On the epistemological significance of the hungarian project

Abstract

There are three elements in this paper. One is what we shall call 'the Hungarian project'. This is the collected work of Andréka, Madarász, Németi, Székely and others. The second is Molinini's philosophical work on the nature of mathematical explanations in science. The third is my pluralist approach to mathematics. The theses of this paper are that (1) the Hungarian project gives genuine mathematical explanations for physical phenomena. (2) A pluralist account of mathematical explanation can help us with appreciating the significance of the Hungarian project. (3) The significance consists in the fruitfulness and spread of the project. The spread is wide because the explanations are written in the very familiar language of first-order logic with identity. For this reason, the explanation is understandable to many mathematicians. (4) Because of the methodology adopted in the Hungarian project, the explanations are fruitful in another sense. In the Hungarian project certain questions are asked that would not be asked with a more usual methodology. The Hungarians are distinguished from other scientists in asking logical and mathematical questions, and these both deepen our understanding of the physical theories and induce further spread to mathematics and philosophy.I should like to thank Molinini and Nait-Abdallah for reading early draft versions of the paper, and giving several helpful corrections and suggestions. I should also like to acknowledge the helpful comments from members of the audience at the conference celebrating István Németi's 70th birthday, and for the enthusiasm and inspiration I received from Andréka, Németi, Székely and Madarász. They also paid careful attention to a better draft, and gave many helpful suggestions. Lastly, I should like to thank the anonymous reviewers for careful and invaluable comments. M. Friend (B)

Groups of Worldview Transformations Implied by Einstein’s Special Principle of Relativity Over Arbitrary Ordered Fields

“…By showing the connection between two radically different approaches, Andréka & Németi (2014) takes an important first step in bringing these sporadic axiom systems together. See Friend (2015) and Friend & Molinini (2015) for general discussions of Andréka-Németi school's project and methodology from points of view of epistemological significance and role in scientific explanation.…”

Groups of Worldview Transformations Implied by Isotropy of Space

“…The investigation presented in this paper is part of the Andréka-Németi school's general project of logic-based axiomatic foundations of relativity theories, see e.g., [AMN06, AMN07, AMNS12, AN14]. Friend and Molinini [Fri15,FM15] discuss the significance of this project and the underlying methodology from the viewpoints of epistemology and explanation in science. One important feature of using a firstorder logic-based axiomatic framework is that it helps avoid hidden assumptions, which is fundamental in foundational analyses of this nature.…”

On some Symmetry Axioms in Relativity Theories

“…(2015), and Stannett and Németi (2014). See Friend (2015) for epistemological significance of the Andréka-Németi approach.…”