Related papers: Formalism 25
The persisting gap between the formal and the informal mathematics is due to an inadequate notion of mathematical theory behind the current formalization techniques. I mean the (informal) notion of axiomatic theory according to which a…
We offer a view of mathematics as an experimental science where axioms play the role of foundational theories like general relativity and quantum mechanics in physics. Under this view, axioms are provisional and inferred from experience…
Formal mathematics is mathematics done within the framework of a formal logic. It offers major benefits to mathematicians as well as to computing professionals, engineers, and scientists who use mathematics in their work. The standard…
We examine Paul Halmos' comments on category theory, Dedekind cuts, devil worship, logic, and Robinson's infinitesimals. Halmos' scepticism about category theory derives from his philosophical position of naive set-theoretic realism. In the…
I defend algebraicism, according to which physical fields can be understood in terms of their structural relations without reference to a spacetime manifold, as a genuine relationalist view against the conventional wisdom that it is…
The aim of this essay is to propose a conception of mathematics that is fully consonant with naturalism. By that I mean the hypothesis that everything that exists is part of the natural world, which makes up a unitary whole.
Logical bilateralism challenges traditional concepts of logic by treating assertion and denial as independent yet opposed acts. While initially devised to justify classical logic, its constructive variants show that both acts admit…
A classical reconstruction of Wright's first-order logic of strict finitism is presented. Strict finitism is a constructive standpoint of mathematics that is more restrictive than intuitionism. Wright sketched the semantics of said logic in…
Relationalism -- along the lines developed by Barbour and collaborators in the past 3 decades -- can be considered an advance with 1/4 of the facets of the canonical approach's Problem of Time as identified by Isham and Kuchar. Indeed,…
In this paper I show that, while Einstein and Bohm both pursued a deterministic description of quantum mechanics, their philosophical concern was in fact primarily realism and not determinism. Their alleged firm adherence to determinism is…
This article contributes to the debate of the meaning of relationalism and background independence, which has remained of interest in theoretical physics from Newton versus Leibniz through to foundational issues for today's leading…
The example of the calculus is used to explain how simple, practical math was made enormously complex by imposing on it the Western religiously-colored notion of mathematics as "perfect". We describe a pedagogical experiment to make math…
We recently presented the so-called allagmatic method, which includes a system metamodel providing a framework for describing, modelling, simulating, and interpreting complex systems. Its development and programming was guided by…
All sciences need and many arts apply mathematics whereas mathematics seems to be independent of all of them, but only based upon logic. This conservative concept, however, needs to be revised because, contrary to Platonic idealism…
The chapter advances a reformulation of the classical problem of the nature of mathematical objects (if any), here called "Plato's problem," in line with the program of a philosophy of mathematical practice. It then provides a sketch of a…
The traditional metaphysical debate between static and dynamic views in the philosophy of time is examined in light of considerations concerning the nature of time in physical theory. Adapting the formalism of Rovelli (1995, 2004), I set…
Determinism is (roughly) the thesis that the past determines the future. But efforts to define it precisely have exposed deep methodological disagreements. Standard possible-worlds formulations of determinism presuppose an "agreement"…
We rely on the strength of linguistic and philosophical perspectives in constructing a framework that offers a unified explanation for presuppositions and existential commitment. We use a rich ontology and a set of methodological principles…
It has been shown at other occasions that recent results of modern physics can be used to shed some more light onto the foundations of the world, provided the actual task of philosophy is being re-interpreted in terms of a theory which is…
In this paper we discuss the representational realist stance as a pluralist ontic approach to inter-theoretic relationships. Our stance stresses the fact that physical theories require the necessary consideration of a conceptual level of…