"But surely it is self-evident that every theory is merely a framework or scheme of concepts together with their necessary relations to one another, and that the basic elements can be constructed as one pleases." (Gottlob Frege, "On the Foundations of Geometry and Formal Theories of Arithmetic" , cca. 1903-1909)
"At present, no complete account can be given - one may as well ask for an inventory of the entire products of the human imagination - and indeed such an account would be premature, since mental models are supposed to be in people's heads, and their exact constitution is an empirical question. Nevertheless, there are three immediate constraints on possible models. […] 1. The principle of computability: Mental models, and the machinery for constructing and interpreting them, are computable. […] 2. The principle of finitism: A mental model must be finite in size and cannot directly represent an infinite domain. […] 3. The principle of constructivism: A mental model is constructed from tokens arranged in a particular structure to represent a state of affairs." (Philip Johnson-Laird, "Mental Models" 1983)
"Concepts are inventions of the human mind used to construct a model of the world. They package reality into discrete units for further processing, they support powerful mechanisms for doing logic, and they are indispensable for precise, extended chains of reasoning. […] A mental model is a cognitive construct that describes a person's understanding of a particular content domain in the world." (John Sown, "Conceptual Structures: Information Processing in Mind and Machine", 1984)
"[Language comprehension] involves many components of intelligence: recognition of words, decoding them into meanings, segmenting word sequences into grammatical constituents, combining meanings into statements, inferring connections among statements, holding in short-term memory earlier concepts while processing later discourse, inferring the writer’s or speaker’s intentions, schematization of the gist of a passage, and memory retrieval in answering questions about the passage. [… The reader] constructs a mental representation of the situation and actions being described. […] Readers tend to remember the mental model they constructed from a text, rather than the text itself." (Gordon H Bower & Daniel G Morrow, 1990)
"We build mental models that represent significant aspects of our physical and social world, and we manipulate elements of those models when we think, plan, and try to explain events of that world. The ability to construct and manipulate valid models of reality provides humans with our distinctive adaptive advantage; it must be considered one of the crowning achievements of the human intellect." (Gordon H Bower & Daniel G Morrow, 1990)
"The strangest and most wonderful constructions in the whole animal world are the amazing, intricate constructions made by the primate Homo sapiens. Each normal individual of this species makes a self. Out of its brain it spins a web of words and deeds, and, like the other creatures, it doesn't have to know what it's doing; it just does it. This web protects it, just like the snail's shell. […] As such, it plays a singularly important role in the ongoing cognitive economy of that living body, because, of all the things in the environment an active body must make mental models of, none is more crucial than the model the agent has of itself." (Daniel Dennett, "Consciousness Explained", 1991)
"We construct mental models that provide us with situations in which we can interact with mental objects that represent objects, properties and relations and that behave in ways that simulate the objects, properties and relations that our models represent. […] The concepts and principles that a person understands, in this sense, are embedded in the kinds of objects that he or she includes in mental models and in the ways in which those objects behave, including how they combine and separate to form other objects." (James G Greeno, "Number sense as situated knowing in a conceptual domain", Journal for Research on Mathematics Education Vol. 22 No. 3, 1991)
"We all depend on models to interpret our everyday experiences. We interpret what we see in terms of mental models constructed on past experience and education. They are constructs that we use to understand the pattern of our experiences." (David Bartholomew, "What is Statistics?", 1995)
"The seemingly stable scene you normally see is really a mental model that you construct - the eyes are actually darting all around, producing a retinal image as jerky as an amateur video, and some of what you thought you saw was instead filled in from memory." (William H Calvin, "How Brains Think", 1996)
"According to mental model theory, human reasoning relies on the construction of integrated mental representations of the information that is given in the reasoning problem's premises. These integrated representations are the mental models. A mental model is a mental representation that captures what is common to all the different ways in which the premises can be interpreted. It represents in "small scale" how "reality" could be— according to what is stated in the premises of a reasoning problem. Mental models, though, must not be confused with images. A mental model often forms the basis of one or more visual images, but some of them represent situations that cannot be visualized. Instead, mental models are often likened to diagrams since, as with diagrams, their structure is analogous to the structure of the states of affairs they represent." (Carsten Held et al, "Mental Models and the Mind", 2006)
"Art is constructivist in nature, aimed at the deliberate refinement and elaboration of mental models and worldviews. These are the natural products of cognition itself, the outcome of the brain’s tendency to strive for the integration of perceptual and conceptual material over time. […] human culture is essentially a distributed cognitive system within which worldviews and mental models are constructed and shared by the members of a society. Artists are traditionally at the forefront of that process, and have a large influence on our worldviews and mental models." (Mark Turner, "The Artful Mind : cognitive science and the riddle of human creativity", 2006)
"In specific cases, we think by applying mental rules, which are similar to rules in computer programs. In most of the cases, however, we reason by constructing, inspecting, and manipulating mental models. These models and the processes that manipulate them are the basis of our competence to reason. In general, it is believed that humans have the competence to perform such inferences error-free. Errors do occur, however, because reasoning performance is limited by capacities of the cognitive system, misunderstanding of the premises, ambiguity of problems, and motivational factors. Moreover, background knowledge can significantly influence our reasoning performance. This influence can either be facilitation or an impedance of the reasoning process." (Carsten Held et al, "Mental Models and the Mind", 2006)
"Prom the processing view, the model theory distinguishes between three different operations. In the construction phase, reasoners construct the mental model that reflects the information from the premises. In the inspection phase, this model is inspected to find new information that is not explicitly given in the premises. In most variants of the model theory, the inspection process is conceptualized as a spatial focus that scans the model to find new information not given in the premises.. In the variation phase, reasoners try to construct alternative models from the premises that refute the putative conclusion. If no such model is found, the putative conclusion is considered true." (Carsten Held et al, "Mental Models and the Mind", 2006)
"We all construct mental models that describe our various mental states, bodies of knowledge about our abilities, depictions of our acquaintances, and collections of stories about our pasts. Then, whenever we use our models of ourselves, we tend to use terms like conscious - when those reflections lead to choices we make, and we use unconscious or unintentional to describe those activities that we regard as beyond our control." (Marvin Minsky, "The Emotion Machine: Commonsense thinking, artificial intelligence, and the future of the human mind", 2006)
"Just as physicists have created models of the atom based on observed data and intuitive synthesis of the patterns in their data, so must designers create models of users based on observed behaviors and intuitive synthesis of the patterns in the data. Only after we formalize such patterns can we hope to systematically construct patterns of interaction that smoothly match the behavior patterns, mental models, and goals of users. Personas provide this formalization." (Alan Cooper et al, "About Face 3: The Essentials of Interaction Design", 2007)
"The concepts and constructs about real work things we have in our heads are called mental model." (Hassan Qudrat-Ullah, "System Dynamics Based Learning Environments" [in "Encyclopedia of Information Technology Curriculum Integration"], 2008)
[mental model:] "Internal representations constructed on the spot when required by demands of an external task or by a self-generated stimulus. It enables activation of relevant schemata, and allows new knowledge to be integrated. It specifies causal actions among concepts that take place within it, and it can be interacted with in the mind." (Daniel Churchill, "Mental Models" [in "Encyclopedia of Information Technology Curriculum Integration"], 2008)
"Mental models represent possibilities, and the theory of mental models postulates three systems of mental processes underlying inference: (0) the construction of an intensional representation of a premise’s meaning – a process guided by a parser; (1) the building of an initial mental model from the intension, and the drawing of a conclusion based on heuristics and the model; and (2) on some occasions, the search for alternative models, such as a counterexample in which the conclusion is false. System 0 is linguistic, and it may be autonomous. System 1 is rapid and prone to systematic errors, because it makes no use of a working memory for intermediate results. System 2 has access to working memory, and so it can carry out recursive processes, such as the construction of alternative models." (Sangeet Khemlania & P.N. Johnson-Laird, "The processes of inference", Argument and Computation, 2012)
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