Image Schema Theory And Mathematical Cognition
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Image Schema Theory and Mathematical Cognition
This book uses blending theory in math cognition, and assesses the main aspect of this theory, called image schema theory. Applied work in math pedagogy has used this theory, but no work has assessed its validity. This book provides an overall assessment of the theory with regard to its validity in the study of math cognition. Overall, this book presents image schema theory as it has evolved today to mathematicians, cognitive scientists, and math educators, deriving from it any concrete implications for modeling math in computer science and, on the other side, for making math pedagogy more effective.
From Perception to Meaning
The 1987 landmark publications by G. Lakoff and M. Johnson made image schema one of the cornerstone concepts of the emerging experientialist paradigm of Cognitive Linguistics, a framework founded upon the rejection of the mind-body dichotomy and stressing the fundamentally embodied nature of meaning, imagination and reason - hence language. Conceived of as the pre-linguistic, dynamic and highly schematic gestalts arising directly from motor movement, object manipulation, and perceptual interaction, image schemas served to anchor abstract reasoning and imagination to sensori-motor patterns in the conceptual theory of metaphor. Being itself informed by preceding crosslinguistic work on semantic primitives in the linguistic representations of spatial relations (carried out by L. Talmy, R. Langacker, and others), the notion has inspired a large amount of subsequent research and debate on diverse issues ranging from the meaning, structure and acquisition of natural languages to the embodied mind itself. From Perception to Meaning is the first survey of current image-schema theory and offers a collection of original and innovative essays by leading scholars, many of whom have shaped the theory from the very beginning. The edition unites essays on major issues in recent research on image-schemas - from aspects of their definition and linguistic formalization, their psychological status and neural grounding to their role as semantic universals and primitives in language acquisition. The book will thus not only be welcomed by linguists of a cognitive orientation, but will prove relevant to philosophers, psychologists, and anthropologists interested in language, and indeed to anyone studying the embodied mind.
Concept Invention
This book introduces a computationally feasible, cognitively inspired formal model of concept invention, drawing on Fauconnier and Turner's theory of conceptual blending, a fundamental cognitive operation. The chapters present the mathematical and computational foundations of concept invention, discuss cognitive and social aspects, and further describe concrete implementations and applications in the fields of musical and mathematical creativity. Featuring contributions from leading researchers in formal systems, cognitive science, artificial intelligence, computational creativity, mathematical reasoning and cognitive musicology, the book will appeal to readers interested in how conceptual blending can be precisely characterized and implemented for the development of creative computational systems.