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Bridging Informal Reasoning and Formal Proving: The Role of Argumentation in Proof-Events

AbstractThis paper explores the relationship between informal reasoning, creativity in mathematics, and problem solving. It underscores the importance of environments that promote interaction, hypothesis generation, examination, refutation, derivation of new solutions, drawing conclusions, and reasoning with others, as key factors in enhancing mathematical creativity. Drawing on argumentation logic, the paper proposes a novel approach to uncover specific characteristics in the development of formalized proving using “proof-events.” Argumentation logic can offer reasoning mechanisms that facilitate these environments. This paper proposes how argumentation can be implemented to discover certain characteristics in the development of formalized proving with “proof-events”. The concept of a proof-event was introduced by Goguen who described mathematical proof as a multi-agent social event involving not only “classical” formal proofs, but also other informal proving actions such as deficient or alleged proofs. Argumentation is an integral component of the discovery process for a mathematical proof since a proof necessitates a dialogue between provers and interpreters to clarify and resolve gaps or assumptions. By formalizing proof-events through argumentation, this paper demonstrates how informal reasoning and conflicts arising during the proving process can be effectively simulated. The paper presents an extended version of the proof-events calculus, rooted in argumentation theories, and highlights the intricate relationships among proof, human reasoning, cognitive processes, creativity, and mathematical arguments.

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Clothing and the Discovery of Science

AbstractIn addition to natural curiosity, science is characterized by a number of psychological processes and perceptions. Among the psychological features, scientific enquiry relates to uncovering—or discovering—aspects of a world perceived as hidden from humans. A speculative theoretical model is presented, suggesting the evolution of science reflects psychological repercussions of wearing clothes. Specifically, the natural world is perceived as hidden due to the presence of clothing. Three components of scientific enquiry may arise from clothing: detachment from sensual experience, a perception that the world is veiled in mystery, and an intellectual desire to uncover the hidden structure of nature. Rather than beginning with the emergence of Homo sapiens, the proposed connection with clothing implies that psychological foundations for science began to develop during the last ice age, with the invention of complex clothes that fully covered the human body. After the end of the last ice age, elements of scientific thinking began to emerge in societies where clothing was worn routinely for psychosocial reasons, including modesty. Notably, a scientific attitude was essentially absent in hunter-gatherer communities where nakedness remained the norm. This novel perspective aims to advance the history and philosophy of science, revealing the emergence of science as a situated phenomenon contingent on humans being covered.

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