Continuum said:
Eclectic Dreck said:
Continuum said:
If this sentence is true, the world will end in a week.
This is not a paradox. If the sentence is false, the world does not end in a week. There is no logic loop to be had. A better example of a paradox is the famous "tree falling in the woods" scenario. Of course, from a purely scientific standpoint, if nobody was around to observe the tree falling the question of it making noise is moot - how do you even know it fell?
No you are wrong. "if this sentence is
false the world will end in a week"
http://en.wikipedia.org/wiki/Curry%27s_paradox
Your statement has no paradox in it. The thing is, all such statements are based upon a misuse of english and as such do not actually result in a true paradox. The most famous example is the statement that "all natural numbers can be named in fourteen sylables or less".
The proof generally given lacks rigour:
Find the first word that cannot be unambiguously described using fourteen words or less.
This number may be unambiguously described as "the first natural number that cannot be unambiguously described in fourteen words or less" (A description which is fourteen words long)
If you follow the logic you find that all natural numbers can be described in fourteen words or less.
A rigorous proof is simpler - when dealing with the natural number set (all integers greater than zero), you come to realize you are dealing with a set who's cardinal (that is the number of members in the set) is trans-finite. This generally means that in order to actually unambiguously describe the contents of the set in turn requires an infinite number of words. Unfortunately, the sum total of all languages ever spoken does not contain such a number of words thus we seem to hit a road block until you realize words can simply be generated via a system. If the system readily reveals the meaning of the word, the standard rules of communication apply.
Thus you have a proof with actual rigor that doesn't rely on flawed use of english. Find the first number that cannot be unambiguously described in fourteen words or less. This number is to be described as n. Find the second number that cannot be unambiguously described in fourteen words or less; this number shall be described as nn. All numbers in the set shall be described as such, so that as each instance of a number that cannot otherwise be unambigiously described with fourteen or fewer words adds a new n to the previous word. As such, by demonstration of a working system that generates an infinite number of unambigious words, you give a deductive proof that all natural numbers can unambigiously be described using fourteen or fewer words. The paradox as such collapses because once a paradox can be resolved with logic it ceases to be a paradox.
Your assertion is "if this statement is true, the world will end in a week". If the world does not end in a week then the statement is both proven true and false simultaneously and thus you arrive at the supposed paradox. However, in this particular case we do not rely on an intellectual exercise to determine the truth of the statement. I can take your statement and then wait a week and see. Since there is no need to rely on a deductive solution to the problem, the inductive proof becomes clear. If the world does not end in a week and the statement reaches it's supposed paradox we are given a clear answer - the end of the world does not rely on the statement in question. Of course, one can make this statement an infinite number of times until time itself ceases to be, but invariably the truth of the statement is inevitably revealed and the paradox is resolved.
