Related papers: Inconsistency of Measure-Theoretic Probability
The fundamental proposal in this article is that logical formulas of the form (f <-> ~f) are not contradictions, and that formulas of the form (t <-> t) are not tautologies. Such formulas, wherever they appear in mathematics, are instead…
I argue that the Oxford school Everett interpretation is internally incoherent, because we cannot claim that in an Everettian universe the kinds of reasoning we have used to arrive at our beliefs about quantum mechanics would lead us to…
The conventional postulate for the probabilistic interpretation of quantum mechanics is asymmetric in preparation and measurement, making retrodiction reliant on inference by use of Bayes' theorem. Here, a more fundamental symmetric…
We elicit incomplete preferences over monetary gambles with subjective uncertainty. Subjects rank gambles, and these rankings are used to estimate preferences; payments are based on estimated preferences. About 40\% of subjects express…
From mostly a measure-theoretic consideration, we show that for every nonnegative, finite, and $L^{1}$ function on a given finite measure space there is some nontrivial sequence of real numbers such that the series, obtained from summing…
We consider a finite-dimensional quantum system, making a transition between known initial and final states. The outcomes of several accurate measurements, which {\it could be} made in the interim, define virtual paths, each endowed with a…
Quantum mechanics predicts that measurements of incompatible observables carry a minimum uncertainty which is independent of technical deficiencies of the measurement apparatus or incomplete knowledge of the state of the system. Nothing yet…
Uncertainty relations express limits on the extent to which the outcomes of distinct measurements on a single state can be made jointly predictable. The existence of nontrivial uncertainty relations in quantum theory is generally considered…
This paper introduces a qualitative measure of ambiguity and analyses its relationship with other measures of uncertainty. Probability measures relative likelihoods, while ambiguity measures vagueness surrounding those judgments. Ambiguity…
In a prediction tournament, contestants "forecast" by asserting a numerical probability for each of (say) 100 future real-world events. The scoring system is designed so that (regardless of the unknown true probabilities) more accurate…
One of the most discussed peculiarities of Einstein's theory of relativity is the twin paradox, the fact that the time between two events in space-time appears to depend on the path between these events. We show that this time discrepancy…
The systematic biases seen in people's probability judgments are typically taken as evidence that people do not reason about probability using the rules of probability theory, but instead use heuristics which sometimes yield reasonable…
We propose partial measurements as a conceptual tool to understand how to operate with counterfactual claims in quantum physics. Indeed, unlike standard von Neumann measurements, partial measurements can be reversed probabilistically. We…
We demonstrate that the forecasting combination puzzle is a consequence of the methodology commonly used to produce forecast combinations. By the combination puzzle, we refer to the empirical finding that predictions formed by combining…
I defend an analog of probabilism that characterizes rationally coherent estimates for chances. Specifically, I demonstrate the following accuracy-dominance result for stochastic theories in the C*-algebraic framework: supposing an…
Education in statistics, the application of statistics in scientific research, and statistics itself as a scientific discipline are in crisis. Within science, the main cause of the crisis is the insufficiently clarified concept of…
Null Hypothesis Statistical Testing is a dominant framework for conducting statistical analysis across the sciences. There remains considerable debate as to whether, and under what circumstances, evidence can be said to be confirmatory of a…
Recent work by Faizal et al. (2025) claims that G\"odelian undecidability of non-algorithmic truths in our universe imply the impossibility of a formal, algorithmic simulation of the universe. This paper clarifies the distinction between…
Curiously overlooked in physics is its dependence on the transmission of numbers. For example the transmission of numerical clock readings is implicit in the concept of a coordinate system. The transmission of numbers and other logical…
The world appears to be well described by gauge theories; why? I suggest that gauge is more than mathematical redundancy. Gauge-dependent quantities can not be predicted, but there is a sense in which they can be measured. They describe…