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Comment by gibsonf1 | Hacker News Reader

The error with that is that human reasoning is not mathematical. Math is just one of the many tools of reason.

Intransitive preferences is well known to experimental economists, but a hard pill to swallow for many, as it destroys a lot of algorithms (which depends on that) and require more robust tools like https://en.wikipedia.org/wiki/Paraconsistent_logic

> just one of the many tools of reason.

Read https://en.wikipedia.org/wiki/Preference_(economics)#Transit... then read https://pmc.ncbi.nlm.nih.gov/articles/PMC7058914/ and you will see there's a lot of data suggesting that indeed, it's just one of the many tools!

I think it's similar to how many dislike the non-deterministic output of LLM: when you use statistical tools, a non-deterministic output is a VERY nice feature to explore conceptual spaces with abductive reasoning: https://en.wikipedia.org/wiki/Abductive_reasoning

It's a tool I was using at a previous company, mixing LLMs, statistics and formal tools. I'm surprised there aren't more startups mixing LLM with z3 or even just prolog.

Thanks for the links, the "tradeoff" aspect of paraconsistent logic is interesting. I think one way to achieve consensus with your debate partner might be to consider that the language rep is "just" a nondeterministic decompression of "the facts". I'm primed to agree with you but

https://news.ycombinator.com/item?id=41892090

(It's very common, esp. with educationally traumatized Americans, e.g., to identify Math with "calculation"/"approved tools" and not "the concepts")

"No amount of calculation will model conceptual thinking" <- sounds more reasonable?? (You said you were ok with nondeterministic outputs? :)

Sorry to come across as patronizing

if conceptual thinking is manipulating abstract concepts after having been given concrete particulars, I'd say it relies heavily upon projection, which, as generalised "K" (from SKI), sounds awfully like calculation.

And this is why I think gibson1 is wrong: we can argue about which projections or systems of logic should be used, concepts are still "calculations".

Here is why I think Gibson could in principle still be right (without necessarily summoning religious feelings)

[if we disregard that he said "concepts are key" -- though we can be yet more charitable and assume that he doesn't accept (median) human-level intelligence as the final boss]

  Para-doxxing ">" Under-standing

(I haven't thought this through, just vibe-calculating, as it were, having pondered the necessity of concrete particulars for a split-second)

(More on that "sophistiKated" aspect of "projeKtion": turns out not to be as idiosynKratic as I'd presumed, but I traded bandwidth for immediacy here, so I'll let GP explain why that's interesting, if he indeed finds it is :)

Wolfram (selfstyled heir to Leibniz/Galois) seems to be serving himself a fronthanded compliment:

https://writings.stephenwolfram.com/2020/12/combinators-a-ce...

>What I called a “projection” then is what we’d call a function now; a “filter” is what we’d now call an argument )

Did you read the slide? It doesn't make the argument you are responding to, you just seem to have been prompted by "Math".

A more generous take on the previous post is that the dominant paradigm of Math (consistent logic, which depends on many things like transitive preference) is wrong, and that another type of Math could work.

If you look at the slide, the subtree of correct answers exists, what's missing is just a way to make them more prevalent instead of less.

Personally, I think LeCun is just leaping to the wrong conclusion because he's sticking to the wrong tools for the job.

My point is no type of math will work to model reason. Math is one of the many tools of reason, it is not the basis for reason. This is a very common error.

> My point is no type of math will work to model reason

Then I disagree with you.

Exactly, we disagree and you are not alone in thinking this. You can use reason to do math, but your can't model reason with math.

I'm ignorantly curious of what type of math will work in your view. Genuine question, I just want to be educated.

There is no type of math that can model conceptual reasoning. You can use conceptual reasoning, however, to do math.

I think I know what math is, though I'm not sure. Logical systems of axioms and inference rules?

But I'm even less sure what conceptual reasoning is.

A less generous take would be that humans are also stoichastic parrots that can't help themselves but say something when they see a trigger word like math, Trump, transgender, or abortion.

Reply on news.ycombinator.com