Comment by delusional
8 days ago
I don't think youre fully comprehending Dijkstra's argument. He's not saying to not use tool to help with translation, he is saying that not thinking in terms of formal symbols HURTS THINKING. Your ideas are worse if you don't think in formal systems. If you don't treat your thoughts as formal things.
In your example, he has no opinion on how to translate the idea of a "business person" because in his view the ideas of the "business person" are already shallow and bad because they don't follow a formalism. They are not worth translating.
If that's correct, then it's very falsifiable. If a businessperson says "there's a gap in the market - let's build X" they will be following a formalism at their level of detail. They see the market, the interactions between existing products and customers, and where things might be going.
Just because they can't spell it out to the nth degree doesn't matter. Their formalism is "this is what the market would like".
Having an LLM then tease out details - "what should happen in this case" would actually be pretty useful.
You're either not really thinking through what you're saying, or you're being disingenuous because you want to promote AI.
A formalism isn't "person says Y". It's about adhering to a structure, to a form of reasoning. Mathematical formalism is about adhering to the structure of mathematics, and making whatever argument you desire to make in the formal structure of formulas and equations.
Saying "A palindrome is a word that reads the same backwards as it does forwards" is not a formal definition. Saying "Let r(x) be the function that when given a string x returns the reversed string, x is then a palindrome iff x = r(x)" (sans the formal definitions of the function r).
Formalism is about reducing the set of axioms (the base assumptions of your formal system) to the minimal set that is required to build all other (provable) arguments. It's not vague hand waving about what some market wants, it's naturally extrapolating from a small set of axioms, and being rigorous if ever to add new ones.
If your hypothetical "business person" every says "it was decided" then they are not speaking a formal language, because formalism does not have deciders.