Science a GoGo's Home Page Forums General Discussion Physics Forum Retiring Infinity from science

Sorry road and bridge got confused when I translated they are close in my native language, uur ancestors really didn't have bridges

So my new correct answer is you can't have an infinite real road but you can have an infinite imaginary road.




I agree but you don't want to look at the really interesting thing your thought experiment actually brings up which is what makes things valid and how do we decide logic.

Your thought experiment is classical in that it creates a problem only for certain sorts of logic operations.

Let me show you thought experiment under Intuitionistic logic which is one of the many forms of logic.

http://en.wikipedia.org/wiki/Intuitionistic_logic

=> In intuitionistic logic are not assigned any definite truth value at all and instead only considered "true" when we have direct evidence, hence proof.
=> Operations in intuitionistic logic therefore preserve justification, with respect to evidence and provability, rather than truth-valuation.
=> Intuitionistic logic is a restriction of classical logic in which the law of excluded middle and double negation elimination are not admitted as axioms.


So lets look at your example using Intuitionistic logic

"if you have an infinite road and you cut it in half do you then have two infinite roads"

Problem 1: infinite road ... no proof can exist assigned to vacancy state

Problem 2: infinite cut in half ... no proof can be done as we haven't seen an infinite road as per above and is infinity odd or even to divide ... so assign to vacancy state

Double negation elimination are not allowed so the question and thought experiment is not valid

Note that proof in Intuitionistic logic doesn't mean it can't exist it just means you haven't seen a clear example to determine any justification for an answer.

Russian science which I studied under uses Intuitionistic logic and so your thought experiment is completely invalid.

Interestingly however your thought experiment holds together under Western science which uses classical logic and I will leave them to defend it which Rede is doing I assume

Can you see that GOD and his pizza pocket resolves the same way for me as a nonsensical thing and yet causes angst with people using classical logic.

So perhaps the more interesting part I felt was to look at putting your example through different sorts of logic.

The one I was most interested myself in doing was putting it through a new sort of logic developed in 2003 called computability logic after all we are supposed to be a simulation according to some

http://en.wikipedia.org/wiki/Computability_logic


Logic determines validity and so the really interesting thing to do with your rather crazy example is look at it under different logic schemes and see what we get.




Wrong there is no difference we both don't exist please use Intuitionistic logic