In this blog series, I will try to explore topics in the foundations of AI by discussing them with state-of-the-art LLMs such as OpenAI’s ChatGPT and Anthropic’s Claude. My goal is to examine foundational issues in AI from the perspective of mathematics and the natural sciences.

Before getting started, it may be helpful for me to disclose my standpoint on AI. For this, I will take the following paragraph from Turing’s seminal paper “Computing Machinery and Intelligence” as a starting point:

“The original question, ‘Can machines think?’ I believe to be too meaningless to deserve discussion. Nevertheless, I believe that at the end of the century the use of words and general educated opinion will have altered so much that one will be able to speak of machines thinking without expecting to be contradicted. I believe further that no useful purpose is served by concealing these beliefs. The popular view that scientists proceed inexorably from well-established fact to well-established fact, never being influenced by any unproved conjecture, is quite mistaken. Provided it is made clear which are proved facts and which are conjectures, no harm can result. Conjectures are of great importance since they suggest useful lines of research.”

My position on AI is well summarized by Turing’s assertion that the question, ‘Can machines think?’ is meaningless. One might wonder, then, why a discussion of the topic is meaningful or necessary to begin with. This has to do with what I see as the unfortunate realization of Turing’s first prediction: the fact that, today, the possibility of machines or algorithms matching—or even surpassing—human cognitive and mental capacities has become widely accepted in academia, industry, and politics.

Although I share Turing’s view, which distances itself from the idealized notion that science proceeds neatly from one well-established fact to another, I believe the distinction between proven facts and conjectures—stressed by Turing—has been almost entirely abandoned in current discussions on AI, including academic research, with many harmful consequences. And if we are to believe AI proponents, we are just getting started!

Here, I must emphasize that I am not referring to the current or future harms caused by algorithms or technologies marketed as AI, but rather to the harms caused by misguided optimism and deliberately misleading claims about the feasibility—or even imminence—of intelligent machines. These include the misallocation of resources, including human talent and attention, and the economic and financial risks such as those posed by inflated stock prices of AI-related companies.

It is hard to deny that Turing’s ideas, put forward 75 years ago, have been incredibly useful—particularly in inspiring subsequent generations of scientist and engineers to pursue ever more ambitious goals. However, history shows many examples where useful conjectures have been proven wrong. Once disproven, by definition, they cease to be conjectures—a point with which, as a great mathematician, Turing would undoubtedly have agreed.

Nowadays, Turing’s thought experiment—where a machine passes for a human in a short, everyday conversation—is often discussed in a maximalist context. Machines are imagined to match humans in all cognitive and mental aspects, with some even advocating that machines will soon surpass human intelligence and render all human intellectual activity obsolete.

Despite the temptation to ridicule the prevalent irrationality in the field, I will do my best to keep the discussion within the bounds of rational argument whenever possible. Here, I should also stress that I make a clear distinction between research aimed at developing computational methods for well-defined scientific or engineering problems—such as protein folding or voice recognition, which are also frequently referred to as AI—and research claiming to develop algorithms with human-like intelligence. The former, in my opinion, constitutes perfectly respectable and highly useful scientific work, while its association with the latter has, if anything, a discrediting effect.

Finally, the irony of using LLMs in such a discussion is not lost on me. However, I believe it adds an interesting twist and helps keep the discussion rational and civil. Of course, the fact that part of the discussion is generated by an algorithm should not be seen as providing additional credibility or objectivity. This is especially true given that, in practice, LLMs can easily be manipulated to produce diverging or even contradictory outputs. Needless to say, I do not always agree with the outputs of LLMs, but correcting every inaccuracy would make this exercise impractical. Therefore, I will not address inaccuracies unless they directly affect the main arguments being discussed.

In general, I find that current LLMs do a respectable job of summarizing known arguments and counterarguments. However, their outputs can sometimes be overly exhaustive and verbose, and in such cases, I try to guide the discussion so that it stays on topic.