"There's only one hard and fast rule in running: sometimes you have to run one hard and fast."

Friday, November 5, 2010

Liar Paradox and Observer Paradox

I've been trying to solve a problem for about 20 years and I just need to write some stuff down to get my thoughts straight. If you want to know what I think about while running, this is the starting point. Everyone else: run away now, while you still can!

Premise: 1) There are four essential unsolvable problems in philosophy. 2) Each of these has a counterpart in the hard sciences. 3) The problems are intrinsically the same problem. 4) Viewing the problems correctly does not resolve them, but makes them disappear. [The consequences of number 4 are troubling.]

Trying to solve problems logically is futile, as long as there is a hole in logic itself. There is a family of paradoxes, based upon the Liar's Paradox: "I always lie."

The paradox is that, if that statement is true, it must be false and if false, must be true. I don't know when I first heard it, but I was younger than 6 (when it came up in a favorite episode of "Star Trek"). The paradox goes back to at least ancient Greece, where Epimenedes said "All Cretans are liars," being a Cretan himself. This version of the paradox is even in the Bible (Titus 1:12-13a): It was one of them, their very own prophet, who said, "Cretans are always liars, vicious brutes, lazy gluttons." That testimony is true. The second sentence, some believe, adds a second paradox. A variant of the paradox occurs in Don Quixote, when Sancho Panza is stopped at a bridge and told that he can pass if he tells the truth and that he will be hanged if he lies; he says, "I came to be hanged." There are many other variants of the paradox, such as the barber who shaves all men who don't shave themselves, but I believe them all to be essentially the same.

The simplest version is: This sentence is not true.

Many have tried to work around the paradox. One attempt was to separate truths from necessary truths, but the paradox remains: "This is not a necessary truth." Another was to say that the liar paradox is neither true nor false, but the paradox remains: "The liar paradox is neither true nor false" is itself a paradox, exactly the same in essence as the original. Other failed attempts and their versions:

Nobody knows that this is true.
Either the reader has no slightest doubt that this is true, or this is not true.
(Buridan's 8th sophism) S: P is false. P: S is true.
This sentence is nonsense.
This sentence is meaningless.
(after George Moore) This is true, but I don't believe it.

Bertrand Russell tried to skirt the issue with symbolic logic, but ended up discovering that it has its own version: The set of all sets not containing themselves.  (Or perhaps the set containing sets that are not members of themselves). Zermelo and Fraenkel came up with a system that avoids that paradox and, if you want to scurry down that particular rabbit hole, look here. Unfortunately, I don't think their system has any "real world" validity.

There is another way out of the paradox, and that comes from quantum mechanics' own observer paradox and quantum indeterminacy, stemming from the Heisenberg Uncertainty Principle. [Go ahead, try to understand Wikipedia's thumbnail sketches of this!] Without going into detail, what is proposed is that the act of observing something changes what is being observed. A point I need to keep in mind for a later part of this ramble (assuming I continue in later posts) is that all our knowledge of the physical world comes from our senses and that these are dependent upon bouncing energy packets or waves off things; this energy momentarily changes the energy state of the thing being sensed (on a submicroscopic level).

The payoff

"This sentence is not true." can be considered to be neither true nor false until one tries to assign it a truth value, at which point it has the truth value opposite to that one attempts to assign it. Whether the sentence has no truth value, or is indeterminate or has a truth value that one can not know is all a matter of semantics.


Glaven Q. Heisenberg said...

ZOMG, SteveQ!1! You just killed Schrödinger's cat!1!

After reading this post he was irresistibly pulled up into the singularity of his own butthole!1! And thus disappeared inside himself where you should look for him except there's no longer any him for you to look inside of, where he'll be found if you'd only look!

Hahahahaha! Just kidding! Cats can't f*cking read!

SteveQ said...

@G: to keep the thread going, it was Nansen who killed the cat. http://www.kuro5hin.org/story/2006/11/8/82839/8053
Niels Bohr was the first to appreciate how particle physics is much like Taoism and Zen.

Glaven Q. Heisenberg said...

The only other thing I took away from the Periodic Table book I just read:

Einstein was extremely suspicious of quantum physics, saying, famously: "God does not play dice." (Which is actually a misquote. Actual quote: "I, at any rate, am convinced that He does not throw dice.")

But people forget what Bohr said in response: "Einstein, stop telling God what to do."

Hahahahahahaha! In truth, I had heard this before, but I forgot it.

Also, in one Simpsons ep, Homer wants to watch When Dinosaurs Get Drunk but it's preempted by The Boring World of Niels Bohr.

So it all comes back to The Simpsons.