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You are here		unstableontology.com Dequantifying first-order theories - Unstable Ontology
\|	\|	www.lesswrong.com Self-Referential Probabilistic Logic Admits the Payor's Lemma - LessWrong	4.2 parsecs away Travel
\|	\|	A community blog devoted to refining the art of rationality	4.2 parsecs away Travel
\|	\|	xorshammer.com What Happens When You Iterate Gödel's Theorem? - XOR's Hammer	3.0 parsecs away Travel
\|	\|	Let $latex \mathrm{PA}$ be Peano Arithmetic. Gödel's Second Incompleteness Theorem says that no consistent theory $latex T$ extending $latex \mathrm{PA}$ can prove its own consistency. (I'll write $latex \mathrm{Con}(T)$ for the statement asserting $latex T$'s consistency; more on this later.) In particular, $latex \mathrm{PA} + \mathrm{Con}(\mathrm{PA})$ is stronger than $latex \mathrm{PA}$. But certainly, given that...	3.0 parsecs away Travel
\|	\|	www.lesswrong.com Dequantifying first-order theories - LessWrong	0.0 parsecs away Travel
\|	\|	The Löwenheim-Skolem theorem implies, among other things, that any first-order theory whose symbols are countable, and which has an infinite model, h...	0.0 parsecs away Travel
\|	\|	rationallyspeaking.blogspot.com Rationally Speaking: You don't really exist, do you?	25.3 parsecs away Travel
\|		by Massimo Pigliucci www.universaltheory.org For some time I have been noticing the emergence of a strange trinity of beliefs am...	25.3 parsecs away Travel