The authors advance a comprehensive theory to explain all the main varieties
of deduction: propositional reasoning (that uses the connectives "and", "or"
and "not"), relational reasoning (that depends on relations between entities),
quantificational reasoning (that uses quantifiers such as "any" and "some").
And justify it with a variety of psychological experiments.
In order to understand discourse, humans construct an internal representation of the state of affairs that is described in that discourse. These mental models have the same structure as human conceptions of the situations they represent. Deduction does not depend on formal rules of inference but rather on a search for alternative models of the premises that would refute a putative conclusion. Central to the theory is the principle that people use models that make explicit as little information as possible. The theory also make sense of how people deal with conditionals.
The theory explains phenomena such as: that modus ponens ("if p then q" and "p" then "q") is easier than modus tollens ("if p then q" and "not q" then "not p").
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