I first encountered the Liar's Paradox in "Sideways Arthimatic from Wayside School." There it is "1. the answer to question 2 is false" "2. the answer to question 1 is true". the 'solution' i came up with in elementary school was focused on breaking the infinite chain. so i said if 1 is true, 2 is false, but if 2 is false, then 1 can't be true, so 1 is false. however, just because 1 is false, doesn't mean 2 is true, it just means that 2 is a different kind of false than 1 is refering to. therefore both of them are false. i guess it was based on the idea that there is only one way to be right but many to be wrong. i don't really fully remember the reasoning, but the answer stuck with me all these years.
if i wanted to follow young me's ideas and explore them, being my own historian, i might argue:
"if 1 is true, then 2 must be false. but then if 2 is false, one just has to be not true. If 1 is not true, that doesn't mean it is false (just like not white doesn't mean black), therefore, 2 is false, and 1 is just not true. therefore, the problem is the idea that a statement is only true or false."
i don't think i'm hitting on any real solution, just thought i'd share, however.
Liar's Paradox
I first encountered the Liar's Paradox in "Sideways Arthimatic from Wayside School." There it is "1. the answer to question 2 is false" "2. the answer to question 1 is true". the 'solution' i came up with in elementary school was focused on breaking the infinite chain. so i said if 1 is true, 2 is false, but if 2 is false, then 1 can't be true, so 1 is false. however, just because 1 is false, doesn't mean 2 is true, it just means that 2 is a different kind of false than 1 is refering to. therefore both of them are false. i guess it was based on the idea that there is only one way to be right but many to be wrong. i don't really fully remember the reasoning, but the answer stuck with me all these years.
if i wanted to follow young me's ideas and explore them, being my own historian, i might argue:
"if 1 is true, then 2 must be false. but then if 2 is false, one just has to be not true. If 1 is not true, that doesn't mean it is false (just like not white doesn't mean black), therefore, 2 is false, and 1 is just not true. therefore, the problem is the idea that a statement is only true or false."
i don't think i'm hitting on any real solution, just thought i'd share, however.