Changing the topic into something lighter than metaphysics…
Are you familiar with the liar paradox? There are several variations of it, but the most common is probably this:
The next sentence is false. The previous sentence is true.
Now, if sentence 1 is true, then 2 must be false, which means that sentence 1 isn’t true after all… but then it means that 2 must be true… and so on. It’s impossible to solve; it’s a paradox.
An even simpler version is the following:
This sentence is false.
Now, is it true or false?
Finally, let’s consider a third case:
Everything I say is false.
My question is: is this the liar paradox again? Or is it actually possible, and not a paradox at all?
If you’re reading this on the front page, you’ll have to click on “Continue reading…” for the answer. If you’re using your feed reader, or Planet Atheism, or arrived directly at this post, the answer is below, so… close your eyes now and think about it before you open them again.
Well?
Thought about it? You didn’t cheat, did you?
That third case is a trap, because of a commonly made mistake. Many people, when asked, will reply that the negation of “always” is “never”. But it isn’t. It’s “not always”.
The person who says “everthing I say is false” can’t certainly be telling the truth, because, if he is, he isn’t.
But he can perfectly well be lying, because the negation of that (false) sentence is “not everything I say is false” - which is true.
Unlike he claims to, he doesn’t lie all the time, but he is lying now.
So, did you find this interesting, or incredibly boring?
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Interesting, actually.
I write logical true/false statements for a living, so when it comes down to a logic problem like this, I’ll pretend I’m programming at work.
A = everything I say is false !given, this is my statement
if(A.eq..true.)then !if everything I say is false
!assuming everything I say is false, then A would be
!false if I said it, so this condition cannot exist
elseif(A.eq..false.)then !if .not.(everything I say is false)
!this condition can exist, but
!some thins I say are false, because that was false
endif
I like to get into an “Everything I say is false. Except that. And that. And that….” cycle with my friends. They are not sophisticated enough to point out the logical linguistic argument that you pointed out. Very nice.
[quote comment="7006"] …my friends … are not sophisticated …[/quote]
Time for new friends? haha
Trying to explain tri-part distinctions to most folks is a chore at best, if not simply impossible, yet most distinctions in our life are not merely two part, but are three or more.
Always, sometimes, and never do not seem to register with most folks as three disctinctions when you apply them to actions. For the moral rules they will claim that you must always obey them, but at the same time claim that you must give to charity (or some other “positive” action) without ever recognizing that the consequence of this assumption is that you cannot morally go to sleep or eat, because in those actions you are not giving to charity.
The point of this example is to show that the introduction of “sometimes” into the two part distinction that they acknowledge, between always and never, then these sorts of problems disappear. But then most folks do not care about understanding..