Related papers: Infinity and the Sublime
This paper aims to show that a simple framework, utilizing basic formalisms from set theory and category theory, can clarify and inform our theories of the relation between mind and matter.
We study a natural variant of the implicational fragment of propositional logic. Its formulas are pairs of conjunctions of positive literals, related together by an implicational-like connective; the semantics of this sort of implication is…
The integration of lexical semantics and pragmatics in the analysis of the meaning of natural lan- guage has prompted changes to the global framework derived from Montague. In those works, the original lexicon, in which words were assigned…
Several formal systems, such as resolution and minimal model semantics, provide a framework for logic programming. In this paper, we will survey the use of structural proof theory as an alternative foundation. Researchers have been using…
This is an informal introduction to the ideas of decoherence and emergent classicality, including a simple account of the decoherent histories approach to quantum theory. It is aimed at undergraduates with a basic appreciation of quantum…
The notion of concept has been studied for centuries, by philosophers, linguists, cognitive scientists, and researchers in artificial intelligence (Margolis & Laurence, 1999). There is a large literature on formal, mathematical models of…
This is a set of 288 questions written for a Moore-style course in Mathematical Logic. I have used these (or some variation) four times in a beginning graduate course. Topics covered are: propositional logic axioms of ZFC wellorderings and…
Theories of natural language and concepts have been unable to model the flexibility, creativity, context-dependence, and emergence, exhibited by words, concepts and their combinations. The mathematical formalism of quantum theory has…
After the development of a self-consistent quantum formalism nearly a century ago there began a quest for how to interpret the theoretical constructs of the formalism. In fact, the pursuit of new interpretations of quantum mechanics…
This document is meant as a pedagogical introduction to the modern language used to talk about quantum theory, especially in the field of quantum information. It assumes that the reader has taken a first traditional course on quantum…
IIn the paper the Space-Time problem is considered as it seen in the informational conception ("the Information as Absolute" conception) comparing with a number of existent physical and philosophical approaches. Since the conception is…
The present paper proposes a novel way to unify Rough Set Theory and Formal Concept Analysis. Our method stems from results and insights developed in the algebraic theory of modal logic, and is based on the idea that Pawlak's original…
Developing and organizing new knowledge is a core activity for scholars. Recently, ontologies have been introduced as an approach for organizing knowledge. However, most ontologies do not readily support the development and organization of…
The purpose of this paper is to describe and elaborate the philosophical ideas behind hyperstructures and structure formation in general and emphasize the key ideas of the Hyperstructure Program.
The philosophical foundations of statistics involve issues in theoretical statistics, such as goals and methods to meet these goals, and interpretation of the meaning of inference using statistics. They are related to the philosophy of…
This text summarizes and expands the content of a general audience talk given in 2018 at the University of Mainz. Motivated by recent developments in dependent type theory and infinity category theory, it presents a history of ideas around…
The aim of the paper is to develop a proper mathematical formalism which can help to clarify the necessary conceptual plugins to the special principle of relativity and leads to a deeper understanding of the principle in its widest…
The long lasting discussion on the completeness of quantum theory (QT) has not yet come to an end. The discussion is impeded by the lack of a clear understanding of what makes up the contents of a theory of physics in general and of QT…
Inquisitive logic is a research program that extends the scope of logic to cover not only statements, but also questions. In the context of this program, a logic that plays a prominent role is inquisitive first-order logic, InqBQ, which…
Did time begin at a Big Bang? Will the present expansion of the universe last for a finite or infinite time? These questions sound philosophical but are becoming, now in the twenty-first century, central to the scientific study of…