Talk:Gödel's incompleteness theorems
"Appeals to the incompleteness theorems in other fields" section is nearly content-free
The section "Appeals to the incompleteness theorems in other fields" currently contains almost nothing substantive. It mentions that various authors have criticised such appeals, names a few (Franzén, Raatikainen, Sokal & Bricmont), and gives a single example (Régis Debray invoking the theorem in sociology). That is the entirety of the section.
A reader who arrives here wanting to understand what these misapplications actually look like, and why they fail, gets almost nothing useful. Knowing that Sokal and Bricmont criticise something tells you very little if you don't know what the thing being criticised is.
The main categories of misapplication are worth at least briefly describing:
- Anti-mechanist arguments (Lucas, Penrose): the claim that Gödel's theorems show human minds transcend formal systems. These are substantial enough to merit their own subsection, which the article already has ("Minds and machines").
- Theological appeals: arguments that the theorems demonstrate an inherent limit on human reason, taken as evidence for the existence or necessity of something beyond human cognition (God, revelation, etc.).
- Postmodernist and social-science invocations: claims that science itself is "provably" incomplete or that the theorems undermine the foundations of rationalism — Debray being one example, but a well-known pattern more broadly.
- Loose metaphorical use: invoking "incompleteness" as a vague analogy in fields like economics, literary theory, or politics, without any meaningful connection to the formal theorems.
Franzén (2005), one of the sources already cited, wrote an entire book cataloguing and explaining these. The section could at minimum summarise the main patterns and explain briefly why each fails to transfer (usually: the theorems apply specifically to formal systems strong enough to express arithmetic, with no clear analogue in the domain being discussed). Right now the section exists in name only.