Attempts at solving what has been labeled as Eugene Wigner’s puzzle of applicability of mathematics are still far from arriving at an acceptable solution. The accounts developed to explain the “miracle” of applied mathematics vary in nature, foundation, and solution, from denying the existence of a genuine problem to designing structural theories based on mathematical formalism. Despite this variation, all investigations treated the problem in a unitary way with respect to the target, pointing to one or two ‘why’ or ‘how’ (...) questions to be answered. In this paper, I argue that two analyses, a semantic analysis ab initio and a metatheoretical analysis starting from the types of unreasonableness involved in this problem, will establish the interdisciplinary character of the problem and reveal many more targets, which may be addressed with different methodologies. In order to address objectively the philosophical problem of applicability of mathematics, a foundational revision of the problem is needed. (shrink)

In a paper titled, “The Unreasonable Effectiveness of Mathematics”, published 20 years after Wigner’s seminal paper, the mathematician Richard W. Hamming discussed what he took to be Wigner’s problem of Unreasonable Effectiveness and offered some partial explanations for this phenomenon. Whether Hamming succeeds in his explanations as answers to Wigner’s puzzle is addressed by other scholars in recent years I, on the other hand, raise a more fundamental question: does Hamming succeed in raising the same question as Wigner? The answer (...) is no. My goal is to show that Hamming’s reading misses Wigner’s highly original formulation of the problem.Through a close and contextual reading of Wigner’s work, as I will show, we are led in new directions in addressing and solving the applicability problem. (shrink)

It is assumed that scientific models contain no superfluous model elements in scientific representation. A representational model is constructed with all the model elements serving the representational purpose. The received view has it that there are no redundant model elements which are non-representational. Contrary to this received view, I argue that there exist some non-representational model elements which are essential in scientific representation. I call them representation-supporting model elements in virtue of the fact that they play the role to support (...) the representational role of representational model elements. Representation-supporting model elements, which have a characteristic of dependability, are not to be eliminated in the process of modeling although they are playing second fiddle to representational model elements in scientific representation. (shrink)

The problem of ‘applicability’ of mathematics to modern physical sciences has been labeled as an ‘unreasonably effective’ and unexplainable ‘miracle’ by prominent physicists such as Eugene Wigner a...

Attempts at solving what has been labeled as Eugene Wigner’s puzzle of applicability of mathematics are still far from arriving at an acceptable solution. The accounts developed to explain the “miracle” of applied mathematics vary in nature, foundation, and solution, from denying the existence of a genuine problem to designing structural theories based on mathematical formalism. Despite this variation, all investigations treated the problem in a unitary way with respect to the target, pointing to one or two ‘why’ or ‘how’ (...) questions to be answered. In this paper, I argue that two analyses, a semantic analysis ab initio and a metatheoretical analysis starting from the types of unreasonableness involved in this problem, will establish the interdisciplinary character of the problem and reveal many more targets, which may be addressed with different methodologies. In order to address objectively the philosophical problem of applicability of mathematics, a foundational revision of the problem is needed. (shrink)