Related papers: The liar paradox is a real problem
This paper is concerned with the well known Jeffreys-Lindley paradox. In a Bayesian set up, the so-called paradox arises when a point null hypothesis is tested and an objective prior is sought for the alternative hypothesis. In particular,…
I outline a new theory of truth that resolves the classical and constructive versions of the liar paradox. The theory features a provably consistent axiomatization of a global self-applicative truth predicate. Truth is defined using…
Confirmation bias, the tendency to seek evidence that supports rather than challenges one's belief, hinders one's reasoning ability. We examine whether large language models (LLMs) exhibit confirmation bias by adapting the rule-discovery…
This study introduces a hypothesis-testing framework to assess whether large language models (LLMs) possess genuine reasoning abilities or primarily depend on token bias. We go beyond evaluating LLMs on accuracy; rather, we aim to…
Established frameworks to understand problems with reproducibility in science begin with the relationship between our understanding of the prior probability of a claim and the statistical certainty that should be demanded of it, and explore…
Fake news poses a significant threat to the integrity of information ecosystems and public trust. The advent of Large Language Models (LLMs) holds considerable promise for transforming the battle against fake news. Generally, LLMs represent…
People often ask questions with false assumptions, a type of question that does not have regular answers. Answering such questions requires first identifying the false assumptions. Large Language Models (LLMs) often generate misleading…
We consider the common-knowledge paradox raised by Halpern and Moses: common knowledge is necessary for agreement and coordination, but common knowledge is unattainable in the real world because of temporal imprecision. We discuss two…
The twin paradox, which evokes from the the idea that two twins may age differently because of their relative motion, has been studied and explained ever since it was first described in 1906, the year after special relativity was invented.…
The Stokes paradox is the statement that in a viscous two dimensional fluid, the "linear response" problem of fluid flow around an obstacle is ill-posed. We present a simple consequence of this paradox in the hydrodynamic regime of a Fermi…
The Sleeping Beauty problem is a probability riddle with no definite solution for more than two decades and its solution is of great interest in many fields of knowledge. There are two main competing solutions to the problem: the halfer…
The way a rational agent changes her belief in certain propositions/hypotheses in the light of new evidence lies at the heart of Bayesian inference. The basic natural assumption, as summarized in van Fraassen's Reflection Principle…
The opportunity to tell a white lie (i.e., a lie that benefits another person) generates a moral conflict between two opposite moral dictates, one pushing towards telling always the truth and the other pushing towards helping others. Here…
In this paper, we present a paradox arising from the acceptance of the Law of Excluded Middle (LEM) within classical mathematics. Specifically, we construct a nonzero analytic function on a connected open subset of the complex plane whose…
Social networks have many counter-intuitive properties, including the "friendship paradox" that states, on average, your friends have more friends than you do. Recently, a variety of other paradoxes were demonstrated in online social…
People are not very good at detecting lies, which may explain why they refrain from accusing others of lying, given the social costs attached to false accusations - both for the accuser and the accused. Here we consider how this social…
A key assumption fuelling optimism about the progress of large language models (LLMs) in accurately and comprehensively modelling the world is that the truth is systematic: true statements about the world form a whole that is not just…
Activation-based probes have emerged as a promising approach for detecting deceptively aligned AI systems by identifying internal conflict between true and stated goals. We identify a fundamental blind spot: probes fail on coherent…
It is often argued that superluminal velocities and nontrivial spacetime topologies, allowed by the theory of relativity, may lead to causal paradoxes. By emphasizing that the notion of causality assumes the existence of a time arrow (TA)…
Reading and evaluating product reviews is central to how most people decide what to buy and consume online. However, the recent emergence of Large Language Models and Generative Artificial Intelligence now means writing fraudulent or fake…