Related papers: The liar paradox is a real problem
Formal logic enables computers to reason in natural language by representing sentences in symbolic forms and applying rules to derive conclusions. However, in what our study characterizes as "rulebreaker" scenarios, this method can lead to…
It is shown that the ``retrodiction paradox'' recently introduced by Peres arises not because of the fallacy of the time-symmetric approach as he claimed, but due to an inappropriate usage of retrodiction.
This paper studies lying in a novel context. Previous work has focused on situations in which people are either fully aware of the economic consequences of all available actions (e.g., die-under-cup paradigm), or they are uncertain, but…
Hallucination is a persistent challenge in large language models (LLMs), where even with rigorous quality control, models often generate distorted facts. This paradox, in which error generation continues despite high-quality training data,…
The supposed information paradox for black holes is based on the fundamental misunderstanding that black holes are usefully defined by event horizons. Understood in terms of locally defined trapping horizons, the paradox disappears:…
A knowledge system S describing a part of real world does in general not contain complete information. Reasoning with incomplete information is prone to errors since any belief derived from S may be false in the present state of the world.…
Like students facing hard exam questions, large language models sometimes guess when uncertain, producing plausible yet incorrect statements instead of admitting uncertainty. Such "hallucinations" persist even in state-of-the-art systems…
Large Language Models (LLMs) can generate content that is as persuasive as human-written text and appear capable of selectively producing deceptive outputs. These capabilities raise concerns about potential misuse and unintended…
Some known relativistic paradoxes are reconsidered for closed spaces, using a simple geometric model. For two twins in a closed space, a real paradox seems to emerge when the traveling twin is moving uniformly along a geodesic and returns…
The rise of misinformation underscores the need for scalable and reliable fact-checking solutions. Large language models (LLMs) hold promise in automating fact verification, yet their effectiveness across global contexts remains uncertain.…
Attempts to quantize general relativity encounter an odd problem. The Hamiltonian that normally generates time evolution vanishes in the case of general relativity as a result of diffeomorphism invariance. The theory seems to be saying that…
The apparently trifling unexpected hanging paradox has generated an enormous philosophical literature. We introduce the mathematician to this literature, paying special attention to aspects that involve nontrivial mathematics. This xxx…
We argue that whether the universe is infinite or finite is less crucial than usually supposed. Paradoxes of repeating behaviour in the infinite, or eternal inflationary, universe can be alleviated by a realistic definition of differing…
In this paper, we will present an algorithm to resolve the counterfeit coins problem in the case that the number of false coins is unknown in advance.
The preeminent view that evaporating black holes should simply be smaller black holes has been challenged by the firewall paradox. In particular, this paradox suggests that something different occurs once a black hole has evaporated to…
We discuss the linearization of a non-autonomous nonlinear partial difference equation belonging to the Boll classification of quad-graph equations consistent around the cube. We show that its Lax pair is fake. We present its generalized…
Explainable artificial intelligence techniques are developed at breakneck speed, but suitable evaluation approaches lag behind. With explainers becoming increasingly complex and a lack of consensus on how to assess their utility, it is…
The paradoxes of thermodynamics and statistical physics are unavoidable in the study of physical paradoxes because of their importance at the time they came to be as well as the frequency of their appearance in historical studies of…
What if the paradoxical nature of quantum theory could find its source in some undecidability analog to that of G\"odel's incompleteness theorem ? This essay aims at arguing for such G\"odelian hunch via two case studies. Firstly, using a…
Large language model (LLM) leaderboards rank AI models using standardized benchmarks and have become highly visible across computer science, despite known limitations in their reliability and robustness. Yet how they shape researchers'…