Mental models are introduced with relational expressions. These may all take the form of predicates or relational expressions. Relations are a bit heavier than ordinary propositions, but still work on the same level. At this point, all mental models are of the form of tableaus.
With the focus on tableaus, mental models can be understood as devices for association, and defining relationships. Both of these can be addressed by non-symbolic and embodied means (Lakoff and Johnson), so even though Johsnon-Laird’s formulation is intended to be computational in nature, it can be more than that.
There are some final bullet points regarding mental models:
- The theory embraces both implicit and explicit inferences. This means that they should be able to represent all arguments.
- Children can learn to reason before understanding rules of inference, because reason is possible without logic.
- The theory is compatible with the fact that people can use logic.
- It is also compatible with the historical origin of logic.
Images, Propositions, and Models
There is a conflict over how images fit into cognition and psychology. The two sides are the ‘imagists’ (Paivio, Shepard, and Kosslyn) and ‘propositionalists’ (Baylor, Pylyshyn, Palmer). Johnson-Laird argues for the encoding of images in the mind, and goes for a functional account of mental processing. This does liken the mind to a computer: it can procedurally transform images into systems of symbols.
Johnson-Laird describes the relationship between mental models and propositions. “The crucial problem for the mental language is the nature of its semantics. Propositions can refer to the world. Human beings, of course, do not apprehend the world directly; they posess an internal representation of it, because perception is the construction of a model of the world.” Thus, the mental model operates between the individual’s logic and the world itself. Any propositions in that individual’s mind must act on the model, rather than on the world directly. Models work via analogy, and images are views of models.
Meaning in Model-Theoretic Semantics
This section describes how meaning is constructed and composed (in the sense of built compositionally) in model theory. Johnson-Laird references Tarski here, in terms of understanding truth values. A big bit of this is still in terms of truth vs falsehoods. The discussion raises the issue of worlds, and how models connote not only existing meaning, but a set of potential configurations that are enabled by that model. The world of meaning enabled by a model is called its extension.
There is some discussion of Montague grammar, which is an attempted formalization of natural language. This segues into a model-based formulation of meaning, which derives neatly from mathematical logic. The following passage is dearly familiar to the theory of models in logic. “The power of model-theoretic semantics resides in its explicit and rigorous approach to the composition of meanings. It provides a theory of semantic properties and relations, e.g., a set of premises entails a conclusion if and only if the conclusion is true in every model in which the premises is true.” (p. 180)
What Is Meaning?
The discussion of meaning traverses from psychology to word meanings. THere is a great deal of philosophy and squabbling over where meanings come from, or what concepts like “water” or “jade” are, intrinsically. This entire discussion neglects the use of practice, where words and other signs may hold different meanings to different observers, under different circumstances. The importance of language meaning is critical in this treatment of mental models, because the models are based on language.
The conflict in this is between meaning Psychologism and Realism, which respectively attest that meaning is in the mind or outside of the mind. Johnson-Laird is attempting to find a middle ground in this, and looks to an encoding of meaning that allows for intersections and vagueness. However, fuzzy logic exposes the same problem. Propositions, even with values of confidence, are divorced from a knower. For language to work, the knower must have a context and a state of mind. The relative values of “tallness” (given in his example on p. 200) are only meaningful in context.
To address the question of meaning, the psychological perspective asserts that meaning is wholly in the mind, whereas the realistic perspective asserts that meaning is wholly outside of it. Johnson-Laird seems to claim that meaning works within a model, which is grounded in language, which has elements that are both inside and outside the mind. There is an added dimension of culture, though which is extremely relevant. Meanings (and models) are shared between individuals in a culture, so meaning exists beyond the individual, but also beyond the literalism of language. I would argue that it is instead a consensus. This position is not incompatible with models, but requires a reppropriation of Johnson-Laird’s use of models.
The Psychology of Meaning
Models are procedural structures that may be adjusted over time or through discourse according to some rules. There is a set of bullet points describing these:
- “The processes by which fictitious discourse is understood are not essentially different from those that occur with true assertions.” Thus we use the same logic for processing information into models, even if we know the information is fictional or false.
- “In understanding a discourse, you construct a single model of it.”
- “The interpretation of discourse depends on both the model and the processes that construct, extend, and evaluate it.” The model for discourse can vary over time.
- “The functions that construct, extend, evaluate, and revise mental models, unlike the interpretation functions of model-theoretic semantics, cannot be treated in an abstract way.” There must be some formal algorithms for changing mental models.
- “A discourse is true if it has at least one mental model that satisfies its truth conditions that can be embedded in a model corresponding to the world.”
The next couple of chapters deal with the understanding of grammar and the parsing of language into propositional expressions. There is a great deal of noun-phrase, verb-phrase stuff. The analysis of grammar is heavily extended from Chomsky.
The Coherence of Discourse
Johnson-Laird gives a surprising interjection regarding story grammars. This makes some sense given the focus in the preceeding chapters on the relationship between language grammar and models. The challenge to story grammars can be seen as a critique of a particular kind of structuralism. Earlier pages compare blocks of text that form coherent paragraphs versus those that do not. Coherency relates to consistency and discourse history, which is a type of context. Models have the formal power to use this context in a way that grammar lacks.
The Nature of Mental Models
Some properties of mental models:
- Computability. Mental models are computable, and so are the tools for manipulating them.
- Finitism. A mental model must be finite, and cannot directly represent an infinite domain.
- Constructivism. A model is constructed from symbolic tokens and structurally composed.
A typology/heirarchy of models:
- Relational. This is a finite set of tokens representing entities, a finite set of properties, and a finite set of relations connecting entities to properties.
- Spatial. This is a relational model where the relations are spatial.
- Temporal. A temporal model consists of frames of spatial models, that occur in a temporal order.
- Kinematic. This is a temporal model that is psychologically continuous, there are no temporal discontinuities.
- Dynamic. A kinematic model which relates causal relations between frames.
- Image. The image is a viewer-centric representation of a spatial or kinematic model.
It seems to me that this formulation reverts to computational models, and begins to become severely detached from underlying psychology.
Consciousness and Computation
The final chapter works to give a formal and procedural account for consciousness. Essentially, consciousness is already computational, when understood as processing of mental models. An excuse is given here, that while cognition may be computational, other human traits, such as spirituality, morality, and imagination cannot be modeled and will “remain forever inexplicable.” This is a cop out. Johnson-Laird cannot introduce a hulking device for representing psychology and then blow off its application to other psychological traits.
There are significant critiques to be had with the computational formulation of mental models. I would argue that the computational imposition is severely flawed, but models remain invaluable as a tool for understanding cognition. The use of modeling is especially important in the representations of spirituality (cultural beliefs), morality, and imagination.