Let Q be the set of all statements that can be either true or false.
Denote the statement "This statement is false!" as x. If x is a member of Q, then x can be judged either true, or false, and either way there is no paradox. Because it is a member of Q, Q(x)=TRUE or Q(x)=FALSE.
If x is not a member of Q, then x cannot be judged either true or false, and there is no paradox.
The apparent paradox emerges from attempting to honor the content of the statement without reference to its context. Brains seem to resent the idea that a sentence can say "I'm false!" while it resides in a domain where "true" and "false" are not applicable. It's not that the statement is paradoxical; it's that it's simply not a member of the set it references. It's in logical drag.
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wankgate2015-03-23 07:32 pm
Re: SURVIVOR: ANON HATE EDITION, ROUND 4
(Anonymous) 2015-03-28 07:15 pm (UTC)(link)Re: SURVIVOR: ANON HATE EDITION, ROUND 4
DOES NOT COMPUTE
Re: SURVIVOR: ANON HATE EDITION, ROUND 4
(Anonymous) 2015-03-28 07:37 pm (UTC)(link)Re: SURVIVOR: ANON HATE EDITION, ROUND 4
(Anonymous) 2015-03-28 08:10 pm (UTC)(link)Denote the statement "This statement is false!" as x. If x is a member of Q, then x can be judged either true, or false, and either way there is no paradox. Because it is a member of Q, Q(x)=TRUE or Q(x)=FALSE.
If x is not a member of Q, then x cannot be judged either true or false, and there is no paradox.
The apparent paradox emerges from attempting to honor the content of the statement without reference to its context. Brains seem to resent the idea that a sentence can say "I'm false!" while it resides in a domain where "true" and "false" are not applicable. It's not that the statement is paradoxical; it's that it's simply not a member of the set it references. It's in logical drag.
Re: SURVIVOR: ANON HATE EDITION, ROUND 4
(Anonymous) 2015-03-28 08:19 pm (UTC)(link)Re: SURVIVOR: ANON HATE EDITION, ROUND 4
(Anonymous) 2015-03-31 09:25 am (UTC)(link)