Related papers: Intuitionistic Mathematics and Logic
In this paper, we first study the arithmetic properties of intuitionistic fuzzy number, the monotonicity of intuitionistic fuzzy function and the derivative of intuitionistic fuzzy functions and then we study the fundamental properties on…
In a previous article we gave the general foundations of the theory of movement considered from a philosophical and mathematical point of view. Philosophical it meant to understand the opposition of the one and the multiple, mathematically…
We reproduce Hilbert's axiomatic formalisation of Number Theory, and argue that his enunciation of the Law of the Excluded Middle is inconsistent with a Turing-verifiable model of the axioms under the standard interpretation.
We construct a rigorous mathematical framework for an abstract continuous evolution of an internal state, inspired by the intuitive notion of a flowing thought sequence. Using tools from topology, functional analysis, measure theory, and…
The following notes are intended to make a small digression on the topics mentioned in the title of the same, since these were not addressed in the past tribute by the Institute of Physics of the UdeA. We believe more than platitude try to…
My purpose is to examine some concepts of mathematical logic, which have been studied by Carlo Cellucci. Today the aim of classical mathematical logic is not to guarantee the certainty of mathematics, but I will argue that logic can help us…
In 1931 de Finetti proved what is known as his Dutch Book Theorem. This result implies that the finite additivity {\it axiom} for the probability of the disjunction of two incompatible events becomes a {\it consequence} of de Finetti's…
We describe and explain the desire, common among mathematicians, both for unity and independence in its major themes. In the dialogue that follows, we express our spontaneous and considered judgment and reservations by contrasting the…
In the process of evolution, the brain has achieved such perfection that artificial intelligence systems do not have and which needs its own mathematics. The concept of cognitome, introduced by the academician K.V. Anokhin, as the cognitive…
Residues to a given modulus have been introduced to mathematics by Carl Friedrich Gauss with the definition of congruence in the `Disquisitiones Arithmeticae'. Their extraordinary properties provide the basis for a change of paradigm in…
In this essay, I argue that mathematics is a natural science---just like physics, chemistry, or biology---and that this can explain the alleged "unreasonable" effectiveness of mathematics in the physical sciences. The main challenge for…
The aim of this paper is to study the historical evolution of mathematical thinking and its spatial spreading. To do so, we have collected and integrated data from different online academic datasets. In its final stage, the database…
In this paper, we revisit Glivenko's theorems, foundational results relating classical and intuitionistic logic, from an ecumenical perspective. We begin by discussing the historical context and significance of Glivenko's original…
Realizability, introduced by Kleene, can be understood as a concretization of the Brouwer-Heyting-Kolmogorov (BHK) interpretation of proofs, providing a framework to interpret mathematical statements and proofs in terms of their…
We report on a pedagogical experiment to make mathematics easy by changing its philosophy. The Western philosophy of math originated in religious beliefs about mathesis, cursed by the church. Later, mathematics was "reinterpreted", in a…
Examples of discontinuous functions already appear in the work of Euler, Abel, Dirichlet, Fourier, and Bolzano. A ground-breaking discovery due to Baire was that many discontinuous functions are well-behaved in that they are the pointwise…
The integration of the history and philosophy of statistics was initiated at least by Hacking (1975) and advanced by Hacking (1990), Mayo (1996), and Zabell (2005), but it has not received sustained follow-up. Yet such integration is more…
In 1979, building on S. Lie's theory of symmetries of (partial) differrential equations, P.J. Olver formulated inductive formulas which are appropriate for the computation of the prolongations of an infinitesimal Lie symmetry to jet spaces,…
The history of computability theory and and the history of analysis are surprisingly intertwined since the beginning of the twentieth century. For one, \'Emil Borel discussed his ideas on computable real number functions in his introduction…
In this paper we discuss how teaching of mathematics for middle school and high school students can be improved dramatically when motivation of concepts and ideas is done through the classical problems and the history of mathematics. This…