The Unprovable Liar

Quoting saw038

What do you think this states about the human mind and our ability to comprehend the world?

We've improved our ability to comprehend the world. I recall Gödel was a platonist.

Quoting saw038

Math is our most precise measure of arriving at truth.

Pretty certain that this was blown out of the water by Deep Thought's answer to the question about Life, the Universe, and Everything.

Quoting saw038

"What I am saying cannot be proven."

But what was he saying?

(Or in other words, I think there's a problem with the idea of taking sentences like that to refer to themselves.)

He would take a statement such as this and then run it through different schools of mathematics and the paradox would always persist.

Reply to saw038 It says if we knew of a better way to use language than to normally assume someone either means what they say or are joking we'd use it.

Reply to wuliheron

As that manifestly is not how we use language, we do and we do!

Reply to Barry Etheridge

Its actually been proven. Children acquire grammar the hard way by using pattern matching and an examination of how often people misinterpret each other showed that the frequency is rather high to say the least but, thankfully, language is forgiving and much of life is self-organizing. These are features of a self-organizing systems logic where roughly one quarter of the system is dedicated to maintenance, which is high, but the advantages outweigh the disadvantages. It also means language should prove to display the resilience of chaotic systems which can now be calculated. Its along the lines of being able to calculate the temperature at which water boils.

Reply to wuliheron

You: x + y = z

Me: No, x + y = a

You: Proof is ij(k+l)/q > 3

Me: :-O

Reply to Barry Etheridge

Pattern matching is synonymous with yin-yang dynamics and self-organizing systems logic and, in recent years, all the doubts about it applying to language have been vanquished with even the first five neural networks responsible for pattern matching having already been mapped out in the brain. Noam Chomsky was just plain wrong and we don't inherit grammar because the human brain doesn't obey classical causal logic which is just way too inefficient to be survival oriented. There's even a new science known as Quantum Cognition that shows how we think is often blatantly quantum mechanical or context dependent.

The mathematics and logic are entirely different requiring fuzzy logic at the very least. My favorite example is Monty Hall on "Let's Make A Deal!" He has someone choose from door number one, two, or three and then shows them a booby prize behind one of the doors they didn't choose. Next he offers to trade them the door they choose for the other door they haven't seen yet. According to classical logic and probability there's no advantage in trading, but fuzzy logic insists that since your first choice was between three doors it was even more likely wrong than swapping between the two. Fuzzy logic is used in Backgammon, high speed elevators, and missile guidance systems today and has a big future when the next generation computers come out.

With Quantum Cognition it was sociologists who discovered even more surprising results. They offered people a fifty-fifty gamble where they would loose a hundred bucks or win two hundred. Such simple odds are easy for anyone to understand and they would keep playing even if they lost a few rounds, but the minute the researchers didn't tell them whether they had won or lost a particular round most stopped playing even though it was a "sure thing". According to quantum mechanics and how even your brain has been proven to work, without information on the last round you cannot predict the next.

So we do use additional logic to determine what language means other than merely deciding whether someone means what they say or is joking, but it gets complicated. However, metaphorically you could say sex is never about survival of the fittest, but the most creative and the human brain and languages are creative engines that only incidentally happen to resemble computers.

Reply to saw038
It implies that there something wrong on how we do mathematics.

Reply to Terrapin Station
Apparently, self-reference is inevitable, meaning, that there is nothing wrong with it. (proven as the diagonal lemma or fixed-point lemma)