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cognition

AI Hallucination is Inevitable

In a published article, “Hallucination is Inevitable: An Innate Limitation of Large Language Models“, authors Ziwei Xu et al. recognize the following: “[It is] impossible to eliminate hallucination in LLM.” “Hallucination has been widely recognized to be a significant drawback for large language models (LLMs). There have been many works that attempt to reduce the extent of hallucination. These efforts have mostly been empirical so far, which cannot answer the fundamental question whether it can… Read More »AI Hallucination is Inevitable

Man and machine, intuitive logic and arithmetic logic

The barber paradox If the barber shaves everyone who does not shave himself, who shaves the barber? The question is the so-called Barber paradox. It is paradoxical because it always leads to a self-contradictory answer. The barber paradox may strike as a trivial witty remark to many, but it is related to something far more serious. It is an example of Gödel’s incompleteness theorem, which says that formal logic (arithmetically expressible logic) cannot be both… Read More »Man and machine, intuitive logic and arithmetic logic

Barber paradox and existence of truth

The barber paradox: If the barber shaves everyone who does not shave himself, who shaves the barber? The barber paradox may strike as a trivial witty remark to many, but it is related to something far more serious. It is an example of Gödel’s incompleteness theorem, which says that formal logic (arithmetically expressible logic) cannot be both self-consistent and self-provable. In other words, the consistency of formal logic cannot be proved in the formal logic… Read More »Barber paradox and existence of truth

The sleeping beauty paradox is a fallacy

The sleeping beauty paradox is a problem that has puzzled mathematicians and many other scholars for decades. Here is a description of the problem: Participants volunteer to undergo the following experiment and are told all of the following details: On Sunday she will be put to sleep. Depending on a coin toss (see below) during the experiment, she will be either awakened, interviewed just once, or after the first interview put back to sleep with… Read More »The sleeping beauty paradox is a fallacy