The Experts below are selected from a list of 6042 Experts worldwide ranked by ideXlab platform

Yoshifumi Ito - One of the best experts on this subject based on the ideXlab platform.

Juarez Acosta Fernando - One of the best experts on this subject based on the ideXlab platform.

  • La equivalencia de activos-derechos sobre activos en el método axiomático
    'World Scientific and Engineering Academy and Society (WSEAS)', 2020
    Co-Authors: Juarez Acosta Fernando
    Abstract:

    "The purpose of the study is to analyze the assets-claims on assets equivalence based on the dual concept of monetary units and the Axiomatic Method. The Methodology is analytical, rationalistic and deductive; it uses Axiomatic theory with set theory and predicate logic to test set equivalence. The Axiomatic theory involves a set of axioms, which are used in combination with accounting axioms to develop a proof of the assets-claims on the assets considered as finite sets. The analysis uses a bijective function based on the dual concept of monetary units, and proof by contraposition to test the fulfillment of the requirement of a bijective function. Results show that assets cardinality is not equal to claims on assets cardinality when taking into account the dual concept of monetary units, and as a consequence assets and claims on assets are not equivalent

  • El Balance y la Relación Activos-Reclamos sobre Activos en el Método Axiomático
    'World Scientific and Engineering Academy and Society (WSEAS)', 2020
    Co-Authors: Juarez Acosta Fernando
    Abstract:

    "The purpose of this study is to analyze the set structure of the balance sheet and assets-claims on assets relationship, considering the dual concept of monetary units, the Axiomatic theory and accountingspecific axioms. The structure of the balance sheet and assets-claims on assets relationship are examined using a rationalistic, analytical and deductive Method; this Method uses the Axiomatic set theory and predicate logic to define a set of axioms and the logical rationale to apply them to any deductive proof. The Method includes accounting primitives and axioms to use in combination with those of the Axiomatic theory. A direct proof is applied to test the balance sheet fit to a hereditary set structure according to the Axiomatic theory, and proof by contraposition is employed to examine the assets-claims on assets equality by comparing their elements. Results show that balance sheet has a set structure that can be defined and analyzed with the Axiomatic Method and fits a hereditary set structure. Also, by comparing the elements of assets and claims on assets and considering their financial classification, it is shown that these sets do not contain the same elements and, consequently, they are not equal under the postulates of the Axiomatic Method.

Nicola Giocoli - One of the best experts on this subject based on the ideXlab platform.

  • Blanqui Lecture - In the Sign of the Axiomatic Method: Mathematics as the Role Model for Neoclassical Economics
    SSRN Electronic Journal, 2006
    Co-Authors: Nicola Giocoli
    Abstract:

    Born out of the conscious effort to imitate mechanical physics, neoclassical economics ended up in the mid 20th century embracing a purely mathematical notion of rigor as embodied by the Axiomatic Method. This lecture tries to explain how this could happen, or, why and when the economists' role model became the mathematician rather than the physicist. According to the standard interpretation, the triumph of Axiomatics in modern neoclassical economics can be explained in terms of the discipline's increasing awareness of its lack of good experimental and observational data, and thus of its intrinsic inability to fully abide by the paradigm of mechanics. Yet this story fails to properly account for the transformation that the word rigor itself underwent first and foremost in mathematics as well as for the existence of a specific motivation behind the economists' decision to pursue the Axiomatic route. While the full argument is developed in Giocoli 2003, these pages offer a taste of a (partially) alternative story which begins with the so-called formalist revolution in mathematics, then crosses the economists' almost innate urge to bring their discipline to the highest possible level of generality and conceptual integrity, and ends with the advent and consolidation of that very core set of Methods, tools and ideas that constitute the contemporary image of economics.

  • mathematics as the role model for neoclassical economics blanqui lecture
    MPRA Paper, 2005
    Co-Authors: Nicola Giocoli
    Abstract:

    Born out of the conscious effort to imitate mechanical physics, neoclassical economics ended up in the mid 20th century embracing a purely mathematical notion of rigor as embodied by the Axiomatic Method. This lecture tries to explain how this could happen, or, why and when the economists’ role model became the mathematician rather than the physicist. According to the standard interpretation, the triumph of Axiomatics in modern neoclassical economics can be explained in terms of the discipline’s increasing awareness of its lack of good experimental and observational data, and thus of its intrinsic inability to fully abide by the paradigm of mechanics. Yet this story fails to properly account for the transformation that the word “rigor” itself underwent first and foremost in mathematics as well as for the existence of a specific motivation behind the economists’ decision to pursue the Axiomatic route. While the full argument is developed in Giocoli 2003, these pages offer a taste of a (partially) alternative story which begins with the so-called formalist revolution in mathematics, then crosses the economists’ almost innate urge to bring their discipline to the highest possible level of generality and conceptual integrity, and ends with the advent and consolidation of that very core set of Methods, tools and ideas that constitute the contemporary image of economics.

Michael Stoltzner - One of the best experts on this subject based on the ideXlab platform.

  • hilbert s Axiomatic Method and carnap s general Axiomatics
    Studies in History and Philosophy of Science, 2015
    Co-Authors: Michael Stoltzner
    Abstract:

    This paper compares the Axiomatic Method of David Hilbert and his school with Rudolf Carnap's general Axiomatics that was developed in the late 1920s, and that influenced his understanding of logic of science throughout the 1930s, when his logical pluralism developed. The distinct perspectives become visible most clearly in how Richard Baldus, along the lines of Hilbert, and Carnap and Friedrich Bachmann analyzed the axiom system of Hilbert's Foundations of Geometry—the paradigmatic example for the axiomatization of science. Whereas Hilbert's Axiomatic Method started from a local analysis of individual axiom systems in which the foundations of mathematics as a whole entered only when establishing the system's consistency, Carnap and his Vienna Circle colleague Hans Hahn instead advocated a global analysis of axiom systems in general. A primary goal was to evade, or formalize ex post, mathematicians' 'material' talk about axiom systems for such talk was held to be error-prone and susceptible to metaphysics.

  • theoretical mathematics on the philosophical significance of the jaffe quinn debate
    2005
    Co-Authors: Michael Stoltzner
    Abstract:

    Answering to the double-faced influence of string theory on mathematical practice and rigour, the mathematical physicists Arthur Jaffe and Frank Quinn have contemplated the idea that there exists a 'theoretical' mathematics (alongside 'theoretical' physics) whose basic structures and results still require independent corroboration by mathematical proof. In this paper, I shall take the Jaffe-Quinn debate mainly as a problem of mathematical ontology and analyse it against the backdrop of two philosophical views that are appreciative towards informal mathematical development and conjectural results: Lakatos's Methodology of proofs and refutations and John von Neumann's opportunistic reading of Hilbert's Axiomatic Method. The comparison of both approaches shows that mitigating Lakatos's falsificationism makes his insights about mathematical quasi-ontology more relevant to 20 th century mathematics in which new structures are introduced by axiomatisation and not necessarily motivated by informal ancestors. The final section discusses the consequences of string theorists' claim to finality for the theory's mathematical make-up. I argue that ontological reductionism as advocated by particle physicists and the quest for mathematically deeper axioms do not necessarily lead to identical results.

  • bell bohm and von neumann some philosophical inequalities concerning no go theorems and the Axiomatic Method
    2002
    Co-Authors: Michael Stoltzner
    Abstract:

    The present paper investigates the philosophical relationship between John von Neumann’s Nohidden-variable theorem and Bell’s inequalities. Bell erroneously takes the Axiomatic Method as implying a finality claim and thus ignores von Neumann’s strongly pragmatist stance towards mathematical physics. If one considers, however, Hilbert’s Axiomatic Method as a critical enterprise, Bell’s theorem improves von Neumann’s by defining a more appropriate notion of ‘ hidden variable’ that permits one to include Bohm’s interpretation which recovers the predictive content of quantum mechanics. Contrary to Bell’s belief, accepting this model does not require adopting the metaphysically realist Bohm picture. If one takes the latter as a physical research programme one sees that it only partly disputes a common domain of facts with the mathematically oriented research programme of von Neumann.

  • how metaphysical is deepening the foundations hahn and frank on hilbert s Axiomatic Method
    2002
    Co-Authors: Michael Stoltzner
    Abstract:

    Only recently has David Hilbert’s program to axiomatize the sciences according to the pattern of geometry left the shade of his formalist program in the foundations of mathematics.1 This relative neglect — which is surprising in view of the enormous efforts Hilbert himself had devoted to it — was certainly influenced by Logical Empiricists’ almost exclusively focusing on his contributions to the foundational debates. Ulrich Majer puts part of the blame for this neglect on Hilbert himself because “he failed to make his position sufficiently clear, and he did not take much effort to promote his views beyond the narrow circle of mathematical physics in Gottingen.”2

Andrei Rodin - One of the best experts on this subject based on the ideXlab platform.

  • on constructive Axiomatic Method
    Logique Et Analyse, 2014
    Co-Authors: Andrei Rodin
    Abstract:

    The formal Axiomatic Method popularized by Hilbert and recently defended by Hintikka is not fully adequate to the recent practice of axiomatizing mathematical theories. The Axiomatic architecture of Topos theory and Homotopy type theory do not fit the pattern of the formal Axiomatic theory in the standard sense of the word. However these theories fall under a more general and in some respects more traditional notion of Axiomatic theory, which I call after Hilbert constructive. I show that the formal Axiomatic Method always requires a support of some more basic constructive Method.

  • on constructive Axiomatic Method
    arXiv: History and Overview, 2014
    Co-Authors: Andrei Rodin
    Abstract:

    In this last version of the paper one may find a critical overview of some recent philosophical literature on Axiomatic Method and Genetic Method.

  • new Axiomatic Method instead of conclusion
    2014
    Co-Authors: Andrei Rodin
    Abstract:

    In the following long promised presentation of the New Axiomatic Method I shall use as a guide Lawvere’s description of Axiomatic Method as “unification and concentration” (Lawvere 2003, p. 213) and generalize upon some examples of Axiomatic thinking due to Lawvere and Voevodsky. I begin with the unification, then turn to the concentration and, finally, discuss the place and the special character of logic in the New Axiomatic Method.

  • formal Axiomatic Method and the twentieth century mathematics
    2014
    Co-Authors: Andrei Rodin
    Abstract:

    The Formal Axiomatic Method has been proposed by Hilbert about a century ago and it is appropriate to ask how it performed during the past century. It appears to me that its impact is somewhat controversial. On the one hand, during this time period the Formal Axiomatic Method was and still remains the standard Method of theory-building in eyes of logicians and logically-minded mathematicians, physicists, biologists and philosophers. On the same side of the scale I put the progress in the logico-mathematical investigations (some of which use the title of foundations of mathematics), which apply this Method in some form.

  • Axiomatic Method and category theory
    2013
    Co-Authors: Andrei Rodin
    Abstract:

    Lawvere’s axiomatization of topos theory and Voevodsky’s axiomatization of heigher homotopy theory exemplify a new way of Axiomatic theory-building, which goes beyond the classical Hibert-style Axiomatic Method. The new notion of Axiomatic Method that emerges in Categorical logic opens new possibilities for using this Method in physics and other natural sciences.