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Formalization of Natural Language

Theoretical discussions on overcoming LLM limitations by mapping natural language to formal logic or proof systems (like Lean). Skeptics argue human language is too "mushy" or context-dependent for this to be a silver bullet for AGI or perfect reasoning.

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Proponents suggest that pairing LLMs with formal proof-checkers could overcome current reasoning deficits, yet skeptics counter that natural language is far too "mushy" and context-dependent to be reliably reduced to rigid logic. This tension highlights a historical philosophical divide, where the precision of coding provides a successful but narrow model for AI, while the "lossy" and ambiguous nature of human speech resists the deterministic feedback loops found in compilers. Ultimately, the consensus suggests that the true bottleneck may not be the technology itself, but the "human factor"—the inherent difficulty people face in translating complex, vague intentions into the exact specifications required for formal verification.

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> the current algorithms are clearly a dead end for thinking machines. These discussions often get derailed into debates about what "thinking" means. If we define thinking as the capacity to produce and evaluate arguments, as the cognitive scientists Sperber and Mercier do, then we can see LLMs are certainly producing arguments, but they're weak at the evaluation. In some cases, arguments can be formalised, and then evaluating them is a solved problem, as in the examples of using the Lean proofchecker in combination with LLMs to write mathematical proofs. That suggests a way forward will come from formalising natural language arguments. So LLMs by themselves might be a dead end but in combination with formalisation they could be very powerful. That might not be "thinking" in the sense of the full suite of human abilities that we group with that word but it seems an important component of it.
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> suggests a way forward will come from formalising natural language arguments If by this you mean "reliably convert expressions made in human natural language to unambiguous, formally parseable expressions that a machine can evaluate the same way every time"... isn't that essentially an unreachable holy grail? I mean, everyone from Plato to Russell and Wittgenstein struggled with the meaning of human statements. And the best solution we have today is to ask the human to restrict the set of statement primitives and combinations that they can use to a small subset of words like "const", "let foo = bar", and so on.
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Whether the Holy Grail is unreachable or not is the question. Of course, the problem in full generality is hard, but that doesn't mean it can't be approached in various partial ways, either by restricting the inputs as you suggest or by coming up with some kind of evaluation procedures that are less strict than formal verifiability. I don't have any detailed proposals tbh
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> That suggests a way forward will come from formalising natural language arguments. Hot take (and continue with the derailment), but I'd argue that analytic philosophy from the last 100 years suggests this is a dead end. The idea that belief systems could be formalized was huge in the early 20th century (movements like Logical Positivism, or Russell's principia mathematica being good examples of this). Those approaches haven't really yielded many results, and by far the more fruitful form of analysis has been to conceptually "reframe" different problems (folks like Hillary Putnam, Wittgenstein, Quine being good examples). We've stacked up a lot of evidence that human language is much too loose and mushy to be formalised in a meaningful way.
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We've stacked up a lot of evidence that human language is much too loose and mushy to be formalized in a meaningful way. Lossy might also be a way of putting it, like a bad compression algorithm. Written language carries far less information than spoken and nonverbal cues.
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True, maybe full formalisation is too strict and the evaluation should be fuzzier
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Besides the ability to deal with text, I think there are several reasons why coding is an exceptionally good fit for LLMs. Once LLMs gained access to tools like compilers, they started being able to iterate on code based on fast, precise and repeatable feedback on what works and what doesn't, be it failed tests or compiler errors. Compare this with tasks like composing a powerpoint deck, where feedback to the LLM (when there is one) is slower and much less precise, and what's "good" is subjective at best. Another example is how LLMs got very adept at reading and explaining existing code. That is an impressive and very useful ability, but code is one of the most precise ways we, as humans, can express our intent in instructions that can be followed millions of times in a nearly deterministic way (bugs aside). Our code is written in thoroughly documented languages with a very small vocabulary and much easier grammar than human languages. Compare this to taking notes in a zoom call in German and trying to make sense of inside jokes, interruptions and missing context. But maybe most importantly, a developer must be the friendliest kind of human for an LLM. Breaking down tasks in smaller chunks, carefully managing and curating context to fit in "memory", orchestrating smaller agents with more specialized tasks, creating new protocols for them to talk to each others and to our tools.... if it sounds like programming, it's because it is.
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That's jump if you are a junior. It falls down hard for the seniors doing more complex stuff. I'm also reminding that we tried whole "make it look like human language" with COBOL and it turned out that language wasn't a bottleneck, the ability of people to specify exactly what they want was the bottleneck. Once you have exact spec, even writing code on your own isn't all that hard but extracting that from stakeolders have always been the harder part of the programming.
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Isn't that what polishing 'the prompt' does? Refine the communication like an editor does for a publication? Only in this case it's instructions for how to get a transformer to mine an existing set of code to produce some sort of vaguely useful output. The human factor adds knowledge of the why that refines the results. Not just any algorithm or a standard pattern that fits, but the correct solution for the correct question.