Related papers: Democritus as Taoist
This book introduces a temporal type theory, the first of its kind as far as we know. It is based on a standard core, and as such it can be formalized in a proof assistant such as Coq or Lean by adding a number of axioms. Well-known…
We review some modern theories about the structure of space and time, in particular those related to discrete space and time. Following an epistemological method we start from theories which discuss discrete space and time as a mathematical…
We study approximations of theories both in general context and with respect to some natural classes of theories. Some kinds of approximations are considered, connections with finitely axiomatizable theories and minimal generating sets of…
Determinism and indeterminism in physical theories are reviewed and some broader implications of determinism are discussed.
Topos theory has been suggested by Doring and Isham as an alternative mathematical structure with which to formulate physical theories. In particular it has been used to reformulate standard quantum mechanics in such a way that a novel type…
In this paper, I aim to clarify the unconscious ideologies and attitudes held by physicists through Prigogine's work. Prigogine was an outstanding chemist and physicist who made significant contributions to the development of…
We introduce judgemental theories and their calculi as a general framework to present and study deductive systems. As an exemplification of their expressivity, we approach dependent type theory and natural deduction as special kinds of…
Is presentism compatible with relativity ? This question has been much debated since the argument first proposed by Rietdijk and Putnam. The goal of this text is to study the implications of relativity and quantum mechanics on presentism,…
We describe and explain the desire, common among mathematicians, both for unity and independence in its major themes. In the dialogue that follows, we express our spontaneous and considered judgment and reservations by contrasting the…
A paraconsistent type theory (an extension of a fragment of intuitionistic type theory by adding opposite types) is here extended by adding co-function types. It is shown that, in the extended paraconsistent type system, the opposite type…
I examine the debate between substantivalists and relationalists about the ontological character of spacetime and conclude it is not well posed. I argue that the so-called Hole Argument does not bear on the debate, because it provides no…
In this essay we describe a platonic metaphysics where time is a fundamental idea such that the passage of time is independent of observers and the laws of physics. Furthermore, time serves to distinguish between a real and an abstract…
I lay out the problem of time facets as arising piecemeal from a number of aspects of background independence. Almost all of these already have simpler classical counterparts. This approach can be viewed as a facet by facet completion of…
It is said that Einstein's conceptual base for the theory of relativity was the philosophy formulated by Immanuel Kant. Then, is it possible to see how Kant played a role in Einstein's thinking without reading Kant's books? This question…
The relationship between inner and outer time is discussed. Inner time is intrinsically future directed and possesses the quality of a distinguished "now". Both of these qualities get lost in the operationalized external physical time,…
We analyse and develop the recent suggestion that a temporal form of quantum logic provides the natural mathematical framework within which to discuss the proposal by Gell-Mann and Hartle for a generalised form of quantum theory based on…
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…
We advocate an account of dualities between physical theories: the basic idea is that dual theories are isomorphic representations of a common core. We defend and illustrate this account, which we call a Schema, in relation to symmetries.…
We develop a formalism for studying descent and codescent in the context of Iwasawa theory. The main result essentially states that to control descent or codescent amounts to the same. Arithmetic applications are given.
Understanding how physicists solve problems can guide the development of methods that help students learn and improve at solving complex problems. Leveraging the framework of cognitive task analysis, we conducted semi-structured interviews…