The blog post explores the limitations of formal systems, particularly in discerning truth. It uses the analogy of two goblins, one always truthful and one always lying, to demonstrate how relying solely on a system's rules, without external context or verification, can lead to accepting falsehoods as truths. Even with additional rules added to account for the goblins' lying, clever manipulation can still exploit the system. The post concludes that formal systems, while valuable for structuring thought, are ultimately insufficient for determining truth without external validation or a connection to reality. This highlights the need for critical thinking and skepticism even when dealing with seemingly rigorous systems.
This blog post, titled "A Brief Meditation on Formal Systems and Lying Goblins," delves into the fascinating intersection of formal systems, logic, and the challenges of extracting truthful information from unreliable sources. The author constructs a thought experiment involving a population of goblins, some of whom invariably speak the truth, and others who consistently lie. The central problem revolves around devising a strategy to reliably determine the veracity of statements made by these goblins, given that one cannot ascertain a priori which type of goblin one is interacting with.
The author meticulously lays out the formal framework for this puzzle. They introduce the concept of truth-telling goblins, represented symbolically, and lying goblins, similarly represented. This symbolic representation allows for the manipulation of statements and the exploration of logical consequences within a clearly defined system. The post then proceeds to examine the complexities introduced by the goblins' deceptive nature. A simple question, such as inquiring about the nature of the goblin itself (truth-teller or liar), proves insufficient, as both types would provide the same answer if attempting to deceive.
The core of the post focuses on the development of a questioning strategy that can circumvent the goblins' inherent deceptiveness. The author explores the idea of nested questions, effectively asking a goblin about what another goblin would say. This indirect approach leverages the predictable nature of the goblins' lies: a liar will always lie about what a truth-teller would say, and vice-versa. By carefully constructing these nested inquiries, one can effectively force the goblins to reveal the truth, irrespective of their individual predilection for truth or falsehood.
The author further elaborates on the underlying principles at play, highlighting the power of formal systems in dissecting and solving such puzzles. By representing the problem within a formal framework, one can systematically explore potential solutions and rigorously test their validity. The post concludes by emphasizing the broader implications of this thought experiment. It serves as a microcosm of the challenges we face in the real world when dealing with information from potentially unreliable sources. The ability to construct robust questioning strategies, analogous to the nested inquiries used with the goblins, becomes crucial for navigating a world awash in misinformation and discerning truth from falsehood. The seemingly simple puzzle of the lying goblins thus provides a valuable lesson in the application of formal systems to complex problems of knowledge and belief.
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https://news.ycombinator.com/item?id=43285485
The Hacker News comments generally praise the clarity and engaging presentation of the article's topic (formal systems and the halting problem, illustrated by a lying goblin puzzle). Several commenters discuss the philosophical implications of the piece, particularly regarding the nature of truth and provability within defined systems. Some draw parallels to Gödel's incompleteness theorems, while others offer alternate goblin scenarios or slight modifications to the puzzle's rules. A few commenters suggest related resources, such as Raymond Smullyan's work, which explores similar logical puzzles. There's also a short thread discussing the potential applicability of these concepts to legal systems and contract interpretation.
The Hacker News post "A brief meditation on formal systems and lying goblins" has generated several comments discussing the article's premise and exploring related concepts.
Several commenters engage with the core idea of the article, which uses the analogy of lying goblins to illustrate how seemingly sound logical systems can lead to incorrect conclusions if based on false premises. One commenter points out the parallel to real-world scenarios where misinformation or flawed assumptions can corrupt a system, regardless of its internal consistency. They mention how this applies to areas like political discourse and conspiracy theories.
Another commenter delves deeper into the concept of formal systems, emphasizing the distinction between validity and soundness. They clarify that a valid argument can still be untrue if its premises are false, echoing the goblin analogy. They also introduce the idea of Gödel's incompleteness theorems, suggesting that even consistent formal systems can contain unprovable truths.
The discussion extends to the practical implications of these ideas. One commenter reflects on the challenge of identifying false premises in real-world situations, highlighting the importance of critical thinking and questioning assumptions. Another commenter draws a connection to Bayesian reasoning, suggesting that incorporating prior probabilities can help mitigate the risk of being misled by false information.
Further comments explore related philosophical themes, touching on the nature of truth and the limits of knowledge. One commenter mentions the concept of "unknown unknowns," emphasizing the difficulty of accounting for information that we are not even aware of.
Some commenters also offer alternative analogies to illustrate the same principles. One suggests the image of a perfectly functioning calculator that produces incorrect results due to a user inputting the wrong numbers.
Overall, the comments on the Hacker News post provide a thoughtful and engaging discussion of the article's core ideas, exploring their implications in various contexts and connecting them to broader philosophical and mathematical concepts. They highlight the importance of critical thinking, the limitations of formal systems, and the challenges of navigating a world filled with potentially misleading information.