Jacek Woźny - Conceptual Integration in the Language of Mathematical Description

The monographs and occasional textbooks published in this series tap directly into the kinds of themes, research findings, and general professional activities of the Fields Cognitive Science Network, which brings together mathematicians, philosophers, and cognitive scientists to explore the question of the nature of mathematics and how it is learned from various interdisciplinary angles.

This series covers the following complementary themes and conceptualizations:

Connections between mathematical modeling and artificial intelligence research; math cognition and symbolism, annotation, and other semiotic processes; and mathematical discovery and cultural processes, including technological systems that guide the thrust of cognitive and social evolution

Mathematics, cognition, and computer science, focusing on the nature of logic and rules in artificial and mental systems

The historical context of any topic that involves how mathematical thinking emerged, focusing on archeological and philological evidence

Other thematic areas that have implications for the study of math and mind, including ideas from disciplines such as philosophy and linguistics

The question of the nature of mathematics is actually an empirical question that canbest be investigated with various disciplinary tools, involving diverse types of hypotheses, testing procedures, and derived theoretical interpretations. This series aims to address questions of mathematics as a unique type of human conceptual system versus sharing neural systems with other faculties, whether it is a series- specific trait or exists in some other form in other species, what structures (if any) are shared by mathematics language, and more.

Data and new results related to such questions are being collected and published in various peer-reviewed academic journals. Among other things, data and results have profound implications for the teaching and learning of mathematics. The objective is based on the premise that mathematics, like language, is inherently interpretive and explorative at once. In this sense, the inherent goal is a hermeneutical one, attempting to explore and understand a phenomenonmathematicsfrom as many scientific and humanistic angles as possible.

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The miracle of the appropriateness of the language of mathematics for the formulation of the laws of physics is a wonderful gift which we neither understand nor deserve. We should be grateful for it and hope that it will remain valid in future research and that it will extend, for better or for worse, to our pleasure, even though perhaps also to our bafflement, to wide branches of learning. (: 14)