Yet another paradox

Great Debates
#1

This showed up in a philosophy class I was taking this semester. The class is over, but I never did figure out how to deal with it.

There is a sentence referring to you that says “X does not say that this sentence is true in his or her post discussing this sentence,” where X is your username. By the law of the excluded middle, this sentence is either true or false, but as soon as you commit to one position, you’ve endorsed the other. This looks kinda bleak, doesn’t it?

So what do you say, logic-loving dopers? Is this sentence true, or is it false? What does it mean if it’s neither?

#2

That’s an interesting sentence.

#3

Beginning at t=4:06 am 5-10-2002 GMT, that sentence is true.

#4

Beginning at t=4:10 am 5-10-2002 GMT (and continuing indefinitely thereafter), that sentence is false.

#5

What was the truth value of that sentence before 4:06 am 5-10-2002 GMT? Then it was like that famous “The present King of France is bald” proposition. I don’t remember how the solution to that one goes, though.

#6

If there is no King of France at the moment, I say that sentence is false.

#7

I would be inclined to say that the question of the king of France (or the statement which becomes false as soon as it is proven true) are best left at “paradox” and not “true” or “false.” It doesn’t make sense to force yourself to assign a truth value to an empty set like that.

#8

I would consider a sentence identical to the one we’re examining to be true; you’ll note that the sentence we’re examining contains the word “zebra” seventeen times.

More precisely, there are ways to discuss a sentence that don’t involve discussing its truth or falsehood. If you want a paradox, I think you need to rephrase the OP:

“When X eventually commits to an absolute position regarding truth of this sentence, X will not declare the sentence to be always true.”

where “an absolute position” is defined as either “always true” or “always false.”

Logic majors can gussy that correction up with proper jargon, but I think the basic principle applies:

As long as I’m allowed to discuss such a sentence without committing to its truth or falsehood, then such a sentence can be true as long as I don’t commit to a position regarding its truth in the post in which I discuss it. Interestingly, such a sentence can’t be false: if I commit to a position regarding such a sentence’s truth, then we get a paradox.

One final note. Your sentence does not, of course, contain the word “zebra.” The fact that I incorrectly suggested that it does in no way affects the sentence’s truth; all it does is satisfy this post’s need to discuss the sentence.

Daniel