Related papers: The liar paradox is a real problem
The prevalence of unwarranted beliefs, spanning pseudoscience, logical fallacies, and conspiracy theories, presents substantial societal hurdles and the risk of disseminating misinformation. Utilizing established psychometric assessments,…
An apparent paradox proposed by Aharonov and Vaidman in which a single particle can be found with certainty in two (or more) boxes is analyzed by way of a simple thought experiment. It is found that the apparent paradox arises from an…
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…
Many writers have observed that default logics appear to contain the "lottery paradox" of probability theory. This arises when a default "proof by contradiction" lets us conclude that a typical X is not a Y where Y is an unusual subclass of…
In this paper, we identify a new category of bias that induces input-conflicting hallucinations, where large language models (LLMs) generate responses inconsistent with the content of the input context. This issue we have termed the false…
The spread of fake news remains a serious global issue; understanding and curtailing it is paramount. One way of differentiating between deceptive and truthful stories is by analyzing their coherence. This study explores the use of topic…
In this paper we analyse some of the classical paradoxes in Social Choice Theory (namely, the Condorcet paradox, the discursive dilemma, the Ostrogorski paradox and the multiple election paradox) using a general framework for the study of…
We present a resolution of the celebrated "Surprise Exam Paradox". We argue that if the surprise exam story is analyzed using the exact same meaning of the notion of "surprise" as is dictated by the story itself, then no paradox arises.
Large Language Models (LLMs) have revolutionised natural language processing, exhibiting impressive human-like capabilities. In particular, LLMs are capable of "lying", knowingly outputting false statements. Hence, it is of interest and…
We introduce two paradoxes concerning jailbreak of foundation models: First, it is impossible to construct a perfect jailbreak classifier, and second, a weaker model cannot consistently detect whether a stronger (in a pareto-dominant sense)…
The special theory of relativity is the foundation of modern physics, but its unusual postulate of invariant vacuum speed of light results in a number of plausible paradoxes. This situation leads to radical criticisms and suspicions against…
In 1957, Lindley published "A statistical paradox" in Biometrika, revealing a fundamental conflict between frequentist and Bayesian inference as sample size approaches infinity. We present a new paradox of a different kind: a conflict…
"Encoded in the large, highly evolved sensory and motor portions of the human brain is a billion years of experience about the nature of the world and how to survive in it. The deliberate process we call reasoning is, I believe, the…
Knights and knaves problems represent a classic genre of logical puzzles where characters either tell the truth or lie. The objective is to logically deduce each character's identity based on their statements. The challenge arises from the…
This paper describes Simpson's paradox, and explains its serious implications for randomised control trials. In particular, we show that for any number of variables we can simulate the result of a controlled trial which uniformly points to…
The persisting gap between the formal and the informal mathematics is due to an inadequate notion of mathematical theory behind the current formalization techniques. I mean the (informal) notion of axiomatic theory according to which a…
While natural-language explanations from large language models (LLMs) are widely adopted to improve transparency and trust, their impact on objective human-AI team performance remains poorly understood. We identify a Persuasion Paradox:…
The standard iterated prisoner's dilemma is an unrealistic model of social behaviour because it forces individuals to participate in the interaction. We analyse a model in which players have the option of ending their association. If the…
The most important problems for society are describable only in vague terms, dependent on subjective positions, and missing highly relevant data. This thesis is intended to revive and further develop the view that giving non-trivial,…
According to Chaitin, G\"odel once told him "it doesn't matter which paradox you use [to prove the First Incompleteness Theorem]". In this paper I will present a few infinitary paradoxes and show how to "translate" them to some undecidable…