Related papers: Hegel and Modern Topology

Metaphysical interpretations of set theory are either inconsistent or incoherent. The uses of sets in mathematics actually involve three distinct kinds of collections (surveyable, definite, and heuristic), which are governed by three…

In this paper we provide a unifying description of different types of semantics of modal logic found in the literature via the framework of topological categories. In the style of categorical logic, we establish an exact correspondence…

The homotopy theory of topological defects is a powerful tool for organizing and unifying many ideas across a broad range of physical systems. Recently, experimental progress has been made in controlling and measuring colloidal inclusions…

Complex networks, which are the abstractions of many real-world systems, present a persistent challenge across disciplines for people to decipher their underlying information. Recently, hyperbolic geometry of latent spaces has gained…

We explore various semantic understandings of dual intuitionistic logic by exploring the relationship between co-Heyting algebras and topological spaces. First, we discuss the relevant ideas in the setting of Heyting algebras and…

We continue work of our earlier paper (Lewitzka and Brunner: Minimally generated abstract logics, Logica Universalis 3(2), 2009), where abstract logics and particularly intuitionistic abstract logics are studied. Abstract logics can be…

Homotopy limits and colimits are homotopical replacements for the usual limits and colimits of category theory, which can be approached either using classical explicit constructions or the modern abstract machinery of derived functors. Our…

There are many examples of dualities between topological spaces and algebras in the literature. Particularly, many of those examples come from the algebraic counterpart of a logical system, e.g, boolean and heyting algebras, MV-algebras,…

This paper is the first in a series whose goal is to develop a fundamentally new way of constructing theories of physics. The motivation comes from a desire to address certain deep issues that arise when contemplating quantum theories of…

This work may be defined as a modern philosophical approach to theoretical physics. Since ancient times science and philosophy evolved in parallel, thus renewing from time to time the epochal paradigms of human thought. We could not…

When teaching an elementary logic course to students who have a general scientific background but have never been exposed to logic, we have to face the problem that the notions of deduction rule and of derivation are completely new to them,…

Topological models of empirical and formal inquiry are increasingly prevalent. They have emerged in such diverse fields as domain theory [1, 16], formal learning theory [18], epistemology and philosophy of science [10, 15, 8, 9, 2],…

This paper develops a basic theory of H-groups. We introduce a special quotient of H-groups and extend some algebraic constructions of topological groups to the category of H-groups and H-maps. We use these constructions to prove some…

In the last couple of years there were a few attempts to apply topological data analysis to text, and in particular to natural language inference. A recent work by Tymochko et al. suggests the possibility of capturing `the notion of logical…

We use Kan injectivity to axiomatise concepts in the 2-category of topoi. We showcase the expressivity of this language through many examples, and we establish some aspects of the formal theory of Kan extension in this 2-category (pointwise…

Many of the properties of sectional category, topological complexity and homotopic distance are in fact derived from a small number of basic properties, which, once established, lead to all the others without further recourse to topology.…

This paper is mainly a semi-tutorial introduction to elementary algebraic topology and its applications to Ising-type models of statistical physics, using graphical models of linear and group codes. It contains new material on systematic…

Knowledge is a network of interconnected concepts. Yet, precisely how the topological structure of knowledge constrains its acquisition remains unknown, hampering the development of learning enhancement strategies. Here we study the…

The paper analyzes dynamic epistemic logic from a topological perspective. The main contribution consists of a framework in which dynamic epistemic logic satisfies the requirements for being a topological dynamical system thus interfacing…

The goal of this paper is to summarise the first steps in developing a fundamentally new way of constructing theories of physics. The motivation comes from a desire to address certain deep issues that arise when contemplating quantum…