Gödel, Escher, Bach: Grelling's Paradox

[dolofonos]

It is perfectly possible make a false statement; yet we marvel at the paradox.

"Imagine an unstoppable and an immovable object in coexistence." The Universe did not just explode because there is no natural law that says I cannot declare an absurdity.

[Abracadabra208]

One could supply a classically based answer to the paradox and simply state that the question itself is nonsense, akin to asking what is north of the North Pole or what there was "before" time began. A priori, truth cannot contradict truth.

[insidetrip101]

@Abracadabra208

I think you mean that you can not talk about everything at the same time and in the same respect: "If everyone who does not shave themself is shaved by the barber, then who shaves the barber?"

[toogoodbw]

I don't understand why the answer isn't a simple "No. The word 'heterological' is not heterological."

[Bakmoon]

@toogoodbw Because if the word "heterological" isn't heterological, then it doesn't describe itself. But if it doesn't describe itself then by definition it is heterological.

[jmarkmusic]

Let's have ~T!=F and ~F!=T and lets have `T=F and `F=T. T=T and F=F. Let's also have ~T=`F and ~F=`T. Heterological is heterological is both ~T and ~F. END OF DISCUSSION, MATHEMATICIANS! I WIN AT MATH. This is the art of infinite reckoning in a nutshell.

[jmarkmusic]

@jmarkmusic oops: `T and `F... same idea.

[ariastoteles]

A marvelous paradox!

[SarahStarmer]

I saw a nice phrase on wikipedia to describe this type of paradox. " vicious circularity."

I am making a collection of paradoxes if anyone knows any good ones let me know.

I think self reference (the very thing that causes so much trouble in many paradoxes) is the process by which complexity is created.

It is feed back loops you see, they are very difficult to make sense of.

[Paulginz]

@SarahStarmer The Banach-Tarski paradox (you can take a sphere, chop it up into 5 pieces and reassemble the pieces into 2 spheres of the same size as the original) is a nice example of paradox that isn't based on self-reference.

[Atmosfferic]

I have listened to a lot of Bach over 60 yrs,& this bachground rendition is simply Beautiful !!.

[cyndie26]

0:28

Yes and no! Heterological does not describe itself in any way, so Heterological is actually both Autological and Heterological.

[DarkShroom]

not really an accurate description i think you just put GEB in to get hits

[jbearden]

If this is your presentation on Godel, then it is a poor thing.

[qigong1001]

Lets just take everything from wikipedia and repost it here in the comments section.

[MrJohnthedoe]

I would say it is a meaningless question

[MartenThuren]

Shit, mental stack overflow :P

[88Cortex]

@MartenThuren :D!

[pietrolunz]

yes, and no, it depends of the observer, as usually lol

[ePhilosopher9]

Fractal Indeed Benoit

/watch?v=KbnFIPtxo3s

[ErnestoGustavM]

what's the surround music?

[websnarf]

The base assumption is that all adjectives can be put into such categories. In an axiomatic system one is forced to operate on already fully defined sets. By describing these words, one is intrinsically redefining the set upon which they are defined (since they are adjectives themselves.) That means the original set (the set of all adjectives) was not yet defined when it was invoked as part of the definitions.

This kind of paradox happens when you don't proceed axiomatically.

[0igres]

is not another not another movie not another not another movie?

[WetlandsRemediation]

We reject your paradox on the grounds that Dedirre's deconstructionism informs us that there can be no such thing as an autological word.

[VolkColopatrion]

the thing i love is that i can simply cheat and give hetero-logical it's own set. Sure, it will be lonely but it will be given it's own unique category because of it's own unique property.

As for the barber... well you've got me there. Mabye I'll just give him split personalities.

[paradoxicus]

No es posible demostrar la verdad y la veracidad en un mismo lenguaje.

La definibilidad y la demostrabilidad en esencia no son mas que intuiciones del propio lenguaje.

[therealdeadrabbit]

Any word W is a set of other words, being described by W. The word heterological is also a set, H. The question is then, whether 'heterological', as H, contains itself, a.k.a. does it describe itself?

H contains non-self-descriptive words W, as a set, are not self-inclusive. This is equivalent to Russell's paradox, in that, if H contains itself, it is non-self-descriptive, then it doesn't contain itself. If it doesn't contain itself, it is non non-self-descriptive, then it does contain itself.

[davidrodgersNJ]

Huh?

[TheeSleapinbeauty]

kathy is an angel to put up with you alex

[Ikkarous]

FOUND IT

Harpsichord Concerto No.5 in F Minor BWV 1056

[docoftheworld]

@Ikkarous man, thank you so much ..

[Ikkarous]

I beg you guys, WHAT IS THIS PIECE OF MUSIC THAT IS BEING PLAYED????????

[faraz1729]

Bach is quite something else, huh?

[docoftheworld]

@faraz1729 Yes ... he is ...

[chdata]

What is the most impossible question of all?

The above question mgiht seem like it is, but if I answered it like this so easily, then it can't be the most impossible question...

By Chdata

[WetlandsRemediation]

@chdataWe asked Santa Rita (patroness of impossible causes) your question, she replied:

Violation of definition.

Like uniqueness, there are NO degrees of impossibility.

[chdata]

I reply: Violation of spelling. Who is chdataWe?

jk

Here's another one I made up. Let's say it's possible to do any thing an infinite amount times, perhaps some super being or computer has the power and such to do so. Then let's say it "counts" for one half of a second. Then it counts a half of a half of a second, or a fourth of a second, and it keeps counting a new half infinitely. When does the next second start? Did it's infinite power freeze time in an infinite loop?

[WetlandsRemediation]

@chdata No, smartass, it is a typo- we claim blindness, what is your excuse?

We hate to disabuse you, but you are not the author of the above paradox.

Zeno predates you by several millennia.

wikipedia, Zeno's_paradoxes

wikipedia, Philosophy_of_space_and_time

[chdata]

Wow dude anger issues I wasn't even trying to offend you. Also I never said that I'm the AUTHOR of it, I just made it up by myself. I never said that I am the one and only person to ever come up with it. You can come up with an idea, and claim to have made it up, even if someone else already has origionated it, you just had the same thought but didn't know about it.

[WetlandsRemediation]

@chdata "Dude" is pejorative in Texas. Ignorance is no excuse for insouciance.

[chdata]

Ok... at least I'm not getting mad over a small joke.

[parquar]

@chdata there are limitations and so that was based on a false premise

[RoulfYelrab]

Hahahahahahaha,

The following statement is true.

The preceding statement is false.

[Krumbz2003]

Is the word "heterological" heterological?

No.

[dirtybitbucket]

Are you sure? If "heterological" is not heterological, that means it must be autological. Which means it applies to itself. Which means it is heterological. So Yarza84 has it exactly right: this is a form of Russell's paradox. So is this:

A barber shaves everyone and only those who don't shave themselves. Does he shave himself?

[scsteeldrums]

The barber's paradox is really just a false premise. The barber does NOT shave everyone and only those who don't shave themselves. Its as silly as saying "I ate my own head. What part chewed my teeth?" The statement just ceases to lack meaning. The only issue in Grelling's paradox is that the initial assumptions are fallacious. Namely, that all adjectives are either autological or heterological.

[okuno54]

@scsteeldrums There is a big difference between the two, and it is one of semantics versus syntax, so you've really created a false analogy.

[scsteeldrums]

@okuno54 websnarf said it.

[okuno54]

@scsteeldrums eh... my (albeit scant) explanation is rather different. I think mine doesn't fall prey to/address a number of philosophical questions, and so should be acceptable to realists and formalists alike. Once again, I guess I'm being scant <.<

[cyndie26]

@Krumbz2003 ...and yes.

[Orione]

Ouch! That hurt my brain LOL  Cool video, thanks for sharing!

[shilohwillcome]

PLEASEEEEEE, Explain this, what is the upshot???

[zardozcs]

pointless linguistic B.S. What purpose does the concept 'self-descriptive adjective' serve apart from being used in Grellings contradiction? This just shows it's possible to formulate invalid concepts which are of no practical use.

[Gazer1234567]

Yes but i think he was expressing his satisfaction with what the book, "an eternal golden braid" has said. I reccomend you read that book

[jhip87]

Who says paradoxes have to be practical? By their very nature, they seem to be purely theoretical.

[zardozcs]

jhip87: every paradox represents an attempt to integrate a contradiction. No knowledge flows from them they always represent an error in thinking. Paradoxes have set back philosophy time and time again. i.e. Zeno's paradox leading to the conclusion that motion is impossible.

[jhip87]

I don't want to talk about this at length, and what you say may indeed be true of some paradoxes, but certainly not all. The Liar Paradox, for instance, or Russell's, Berry's, or Curry's, have all expanded our knowledge of mathematics and language immensely.

[tyrbolo]

just a fancy version of the "all Cretans are liars" said the Cretan.

[2bsirius]

OK..I cheated. SORRY!

If Russell's paradox is shifted into the world of words and grammar, then Grelling's paradox results. Coining the word "heterological", defined as "a word which does not describe itself", creates the same situation as exploring the set of all sets that do not contain themselves. The word heterological describes itself IF it does not describe itself.

The Oxford Dictionary of Philosophy entry

So Jprotevi is spot on! 5*s

[Yarza84]

Thats right!!!

The minute I saw this, I thought "This is just Russell's paradox for adjectives" xD

[paganiniGOGO]

The music should have been the Barber of Seville overture, or Bach's musical offering and the background should have been escher.

[cyndie26]

@2bsirius Heterological is both autological AND heterological.

[zeekoprop]

Let us suppose that the function F(fx) could be its own argument: in that case there would be a proposition 'F(F(fx))', in which the outer function F and the inner function F must have different meanings, since the inner one has the form O(f(x)) and the outer one has the form Y(O(fx)). Only the letter 'F' is common to the two functions, but the letter by itself signifies nothing. This immediately becomes clear if instead of 'F(Fu)' we write '(do) : F(Ou) . Ou = Fu'. Russel's paradox resolved.

[Jprotevi]

It is iff it isn't.

[ChrisPrefect]

it's not

[shilohwillcome]

what?