Related papers: Viewing Simpson's Paradox
When aggregating logically interconnected judgments from $n$ agents, the result might be inconsistent with the logical connection. This inconsistency is known as the doctrinal paradox, which plays a central role in the field of judgment…
Lord's Paradox occurs when a continuous covariate is statistically controlled for and the relationship between a continuous outcome and group status indicator changes in both magnitude and direction. This phenomenon poses a challenge to the…
Reasoning about unpredicted change consists in explaining observations by events; we propose here an approach for explaining time-stamped observations by surprises, which are simple events consisting in the change of the truth value of a…
The quantum three-box paradox considers a ball prepared in a superposition of being in one of three Boxes. Bob makes measurements by opening either Box 1 or Box 2. After performing some unitary operations (shuffling), Alice can infer with…
Classes of linguistic paradoxes and linguistic tautologies are introduced with examples and explanations. They are part of the author's work on the Paradoxist Philosophy based on mathematical logic. The general cases exposed below are…
Paradoxes are interesting puzzles in philosophy and mathematics, and they could be even more fascinating, when turned into proofs and theorems. For example, Liar's paradox can be translated into a propositional tautology, and Barber's…
A new apparent relativistic paradox is presented involving only one space-time event. This is different from earlier relativistic paradoxes involving extended bodies or events at different positions. A collision between a rod and a ring…
Natural philosophy integrates scientific observation with abstract frameworks, often using a mathematical Ansatz to hypothesise about physical phenomena. Exploring the possibility of other universes, however, challenges assumptions that…
The suggestion that particles of the same kind may be indistinguishable in a fundamental sense, even so that challenges to traditional notions of individuality and identity may arise, has first come up in the context of classical…
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…
The study of associations and their causal explanations is a central research activity whose methodology varies tremendously across fields. Even within specialized subfields, comparisons across textbooks and journals reveals that the basics…
To counter a general belief that all the paradoxes stem from a kind of circularity (or involve some self--reference, or use a diagonal argument) Stephen Yablo designed a paradox in 1993 that seemingly avoided self--reference. We turn…
Suppose one desires to randomly sample a pair of objects such as socks, hoping to get a matching pair. Even in the simplest situation for sampling, which is sampling with replacement, the innocent phrase "the distribution of the color of a…
The concept of quantum superposition is reconsidered and discussed from the viewpoint of Bohmian mechanics, the hydrodynamic formulation of quantum mechanics, in order to elucidate some physical consequences that go beyond the simple…
Probabilistic argumentation allows reasoning about argumentation problems in a way that is well-founded by probability theory. However, in practice, this approach can be severely limited by the fact that probabilities are defined by adding…
A logic is defined that allows to express information about statistical probabilities and about degrees of belief in specific propositions. By interpreting the two types of probabilities in one common probability space, the semantics given…
In 1989 Supplee described an apparent relativistic paradox on which a submarine seems to sink to observers at rest within the ocean, but it rather seems to float in the submarine proper frame. In this letter, we show that the paradox arises…
Minimizing divergence measures under a constraint is an important problem. We derive a sufficient condition that binary divergence measures provide lower bounds for symmetric divergence measures under a given triangular discrimination or…
Moores Paradox is a test case for any formal theory of belief. In Knowledge and Belief, Hintikka developed a multimodal logic for statements that express sentences containing the epistemic notions of knowledge and belief. His account…
We revisit the flatland paradox proposed by \cite{ston1976} which is an example of non-conglomerability. The aim of the paper is to show that the improperness of the prior is not directly involved in the inconsistency. First, we show that…