Godel’s incompleteness theorems and Douglas Hofstadter's book Godel, Escher, Bach get hung up (or lost in space in the case of Hofstadter) on self-reference. Granted, Godel uses his overly complicated mathematical "system" as cover to bury self-reference so it isn't as obvious as 2x2=5 but nevertheless it is wrong.
To wit from the article;
Godel’s extra insight was that he could substitute a formula’s own Gödel number in the formula itself, leading to no end of trouble.
This isn't insight or genius it is proof that he made a mistake. Self-reference leads to "infinity" and "no end of trouble" if improperly defined. If you've read the history of mathematics you'll find that many of them (including Godel and Cantor) went insane thinking about infinity but that is what you get when you use an ungrounded base-case for self-reference. Intentional or not, these incompleteness theorems have led to uncertainty and doubt regarding reason.
BTW, we all safely use self-reference virtually every single day when we say "I" but what do you mean by that?
Godel’s incompleteness theorems and Douglas Hofstadter's book Godel, Escher, Bach get hung up (or lost in space in the case of Hofstadter) on self-reference. Granted, Godel uses his overly complicated mathematical "system" as cover to bury self-reference so it isn't as obvious as 2x2=5 but nevertheless it is wrong.
To wit from the article;
This isn't insight or genius it is proof that he made a mistake. Self-reference leads to "infinity" and "no end of trouble" if improperly defined. If you've read the history of mathematics you'll find that many of them (including Godel and Cantor) went insane thinking about infinity but that is what you get when you use an ungrounded base-case for self-reference. Intentional or not, these incompleteness theorems have led to uncertainty and doubt regarding reason.
BTW, we all safely use self-reference virtually every single day when we say "I" but what do you mean by that?