Related papers: Embracing undecidability: Cognitive needs and theo…

Classical interpretations of Goedel's formal reasoning imply that the truth of some arithmetical propositions of any formal mathematical language, under any interpretation, is essentially unverifiable. However, a language of general,…

A simple framework for reasoning under uncertainty and intervention is introduced. This is achieved in three steps. First, logic is restated in set-theoretic terms to obtain a framework for reasoning under certainty. Second, this framework…

The recognition of the agency of the knower has enormously enriched our understanding of knowledge production. There is a growing realization that what we know about how we know affects our interpretation of reality. This realization…

Practicing mathematicians often assume that mathematical claims, when they are true, have good reasons to be true. Such a state of affairs is "unreasonable", in Wigner's sense, because basic results in computational complexity suggest that…

A colloquial interpretation of entropy is that it is the knowledge gained upon learning the outcome of a random experiment. Conditional entropy is then interpreted as the knowledge gained upon learning the outcome of one random experiment…

One of the most remarkable things about the human moral mind is its flexibility. We can make moral judgments about cases we have never seen before. We can decide that pre-established rules should be broken. We can invent novel rules on the…

One finding of cognitive research is that people do not automatically acquire usable knowledge by spending lots of time on task. Because students' knowledge hierarchy is more fragmented, "knowledge chunks" are smaller than those of experts.…

Consider a community of scientists whose labs are each capable of conducting a different set of experiments. The scientists want to work together to confirm a new hypothesis, but to ensure blindness, their labs generally prohibit the…

Defeasible reasoning is a kind of reasoning where some generalisations may not be valid in all circumstances, that is general conclusions may fail in some cases. Various formalisms have been developed to model this kind of reasoning, which…

Notions of unknown truths and unknowable truths are important in formal epistemology, which are related to each other in e.g. Fitch's paradox of knowability. Although there have been some logical research on the notion of unknown truths and…

Although many investigators affirm a desire to build reasoning systems that behave consistently with the axiomatic basis defined by probability theory and utility theory, limited resources for engineering and computation can make a complete…

The predictions that quantum theory makes about the outcomes of measurements are generally probabilistic. This has raised the question whether quantum theory can be considered complete, or whether there could exist alternative theories that…

We formalize two independent computational limitations that constrain algorithmic intelligence: formal incompleteness and dynamical unpredictability. The former limits the deductive power of consistent reasoning systems while the latter…

As artificial agents become increasingly capable, what internal structure is *necessary* for an agent to act competently under uncertainty? Classical results show that optimal control can be *implemented* using belief states or world…

I think we can agree that dealing with uncertainty is not easy. Probability is the main tool for dealing with uncertainty, and we know there are many probability-related puzzles and paradoxes. Here I describe a rather idiosyncratic…

In this paper the theory of flexibly-bounded rationality which is an extension to the theory of bounded rationality is revisited. Rational decision making involves using information which is almost always imperfect and incomplete together…

The goal of this article is to give an overview of the current limitations and epistemological barriers in Science and Scientific Philosophy from a very general point of view. We first list and define the types of knowledge nous, doxa and…

The study of undecidability in problems arising from physics has experienced a renewed interest, mainly in connection with quantum information problems. The goal of this review is to survey this recent development. After a historical…

A tradition handed down among physicists maintains that classical physics is a perfectly deterministic theory capable of predicting the future with absolute certainty, independently of any interpretations. It also tells that it was quantum…

We report an inconsistency found in probability theory (also referred to as measure-theoretic probability). For probability measures induced by real-valued random variables, we deduce an "equality" such that one side of the "equality" is a…