The Experts below are selected from a list of 37515 Experts worldwide ranked by ideXlab platform
John Ryskamp - One of the best experts on this subject based on the ideXlab platform.
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Paradox, Natural Mathematics, Relativity and Twentieth-Century Ideas
SSRN Electronic Journal, 2008Co-Authors: John RyskampAbstract:Here we examine the influence of the new set theory historiography - in particular the works of Garciadiego, Grattan-Guinness and Ferreiros - on our understanding of major twentieth-century ideas, including those of Einstein, Kimura, Sraffa and Godel. Conclusions regarding the nature of set theory have been upended by this new work, and the mathematical approach of readers will be challenged. Therefore, it is recommended that readers familiarize themselves with the new historiography - particularly Garciadiego - before venturing further. In particular, we identify, for the first time, the way Einstein used practical geometry - what today is known as constructivism - in his formulation of the relativity of simultaneity. Not quite knowing what they were looking for, physicists have nevertheless indirectly made this the work of physics since Einstein promulgated the relativity of simultaneity in 1905. Thus, a century-long search comes to an end. We also lay the groundwork for answering the question, where the constructivist intervention is made in the arguments of Sraffa, Kimura and Godel? This question also arises with respect to the Pythagorean theorem.
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On the Unity of Twentieth-Century Ideas
2005Co-Authors: John RyskampAbstract:This paper examines 'Natural' Mathematics--developed to counter perceived paradoxes in early twentieth-century set theory--as an internally consistent unifying factor in the arguments of several disciplines, including economics (Sraffa), physics (Einstein), biology (Kimura), and Mathematics (Godel).
Vaughan R Pratt - One of the best experts on this subject based on the ideXlab platform.
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rational mechanisms and Natural Mathematics
Colloquium on trees in Algebra and Programming, 1995Co-Authors: Vaughan R PrattAbstract:Chu spaces have found applications in computer science, Mathematics, and physics. They enjoy a useful categorical duality analogous to that of lattice theory and projective geometry. As Natural Mathematics Chu spaces borrow ideas from the Natural sciences, particularly physics, while as rational mechanics they cast Hamiltonian mechanics in terms of the interaction of body and mind.
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TAPSOFT - Rational Mechanisms and Natural Mathematics
TAPSOFT '95: Theory and Practice of Software Development, 1995Co-Authors: Vaughan R PrattAbstract:Chu spaces have found applications in computer science, Mathematics, and physics. They enjoy a useful categorical duality analogous to that of lattice theory and projective geometry. As Natural Mathematics Chu spaces borrow ideas from the Natural sciences, particularly physics, while as rational mechanics they cast Hamiltonian mechanics in terms of the interaction of body and mind.
Carlo Cellucci - One of the best experts on this subject based on the ideXlab platform.
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Mathematics and the World
European Studies in Philosophy of Science, 2017Co-Authors: Carlo CellucciAbstract:This chapter discusses the relation of Mathematics to the world considering two questions: What is the relation of mathematical objects to the world? Why is Mathematics applicable to the world? As to the first question, the chapter maintains that mathematical objects are not obtained by abstraction from sensible things, or by idealization from our operations of collecting objects. They are hypotheses we make to solve mathematical problems by the analytic method, several of which have an extra-mathematical origin. As to the second question, the chapter maintains, on the one hand, that the applicability of Natural Mathematics to the world is due to the fact that Natural Mathematics fits in certain mathematical properties of the world. On the other hand, the applicability of artificial Mathematics to the world is due to several factors, starting with the decision of modern science to confine itself to dealing only with some phenomenal properties of the world, mathematical in kind.
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Philosophy of Mathematics: Making a fresh start
Studies in History and Philosophy of Science Part A, 2013Co-Authors: Carlo CellucciAbstract:Abstract The paper distinguishes between two kinds of Mathematics, Natural Mathematics which is a result of biological evolution and artificial Mathematics which is a result of cultural evolution. On this basis, it outlines an approach to the philosophy of Mathematics which involves a new treatment of the method of Mathematics, the notion of demonstration, the questions of discovery and justification, the nature of mathematical objects, the character of mathematical definition, the role of intuition, the role of diagrams in Mathematics, and the effectiveness of Mathematics in Natural science.
Dany Jaspers - One of the best experts on this subject based on the ideXlab platform.
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Properties of primes and Natural Mathematics: a minimalist algorithm for prime numbers
2013Co-Authors: Dany JaspersAbstract:Este trabalho discute a quantificacao precisa por meios de sistemas numericos em analogia a analise anterior de Jaspers (2005) a respeito da quantificacao comparativamente vaga expressa por operadores do calculo de predicados {todos, todo, cada, algum, nenhum}. E defendido que numeros oferecem um interessante teste-base para a validade da abordagem Booleana aos quantificadores (Jaspers, 2005). Mais detidamente, esta excursao na matematica e realizada para mostrar que o mesmo sistema logico-cognitivo de oposicoes subjacente na lingua Natural tambem governa a matematica Natural. O ponto de partida concreto do artigo e o problema dos “twin primes” de Popper, que e seguido por uma discussao de sistemas de numeros, sobretudo a distincao entre sistema dos numeros naturais {(0,) 1, 2,...} e o sistema de numeros primos. Em relacao ao primeiro sera defendido que e organizado pela operacao de adicao/subtracao. A sequencia de numeros primos e diferente, porque e mais multiplicativa/divisional que aditiva. E geralmente reconhecido em circulos matematicos que o ultimo tipo de sequencia e mais complexo que o primeiro. Este fato acompanha bem (e, portanto, oferece suporte indireto para) as descobertas linguisticas em Jaspers (2005), cujo o nucleo foi a defesa que disjuncao na lingua Natural _ conhecida por ser isomorfica a adicao na algebra algebra - e cognitiva e lexicalmente mais complexa que a conjuncao, que e isomorfica a multiplicacao. Palavras-chave: Quantificacao; sistemas numericos; sistema de oposicoes; disjuncao; conjuncao.
Vladimir Trifonov - One of the best experts on this subject based on the ideXlab platform.
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a linear solution of the four dimensionality problem
EPL, 1995Co-Authors: Vladimir TrifonovAbstract:Modelling the measurement ("active observation") process makes it possible to express in strict terms the degree to which the logic of the observer determines what he "sees", and formalize the difficult concept of rational behaviour. Presented here is a rigorous formulation of several implicit assumptions of standard physics which leads to a first-order theory shown to possess a real-world model: if an observer's logic is Boolean, he is bound to perceive his spacetime as a four-dimensional pseudo-Riemannian manifold of signature 2, with an ideal big bang geometry. The connections between the type of an observer's logic and large-scale structure of the observable universe yield a testable prediction, existence of positive cosmological constant and suggest a non-standard integration-over-spacetime technique. They strongly favour non-local reality and deliver an operational explanation of the number of particle generations. The result casts some doubts (arising also from the necessity of renormalization procedures) that classical Mathematics (i.e. the Mathematics of the topos of sets) is the "Natural" Mathematics of our world, and offers a new candidate for this role, that differs from its classical counterpart. In general, the scheme outlines a formal way to unify the logical, physical and, possibly, psychological templates of perception, which can be briefly expressed as "physics is an exponent-image of psychology".
