Prooftexting
Here's a pretty old post from the blog archives of Geekery Today; it was written about 11 years ago, in 2013, on the World Wide Web.
Show me an axiomatic approach to ethics, ideology or anything else in the marketplace of ideas, and I’ll show you a recipe designed to produce a specific result. . . . Besides, everyone since G?@c3;b6;del’s proof knows formal systems degenerate into mental masturbation at some point.[1]
Groundbreaking developments in the history of mathematics and logic: In 1931 Kurt G?@c3;b6;del published "?@c3;153;ber formal unentscheidbare S?@c3;a4;tze der Principia Mathematica und verwandter Systeme I"[2] in the journal Monatshefte f?@c3;bc;r Mathematik. The paper is famous among logicians and mathematicians for the two "Incompleteness Theorems" it contains,[3] logically demonstrating that no formal system rich enough to express truths of ordinary arithmetic can be both consistent and deductively complete while having a finite number of axioms.
The paper is famous among almost everyone else for containing a multi-page Rorschach inkblot, allowing a projection test in which the reader-subject can discern an easy dismissive response to whichever deductive argument they happen to like the least; or, if they prefer, to the exercise of deductive logic as a whole.
- [1]Lorraine Lee, Re: Julian Assange, the Left-Anarch. Comments at Social Memory Complex (21 April 2013). This is actually not even remotely what either of G?@c3;b6;del’s two major Incompleteness Theorem proofs says. –CJ.↩
- [2]A PDF blob of the article in its original German is available online thanks to Wilhelm K. Essler. An English translation of most of the paper is also available online thanks to Martin Hirzel.↩
- [3]Theorem VI and Theorem XI in the paper, specifically.↩
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“… while having a finite number of axioms.”
I think G?@c3;b6;del’s Theorem doesn’t require the formal system to have finite number of axioms. As far as I remember it applies to systems for which there is an algorithm that can verify whether any given statement is an axiom or not.