Related papers: Knowledge is non-fungible
What is the largest number accessible to the human imagination? The question is neither entirely mathematical nor entirely philosophical. Mathematical formulations of the problem fall into two classes: those that fail to fully capture the…
To provide an explanation of the evolution of scientific knowledge, I start from the assumption that knowledge is based on concepts, and propose that each concept about reality is affected by vagueness. This entails a paradox, which I term…
We study knowable informational dependence between empirical questions, modeled as continuous functional dependence between variables in a topological setting. We also investigate epistemic independence in topological terms and show that it…
The constantly growing body of scholarly knowledge of science, technology, and humanities is an asset of the mankind. While new discoveries expand the existing knowledge, they may simultaneously render some of it obsolete. It is crucial for…
Information is everywhere in nature which is very uncertain and unpredictable. But information, in itself, is a very ambiguous term. In this cursory write-up, we attempt to understand the formal meaning of information by quantifying…
Learning to use math in science is a non-trivial task. It involves many different skills (not usually taught in a math class) that help blend physical knowledge with mathematical symbology. One of these is the idea of quantification: that…
There are many ways we can not know. Even in systems that we created ourselves, as, for example, systems in mathematical logic, Go\"edel and Tarski's theorems impose limits on what we can know. As we try to speak of the real world, things…
Awareness has been shown to be a useful addition to standard epistemic logic for many applications. However, standard propositional logics for knowledge and awareness cannot express the fact that an agent knows that there are facts of which…
This article defines a complement of a function and conditions for existence of such a complement function and presents few algorithms to construct a complement.
Science and mathematics help people better to understand world, eliminating different fallacies and misconceptions. One of such misconception is related to arithmetic, which is so important both for science and everyday life. People think…
Mathematicians occasionally discover interesting truths even when they are playing with mathematical ideas with no thoughts about possible consequences of their actions. This paper describes two specific instances of this phenomenon. The…
Human knowledge is subject to uncertainties, imprecision, incompleteness and inconsistencies. Moreover, the meaning of many everyday terms is dependent on the context. That poses a huge challenge for the Semantic Web. This paper introduces…
A model of knowledge representation is described in which propositional facts and the relationships among them can be supported by other facts. The set of knowledge which can be supported is called the set of cognitive units, each having…
What would be the consequences if there were fundamental limits to our ability to experimentally explore the world? In this work we seriously consider this question. We assume the existence of statements whose truth value is not…
Doubts are raised concerning the usual interpretation of the alleged failure, by quantum mechanics, of the distributive law of classical logic. The difficulty raised by incompatible sets of observables is overcome within an epistemic…
This paper discusses the benefits of describing the world as information, especially in the study of the evolution of life and cognition. Traditional studies encounter problems because it is difficult to describe life and cognition in terms…
Interestingness is an important criterion by which we judge knowledge discovery. But, interestingness has escaped all attempts to capture its intuitive meaning into a concise and comprehensive form. A unifying paradigm is formulated by…
Many have wondered how mathematics, which appears to be the result of both human creativity and human discovery, can possibly exhibit the degree of success and seemingly-universal applicability to quantifying the physical world as…
The nature of the scientific method is controversial with claims that a single scientific method does not even exist. However the scientific method does exist. It is the building of logical and self consistent models to describe nature. The…
This paper addresses the problem of merging uncertain information in the framework of possibilistic logic. It presents several syntactic combination rules to merge possibilistic knowledge bases, provided by different sources, into a new…