Also note that if we replace “truth” with “provability”, the liar’s paradox turns into Godel’s first incompleteness theorem, and Curry’s paradox turns into Löb’s theorem.
The wikipedia link for Curry’s paradox claims “It has also been called Löb’s paradox after Martin Hugo Löb.” Given that you require a word substitution I take it that wikipedia is oversimplyifying something? (Or perhaps overloading the Lob keyword at tad.)
The two are related, so the overloading is probably not accidental. When I studied math we used to joke that every area of classical math has a Gauss theorem, and more often than not it’s the most important theorem in the area.
The two are related, so the overloading is probably not accidental.
Not accidental and not surprising either. But still undesirable. It obfuscates the meaning of people who are talking about either of the concepts specifically.
I was curious enough to look into some background. “Different but basically the same for practical purposes” seems to be the conclusion.
The wikipedia link for Curry’s paradox claims “It has also been called Löb’s paradox after Martin Hugo Löb.” Given that you require a word substitution I take it that wikipedia is oversimplyifying something? (Or perhaps overloading the Lob keyword at tad.)
The two are related, so the overloading is probably not accidental. When I studied math we used to joke that every area of classical math has a Gauss theorem, and more often than not it’s the most important theorem in the area.
Not accidental and not surprising either. But still undesirable. It obfuscates the meaning of people who are talking about either of the concepts specifically.
I was curious enough to look into some background. “Different but basically the same for practical purposes” seems to be the conclusion.