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Quantum theory is a tremendously successful physical theory, but nevertheless suffers from two serious problems: the measurement problem and the problem of interpretational underdetermination. The latter, however, is largely overlooked as a…
Tarski's undefinability theorem states that a formal system based on conventional predicate logic (PL) cannot talk about its own truth predicate. PL is, however, not the only formal language imaginable. In this paper, it will be shown that…
The usual reading of logical implication "A implies B" as "if A then B" fails in intuitionistic logic: there are formulas A and B such that "A implies B" is not provable, even though B is provable whenever A is provable. Intuitionistic…
The past century has seen a steady increase in the need of estimating and predicting complex systems and making (possibly critical) decisions with limited information. Although computers have made possible the numerical evaluation of…
Probability theory, epistemically interpreted, provides an excellent, if not the best available account of inductive reasoning. This is so because there are general and definite rules for the change of subjective probabilities through…
Any successful interpretation of quantum mechanics must explain how our empirical evidence allows us to come to know about quantum mechanics. In this article, we argue that this vital criterion is not met by the class of 'orthodox…
I argue that, contrary to the standard view, one cannot understand the structure and nature of our knowledge in physics without an analysis of the way that observers (and, more generally, measuring instruments and experimental arrangements)…
Determinism is (roughly) the thesis that the past determines the future. But efforts to define it precisely have exposed deep methodological disagreements. Standard possible-worlds formulations of determinism presuppose an "agreement"…
The idea of fully accepting statements when the evidence has rendered them probable enough faces a number of difficulties. We leave the interpretation of probability largely open, but attempt to suggest a contextual approach to full belief.…
Experiments in cognitive science and decision theory show that the ways in which people combine concepts and make decisions cannot be described by classical logic and probability theory. This has serious implications for applied disciplines…
When does society eventually learn the truth, or take the correct action, via observational learning? In a general model of sequential learning over social networks, we identify a simple condition for learning dubbed excludability.…
By nature, transmissible human knowledge is enumerable: every sentence, movie, audio record can be encoded in a sufficiently long string of 0's and 1's. The works of G\"odel, Turing and others showed that there are inherent limits and…
Unaided human decision making appears to systematically violate consistency constraints imposed by normative theories; these biases in turn appear to justify the application of formal decision-analytic models. It is argued that both claims…
Generalised Probabilistic Theories (GPTs) provide a unifying framework encompassing classical theories, quantum theories, as well as hypothetical alternatives. We investigate the problem of extending a system with a finite set of…
A typical kind of question in mathematical logic is that for the necessity of a certain axiom: Given a proof of some statement $\phi$ in some axiomatic system $T$, one looks for minimal subsystems of $T$ that allow deriving $\phi$. In…
In many situations humans have to reason with inconsistent knowledge. These inconsistencies may occur due to not fully reliable sources of information. In order to reason with inconsistent knowledge, it is not possible to view a set of…
The process of doing Science in condition of uncertainty is illustrated with a toy experiment in which the inferential and the forecasting aspects are both present. The fundamental aspects of probabilistic reasoning, also relevant in real…
Subjective expected utility theory assumes that decision-makers possess unlimited computational resources to reason about their choices; however, virtually all decisions in everyday life are made under resource constraints - i.e.…
Each cognitive science tries to understand a set of cognitive behaviors. The structuring of knowledge of this nature's aspect is far from what it can be expected about a science. Until now universal standard consistently describing the set…
Being mathematics a natural language to Mankind and to physics, it must be constantly adapted to our necessities and our natural perception. Then, mathematical concepts are not absolute to reality. Although mathematical theories are…