Related papers: Distances between formal theories
We survey a new area of parameter-free similarity distance measures useful in data-mining, pattern recognition, learning and automatic semantics extraction. Given a family of distances on a set of objects, a distance is universal up to a…
The classical information metric provides a unique notion of distance on the space of probability distributions with a well-defined operational interpretation: two distributions are far apart if they are readily distinguishable from one…
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 live at a time of contradictory messages about how successfully we understand gravity. General Relativity seems to work very well in the Earth's immediate neighborhood, but arguments abound that it needs modification at very small and/or…
Terms of Church's $\lambda$-calculus can be considered equivalent along many different definitions, but context equivalence is certainly the most direct and universally accepted one. If the underlying calculus becomes probabilistic,…
In this paper, we argue that there are foundational dilemmas in theoretical physics related to the concept of reality and the nature of mathematics in physics. Physical theory is treated as a conceptual organism which develops under the…
Most educational literature on conceptual change concerns the process by which introductory students acquire scientific knowledge. However, with modern developments in science and technology, the social significance of learning successive…
We introduce a new form of logical relation which, in the spirit of metric relations, allows us to assign each pair of programs a quantity measuring their distance, rather than a boolean value standing for their being equivalent. The…
I argue that it is possible for a theory to be neither quantized nor classical. We should therefore give up the assumption that the fundamental theory which describes gravity at shortest distances must either be quantized, or quantization…
We present several philosophical ideas emerging from the studies of complex systems. We make a brief introduction to the basic concepts of complex systems, for then defining "abstraction levels". These are useful for representing…
To what extent can we distinguish one probability distribution from another? Are there quantitative measures of distinguishability? The goal of this tutorial is to approach such questions by introducing the notion of the "distance" between…
The aim of this paper is to present a new logic-based understanding of the connection between classical kinematics and relativistic kinematics. We show that the axioms of special relativity can be interpreted in the language of classical…
Knowing the distance of an astrophysical object is key to understanding it. However, at present, comparisons of theory and observations are hampered by precision (or lack thereof) in distance measurements or estimates. Putting the many…
We calculate resistance distances between papers in a nearly bipartite citation network of 492 papers and the sources cited by them. We validate that this is a realistic measure of thematic distance if each citation link has an electric…
Logicians and philosophers of science have proposed various formal criteria for theoretical equivalence. In this paper, we examine two such proposals: definitional equivalence and categorical equivalence. In order to show precisely how…
Although cosmic expansion at very small distances is usually dismissed as entirely inconsequential, it appears that these extraordinarily small effects may in fact have a real and significant influence on our world. Calculations suggest…
Action-at-a-distance is a generic property of physical theories. As such, it is not a fruitful idea in theory building. Its absence confers a rigidity on a theory which we exemplify through analysis of long-range correlations of the…
Intuitively, the concept of similarity is the notion to measure an inexact matching between two entities of the same reference set. The notions of similarity and its close relative dissimilarity are widely used in many fields of Artificial…
We propose a covariant and geometric framework to introduce space distances as they are used by astronomers. In particular, we extend the definition of space distances from the one used between events to non-test-bodies with horizons and…
Nearness theory comes into play in homotopy theory because the notion of closeness between points is essential in determining whether two spaces are homotopy equivalent. While nearness theory and homotopy theory have different focuses and…