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00:00 - 02:0002:00 - 00:00

00:00
Derivation is just that: the production of new formulas according to the rules of the game.
The problem is:
i get it now. but. when you say "theorems that you can never derive in that formal system", is this about isomorphism? you have some rules in a system, and when you transpose them to another system, it will not be allowed to do the same derivations as it did in the other?
No, this happens in the same system.
Given a set of axioms, you can keep deriving and deriving theroems (or formulas)
But there are some formulas that can never be derived with that set of axioms.
So you may include another axiom to compensate for that "drawback"
But then there will be other theorems you can't derive in this new system of axioms
And so on.
but when you say that they cannot be derived, it seems that the derivation can be imagined but not applyable? if you do derive, it will become a paradox?
Derivation is a mechanical process.
That's why I said it's like a game.
Take chess, for example.
The knight moves in L.
You cannot make any other move with a knight.
That's part of the game.
right
but you can make infinite moves with it, so that you may occupy any position in the board, can't you?
00:07
Well, the chess game was only an analogy.
I don't mean to say that chess is "incomplete".
hmm
What I mean is: in any formal systems, you may keep applying that mechanical process forever.
And yet you won't reach certain formulas.
Gotta go, now
I'll be back in a bit.
when you say that... it seems that you have some preconception of what you want to reach, despite of what the system offers
ok
@Cerberus are you there? just wanted to say hello
Hi!
I see you have been talking logic?
I'm trying to understand what cathegory theory is about
and it's relation to set theory, if there is
maybe I should begin with Aristotle, and only then try to study more complex stuff
00:21
I've seen those terms come by often.
But somehow they never stuck.
Why don't you read up on the subject and report here, hehe.
I've read the wiki on cathegory theory many times, it feels like there's something missing, so that I can get a full picture
hahah
if I find out something interesting, I'll tell you
I should study 3 'monsters' on category... Aristotle, Kant and Peirce. it seems like something that needs a lifetime
but I should begin with Aristotle, as the other 2 must have studied him
@Tames I often have that with Wiki articles about complicated subjects.
Aristotle is always a good start!
Lacan talks about him all the time.. logic.. ethics..
have you studied his work? (Arist.)
Hi I'm Brazilian, there someone alive here?
Hi Zig
I am, and I'm brazilian as well
00:32
então nos podemos falar em português?
So we can talk in portuguese
poder a gente pode, mas é meio chato com quem não fala portugues, apesar do @Cerberus conseguir entender algumas coisas
is it really necessary?
@Tames Yeah, he he is ubiquitous in ancient philosophy!
@Tames I think I could read that.
hahah
kkkkk
@Cerberus how come you get to understand portuguese like that.. you studied latin?
00:35
"One could do that, but there are more chatters with whom you can't speak Portuguese, although Cerberus can understand some thing?" I am wildly guessing here.
@Tames I am a classicist, Latin is mah thing!
i think Portuguese is not a language that people would like to learn
Why not?
It's nice.
"yes we can, but is is kind of boring (inappropriate) to those who do not speak portuguese, although Cerberus can understand some things"
in my opinion it's very difficult
@Cerberus you are good! oh.. i'd love to learn latin
difficult.. have you ever tried to learn german, @Zignd?
00:37
Ahh OK, so I got nearly everything right except "meio chato". Chato means what exactly? And meio means "somewhat"?
i think it is not easier
@Tames It's great, and it will be easy for you.
Only cases will take some getting used to.
@Cerberus "meio" can be translated as "half", in this case it is "kind of", "a little"
@Zignd But you seem to speak it quite well, hehe.
yeah, from what i know the german alphabet is more large then the portuguese
00:38
@Tames Ahh OK, probably from Latin semi-.
portuguese?
kkk
The alphabet? Nah, you both use the same alphabet (the Latin alphabet).
i'm the most horrible on it on my class
Perhaps there are some letters that you do not use?
But then you have some accents that the Germans don't have.
@Cerberus and "boring" in this sense is not like "dull, tedious", but more like.. not polite
00:40
Hmm yes, dictionary says boring, annoying.
@Cerberus "chato" can mean "flat" as well
when he said "boring"?
chato
adj. boring, annoying; flat, level, even; pokey

chatô
n. chateau, castle; country estate (French)
i could not find it
@Zignd I said!
00:41
hum
pokey? funny word
By the way, although officially we are supposed to speak English here, I don't mind if you speak Portuguese occasionally, especially when I'm not participating.
I also like learning it a bit.
I could teach you some Latin in return, hehe.
hehe
so @Zignd, you may speak portuguese, but if you don't mind i'll answer in english
00:43
no problem
It is interesting that we should have three Brazilians here.
i need to use my english to get better
I haven't met any in other rooms.
So we can all learn!
English, Portuguese, and Latin.
because it's 24:45 on USA
so.. @Zignd, you should speak english, @Cerberus should speak portuguese and I should speak latin lol
or german
00:45
Yay!
great
Except that I couldn't speak a word of Portuguese.
I can only read it, with difficulty and a dictionary.
how come? you translate it perfectly
hahah
can you guys please correct me when i say something wrong?
Always?
Wouldn't that be annoying?
For starters, you should use capitals and punctuation, hehe.
00:46
my english is so horrible like that?
aber Ich konnen nicht Deutsch sprachen
No, that last line was otherwise perfect!
@Zignd Here you should drop either "so" or "like that": it is double.
@Tames Ich kann nicht Deutsch sprechen would be grammatically correct, though unidiomatic; you would normally say ich spreche kein Deutsch.
or you could say "is my english that horrible?"
00:48
OMG, another Brazilian!
hmm
Yeah it is uncanny!
But my active German is not very good either.
I understand
But better than my French.
Ich spreche kein Deutsch, aber @Cerberus unweist mihr
lol
00:50
that last message was for me?
@Tames yeah, because I oversimplified it a bit.
Unterweist mich, I think.
In formal systems, you have a finite set of symbols
With which you can build formulas.
there were so many different words for "teaching" in the dictionary, I just picked up one randomly
And there are rules about how to put the symbols together in order to have a "well formed formula"
00:51
@Tames Haha, well, this one is fine.
So, you can predict all the possible well formed formulas.
Yes, it is unterweist mich (looked it up).
@Tames are you using a real dictionary?
Some of them are true, some are false.
And some are unreachable.
And welcome to our humble room, @Zignd!
Thanks
00:53
pretends to be humble
@Cerberus I thought dutch and german were very similar
@Zignd I'm using michaelis online
@Tames I think like Spanish and Portuguese, roughly.
Or actually a bit more different.
@OtavioMacedo I think I get it.. it is like you get all possible derivations but then some are not useful?
@Tames don't you think google translator is better?
But not so different as Portuguese from French.
00:54
@Zignd I never used it.. I don't know
@Tames No, it's not about usefulness.
Let's get back to the chess analogy again.
Suppose we had a different version of the game, but with an infinite table.
And the same finite set of pieces.
I looks interesting
We could, of course, dispose the pieces in a random way.
Dispose?
Place, or move?
Sorry... not the right word.
Thanks @Cerberus
00:58
It would be a good word to use in Latin.
Hehe.
We could place the pieces in a random way.
But it would generate a infinite game
@Zignd That's the point
It's not going to be fun
But it doesn't mean that all arrangements we could come up with are valid.
According to the rules of the game
01:00
i see.. like having two bishops in white rows (considering it is an infinite board, you would never get to exchange your pawns lol)
Give me an example
@Tames Yes, exactly!
It doesn't even need an infinite board.
That's incompleteness.
it does, because you can exchange a pawn for whatever piece you want, if your pawn was on a white square, and you already had a bishop in white rows, you could get 2 of them
but of course, you'd better get a queen lol
Oh, right. So my infinite board was a good piece in the analogy :)
I see that there are some impossibilities... but I don't get it how does it limite derivation... consider this: if I have wheat flour, I could make pasta, bread, cake or pie... but I could not make barbecue,
01:05
looks like we have a new Guest
@DavidWallace
@Cerberus Really? My German teacher told me that it was actually a grammatical error to use nicht instead of kein.
@Zignd Alas, I am an old guest.
hi David
so @OtavioMacedo, do you think this is a good analogy? I had the impression that it was not about this
@DavidWallace Well, it depends on what you call "grammatical".
i thought it was something like... there's a recipe containing wheat flour, but you cannot make it because of... i don't know why
It was unidiomatic anyway.
01:08
@Cerberus I guess it does.
An argument that periodically arises on ELU.
What did you teacher say exactly?
@Cerberus You want to know her precise words?
@DavidWallace Yes. I think it is a bit of Chomskeyan bs, but hey.
Bearing in mind that this conversation took place in 1986?
Eh no.
01:09
@Tames Sorry, I can't see the point in your analogy.
But you didn't specify under which circumstances you thought nicht was wrong.
Me too
@OtavioMacedo I thought "recipes made from X" was a better image for derivations, but it seems like i was mistaken
lol
@Cerberus In those circumstances where kein would be correct.
@DavidWallace I think that is a bit too strong.
01:10
@OtavioMacedo in your example... i get the idea of an impossibility, but it would be like "I can't breathe in water, because I have no gills"
(yet)
But I guess kein is nearly always preferred when possible.
I'm secure in the knowledge that if I say Ich spreche nicht deutsch, I shall be both understood and believed.
I think your examples don't work because there is not a strict set of rules in them.
Hast du nicht etwas Gelt für mich? — Hast du kein Gelt für mich?
That's the whole point of formal systems.
01:12
@DavidWallace Hehe, yes.
And that's why chess (or any other board game) is a better analogy.
It is a bit like I speak not German.
@Cerberus Are you saying that these two are equally good? "nicht etwas" sounds skodie to me.
hm.. what about "square root of -1", does that point to incompleteness?
@DavidWallace I would think it was acceptable.
01:13
TIL then.
Or consider this. Ich spreche kein Deutsch, aber Französisch. — Ich spreche nicht Deutsch, aber Französisch.
I would probably say Hast du etwas Gelt für mich? - no point in being unnecessarily pessimistic.
And Ich spreche Französisch, aber kein Deutsch.
There's nothing wrong with sqrt(-1).
I speak not German, but French — I speak no German, but French.
It cannot be done, can it? It can only be substituted by "i", so that you can go one with calculation
01:16
sqrt(-1) = 1i
Or Je parle francais, mais je ne parle pas Allemand. Then I'll definitely be believed.
kk
@DavidWallace I am imagining a specific context, obviously, where someone has just asked you, sprichst du Deutsch?
I would still answer the same.
It's better to give an alternative; otherwise they don't know what to talk to you in.
A better example along these lines would be division by zero.
01:17
But you could also pull not into the scope of the object only (as opposed to the verb).
But that's not about incompleteness, because it's stated at the outset that there is no pair x, y so that x/0 = y
maybe it is, if the consistence of it could only be proved outside the system
or not?
There's no need to prove it. It's part of the definition of the function.
If the system is consistent, it cannot be complete.
The consistency of the axioms cannot be proven within the system.
i thought it could be the second case
Yes, consistency is another matter. It's as if you could prove that Fermat's last theorem is both true and false.
I mean, different proofs leading to contradictory results.
01:20
I do not understand the purpose of this conversation. Are you guys philosophizing about anything?
7
it all began with "what is category theory? what is set theory? are paradoxes allowed?"
then.. "Godel's theorem"...
ok
@DavidWallace In any case, as you say, you would normally say ich spreche kein Deutsch as I suggested to Tames, but in some cases nicht is possible, mainly if you echo something the other person said.
which might help understand what's wrong with "colorless green ideas sleep furiously" lol
01:23
@Cerberus I bow to your superior knowledge.
Otavio was trying to give me a concrete example of what is incompleteness in a system
@DavidWallace Me too.
bows to Cerberus
hail to @Cerberus
the canine trinity of hell
@DavidWallace Don't bow too deeply, then; I am using a combination of what I know of German and Dutch, the latter of which having the same distinction between niet and geen. You would normally never say ik spreek niet Duits, except if it served to contrast Duits with something else. It places heavy sentence emphasis on Duits.
@Tames LOL that sounds much better than what I call him!
01:25
@Tames Haha, I appreciate it. My favourite epithet.
so @OtavioMacedo, in the case of x/0=y... I could picture that... given x/z=y, you could substitute z for any number, except for 0, because when you do it.. it doesn't make sense?
@DavidWallace what do you call him?
@Tames gives @Cerberus a kiss in the cheek
@Tames Except that in poetry, x/0 could make sense. In language, everything is possible in some context. Context is everything. You can't really explain any linguistic phenomenon without taking context in consideration, I would say, if only the implicit intuitions that are also part of it.
@Tames I generally use the expression "tri-cephalic mutt", but "canine trinity of hell" has a much nicer ring to it.
Hey!
There's a song by the Eurythmics called "Two divided by zero". I think it's a love song.
01:29
There you go.
Add to that the fact that it has been uttered here in chat.
The whole song?
You may utter the whole song here if you feel the need. But please do so in a pastebin link.
@Tames Cerberus is right. That's why I think the leap from formal systems to natural language semantics may not make sense.
I don't think pastebin links are long enough.
Oops
Wrong reply hehe
01:33
@OtavioMacedo but you may try to leap, and see how far can you go, and then you'll find out what's special about natural languages
I know it's not going to fit completely
that's precisely the interest
formalization is always a reduction, otherwise it wouldn't be useful at all
@Tames Ok. That makes sense.
@DavidWallace Oh no! Well, then sing it in a Youtube video and link it to us?
Let's hope we will be able to listen to it before the copyright Nazis censor it.
@Tames What's special about natural languages is that the obvious part, like a sentence, is only the tip of the iceberg: the implicit context is also part of the language. The tip alone cannot do anything.
And actually even unnatural languages have some icebergs hanging under them, but they are just smaller, or different.
@Cerberus Yeah, I know how much you like my voice.
@DavidWallace You know I love it! Especially when you say Kruif.
I thought you preferred tomatoes.
01:38
what is Kruif?
Yes, I like tomatoes.
Not tomaytoes.
@OtavioMacedo thanks so much for the explanation. I think it is clearer now... but I should really get started with Aristotle and from there move on towards more complex stuff lol
@Cerberus I could provide you with both.
You already have, thank you.
01:41
I'm trying to find out how that Turing machine on google works.. any ideas?
I loved it when they put on moog.. has anyone seen that?
@Tames It wouldn't be too hard to write in Flash.
oh, I didn't mean "how it was done", but how to play with it
I finished the Turing game without understanding it, hehe.
I was too lazy.
in English Language and Usage, 2 hours ago, by MetaEd
But I do want to say in my defense that I failed for lack of interest.
I just tried what worked until I had all the letters.
so you have a sequence.. and it seems like you should reproduce it... the only thing that changes is, when you press "0" it turns into "1"
when i press the arrows, nothing seems to happen
@DavidWallace But oh gad there's no tomeytoes.
01:47
Last time I was in USA, there really were no tomatoes.
May 27 at 3:00, by Cerberus
https://www.dropbox.com/s/5dcsqwz9ahtc7c9/tomatoes2.wmv
@Cerberus and @OtavioMacedo, yesterday I saw something that confirmed the "L"-"R" thing.. some girls were talking, and one said to the other "você está rouca?" (are you hoarse?), and she answered "o que?? louca??" (what?? crazy?)
hahah
Is that one of those Portuguese anomalies, like D and J?
Huh wait, what are L and R?
Ohhh.
I get it.
I was thinking of keys on the Gamecube controller...wake up, Cerberus!
they sound really different, but it seems that in the global experience of the sound of the word, they are almost the same
hahaha
But Otavio said that it also happened with l and other consonants. As in lembro.
Where the m becomes an l.
01:53
yes, me lembro disso! but i don't remember ever seeing someone making confusion on this.. hmm
I know l–r swapping is common in many languages.
For example Latin caelum, "sky, heaven".
I just remember monty python's on this... hilarious..
do you like MP?
The adjective should be cael-u-lus, but owing to dissimilation it becomes caer-u-lus.
I like some PM, yes.
it was like.. a caesar who swapped r for L
and everybody laughed at him
there is one sketch on this, and i think it appears again in "the life of brian" (blian)
I love MP!
Hehe.
01:59
that John Cleese guy is so hilarious.. he's the best, because he's always the most bizarre and serious at the same time..
minister of silly walks lol
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