Based on a potential misreading of this post, I added the following caveat today:
Important Caveat: Arguments in natural language are basically never “theorems”. The main reason is that human thinking isn’t perfectly rational in virtually any precisely defined sense, so sometimes the hypotheses of an argument can hold while its conclusion remains unconvincing. Thus, the Löbian argument pattern of this post does not constitute a “theorem” about real-world humans: even when the hypotheses of the argument hold, the argument will not always play out like clockwork in the minds of real people. Nonetheless, Löb’s-Theorem-like arguments can play out relatively simply in the English language, and this post shows what would look like.
Based on a potential misreading of this post, I added the following caveat today:
Important Caveat: Arguments in natural language are basically never “theorems”. The main reason is that human thinking isn’t perfectly rational in virtually any precisely defined sense, so sometimes the hypotheses of an argument can hold while its conclusion remains unconvincing. Thus, the Löbian argument pattern of this post does not constitute a “theorem” about real-world humans: even when the hypotheses of the argument hold, the argument will not always play out like clockwork in the minds of real people. Nonetheless, Löb’s-Theorem-like arguments can play out relatively simply in the English language, and this post shows what would look like.