2023· M×Φ — Annals of Mathematics and Philosophy· Vol 1, pp. 1-24· 3 citations
Abstract
The article investigates axiomatics as a complex mathematical practice whose inquiry, while taking its cue from the analysis of some specific mathematical theories, requires an interdisciplinary approach. Axiomatics, if analyzed in detail through a study of its foundational component, of the styles with which it is associated and of the rules that govern it, performs a plurality of functions. It serves heuristic, descriptive, genetic-historical, pedagogical and architectural aims. But it can also play the role of conceptual analysis, modular analysis and coordination tool, soliciting a quest for rigor. An example taken from Peano's investigation of axiomatic systems illustrates the kind of results that this interdisciplinary approach to mathematical practice might produce, showing what can be achieved by considering axiomatics as research on the foundations of mathematics, or as a mathematical style, or as a social institution.
The article is devoted to the problem of complexity, appealing to which is a common argument used by theorists and practitioners to justify failures in their endeavors. In such cases, complexity is presented as an objective property of an object, its ontological parameter. The apology for complexity has three important...
This paper develops a nativist approach to mathematical knowledge as an alternative account within the philosophy of mathematics. Rather than beginning with the ontological status of mathematical objects, it argues that any satisfactory account of mathematical knowledge should address three closely related questions: h...
This article presents an introduction to the main concepts of propositional logic aimed at teachers, emphasizing its relationship with mathematical language, the organization of reasoning, and the analysis of arguments. The objective is to provide foundations that help teachers both understand the structural elements o...
Nelson Gomes Carnaval, R. Machado· Revista ft· 0 citations
This article advances a categorial challenge to physicalistic versions of naturalized epistemology as an account of logico-mathematical knowledge and practice. It argues that, qua physically constituted, any putative rule-governed system is logico-mathematically indeterminate: physical facts are systematically insuffic...
Antonio Ramos-Díaz· Principia: An International...· 0 citations
This paper tries to show that problems with the theory of the soul attributed to Thales of Miletus do not exist in Non-Axiomatic Logic, because extensional difference allows building compound terms that can be related to simple terms that are inconsistent with them.
Miguel López-Astorga· Sats: northern european jour...· 0 citations
C-K Theory is currently one of the most sophisticated theoretical frameworks for modelling design processes. Based on the interaction between a space of concepts, C, and a space of knowledge, K, it accurately describes the mechanisms of producing and transforming design objects. However, certain concepts used in archit...
Serge Monnot, Suzanne Monnot· Journal of Architectural and...· 0 citations
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