Naur's "Programming as Theory Building" and LLMs replacing human programmers

Firstly:

> LLMs are capable of appearing to have a theory about a program ... but it’s, charitably, illusion.

To make this point stick, you would also have to show why it's not an illusion when humans "appear" to have a theory.

Secondly:

> Theories are developed by doing the work and LLMs do not do the work

Isn't this a little... anthropocentric? That's the way humans develop theories. In principle, could a theory not be developed by transmitting information into someone's brain patterns as if they had done the work?

This idea has already been explored by thought experiments such as John Searle's so-called "Chinese room" [0]; an LLM cannot have a theory about a program, any more than the computer in Searle's "Chinese room" understands "Chinese" by using lookup tables to generate canned responses to an input prompt.

One says the computer lacks "intentionality" regarding the topics that the LLM ostensibly appears to be discussing. Their words aren't "about" anything, they don't represent concepts or ideas or physical phenomena the same way the words and thoughts of a human do. The computer doesn't actually "understand Chinese" the way a human can.

[0] https://en.wikipedia.org/wiki/Chinese_room

The computer understands Chinese better than Searle (or anyone else) understood the nature and functionality of language.

Wow.

How do you know you're not arguing with an LLM at the moment? You don't... any more than I do.

I wish I was right now. It would probably provide at least the semblance of greater insight into these topics.

> the Chinese Room was a weak test the day it was proposed

Why?

Simple arithmetic ("What is 2+2") is obviously going to be well-represented in the training data, so the model will simply regurgitate "4."'

For more advanced questions like "What are the roots of 14.338x^5 + 4.005x^4 + 3.332x^3 - 99.7x^2 + 120x = 0?", the model will either yield random nonsense as GPT-4o did, or write a Python script and execute it to return the correct answer(s) as o4-mini-high did: https://chatgpt.com/share/680fb812-76b8-800b-a19e-7469cbcc43...

Now, give the model an intermediate arithmetic problem, one that isn't especially hard but also isn't going to be in-distribution ("If a is 3 and b is 11.4, what is the fourth root of a*b?").

How would YOU expect the operator of a Chinese Room to respond to that?

Here's how GPT-4o responded: https://chatgpt.com/share/680fb616-45e0-800b-b592-789f3f8c58...

Now, that's not a great answer, it's clearly an imprecise estimate. But it's more or less right, and the fact that it isn't a perfect answer suggests that the model didn't cheat somehow. A similar but easier problem would almost certainly have been answered correctly. Where did that answer come from, if the model doesn't "understand" the math to a nontrivial extent?

If it can "understand" basic high-school math, what else can it "understand?" What exactly are the limits of what a transformer can "understand" without resorting to web search or tool use?

An adherent of Searle's argument is going to have a terrible time explaining phenomena like this... and it's only going to get worse for them over time.