godelski • yesterday at 9:40 PM

  > he seems to completely equate ease of language with ability to do undetectable mistakes.

I do not believe this is his argument. He was making the point that there is a balance. You need to consider the context of the times, and remember that in this context a language like C is considered "high-level", not a language like Python. He later moves on to discuss formalism through mathematics (referencing Vieta, Descartes, Leibniz, and Boole), in how this symbolism is difficult to perform and many are adverse to it, but that through its birth we've been able to reap a lot of rewards. He precisely makes the claim that were we not to move to formal methods and instead maintain everyday language, we would still be stuck at the level of the Greeks.

Actually in one season of An Opinionated History of Mathematics, the host (a mathematician) specifically discusses the transition in the Greeks and highlights how many flaws there were in this system. How the slow move to mathematical formalism actually enabled correctness.

The point is that human language is much more vague. It has to be this way. But the formalism in symbolics (i.e. math) would similarly make a terrible language for computing. The benefit of the symbolic approach is the extreme precision, but it also means the language is extremely verbose. While in human languages we trade precision for speed and flexibility. To communicate what I have with a mathematical language would require several pages of text. Like he says, by approaching human language this shifts more responsibility to the machine.