Let’s call the claim that “there is a binary property R which holds for all natural numbers and that there is no counter example that can or will ever be found, but which also cannot be proven to hold for all natural numbers” the “first Potato conjecture”. How would one ever show the first potato conjecture, or even offer evidence in it’s favor?
Well, you could do it like Goedel did. I don’t think you’re grokking the distinctions between different sorts of proofs, so reading up on Goedel’s proof might be what you want.
P.S. To get links to work on LW, replace problematic characters by a percent sign and then the ASCII hex code for the character, e.g. using %5F instead of an underscore ( _ ), or %2B instead of a plus sign ( + ). Or just put them inside brackets and use a link text, in which case you just need to know the ASCII codes for the brackets.
Well, you could do it like Goedel did. I don’t think you’re grokking the distinctions between different sorts of proofs, so reading up on Goedel’s proof might be what you want.
P.S. To get links to work on LW, replace problematic characters by a percent sign and then the ASCII hex code for the character, e.g. using %5F instead of an underscore ( _ ), or %2B instead of a plus sign ( + ). Or just put them inside brackets and use a link text, in which case you just need to know the ASCII codes for the brackets.