[The Monkey]

Quote:

Originally Posted by crappyjones123 /img/forum/go_quote.gif closing remarks - never say "logic is stupid" not because there might be a giant math nerd trolling the forums but because that very statement might be recursively paradoxical in the nth degree!

You, sir, are a giant math nerd.

I guess logic is--at once--stupid and not stupid?

 

[Voltron]

Quote:

Originally Posted by The Monkey /img/forum/go_quote.gif You, sir, are a giant math nerd. I guess logic is--at once--stupid and not stupid?

Sheesh, now the philosophy nerds are going to join into the fray!

 

[GlendaleViper]

Any room for the surreal absurdists to play around?

 

[Voltron]

Quote:

Originally Posted by GlendaleViper /img/forum/go_quote.gif Any room for the surreal absurdists to play around?

But of course!

 

[GlendaleViper]

Ah, if only some weirdo would make a feature-length cartoon starring ol' Sal's moustachio. Think of the adventures it would have!

 

[Mazz]

Quote:

Originally Posted by crappyjones123 /img/forum/go_quote.gif one possible interpretation of that in simple english is this...even the most basic math is inconsistent. that in itself does not bode well for higher math or for any other form of learning that has a mathematical basis.

Incomplete means there are truths about any given logical system that can only be shown by looking into the system from outside. You could say that it's a bit like not being able to paint the entire floor within a closed room - because you always have to leave a bit to stand on. But if there's a door you can open you can stand outside and paint the last piece.

But it's not inconsistent - that means something else entirely. A logical system may be inconsistent (because some of the axioms - the assumptions - and the rules contradict others). That means you can generally "prove" the same hypothesis to be both true and false depending on how you construct your proof from those axioms & rules - which isn't very useful (unless perhaps you are Schrödinger's cat - but that entity has other problems...)

Gödel was talking about consistent logical systems - where anything that can be proved is known for sure, and all valid reasoning about the same hypothesis must lead to the same conclusion. IIRC prior to his work the belief amongst mathematicians was that mathematics was complete - everything that was true about a system could be proved from within if only you were clever enough. His Incompleteness Theorem came as a great shock to the mathematics world.

Quote:

Originally Posted by crappyjones123 /img/forum/go_quote.gif closing remarks - never say "logic is stupid" not because there might be a giant math nerd trolling the forums

And never say "incomplete equates to inconsistent" when there's another maths/comp sci nerd around

But perhaps we should keep the volume down before the philosophy nerds are attracted by the apparent paradoxes...

 

[The Monkey]

Well, to bring us back OT (not that I care much), I went to CanJam intending to listen to a lot of 'stats. And that I did. And CanJam confirmed what I had thought for a long time: I like 'stats. I'm listening to my "new" vintage Stax rig at the moment, and it's the most excited I have been about a rig in a long time. If I hadn't started going to meets, I would have missed out on these phones. Lesson: go to meets, drink beer, argue about math.

 

[Dominat0r]

Well lets see, crappy forgive my meager math skills...

Monkey + Stats = Happy = Monkey sending HighLife his Balanced Desktop and DPS + HighLife's 650s + recabled.

 

[Grahame]

Gödel, Escher, Bach: an Eternal Golden Braid Definitely a mind altering read. In a good way.

There are known knowns.
These are things we know that we know.
There are known unknowns.
That is to say, there are things that we know we don't know.
But there are also unknown unknowns.
There are things we don't know we don't know.
Donald Rumsfeld

Who knew Rummy was a Gödel fan?

 

[aaron313]

My math:

Blue Hawaii pic + my eyes = wallet is $4,500 lighter.

 

[immtbiker]

Quote:

Originally Posted by Mazz /img/forum/go_quote.gif But perhaps we should keep the volume down before the philosophy nerds are attracted by the apparent paradoxes...

From my college days, I can say unequivocally (in an unequivocal manner) without fear of being ostracized, that paradigms are equal to 20 cents

 

[crappyjones123]

Quote:

Originally Posted by Mazz /img/forum/go_quote.gif Incomplete means there are truths about any given logical system that can only be shown by looking into the system from outside. You could say that it's a bit like not being able to paint the entire floor within a closed room - because you always have to leave a bit to stand on. But if there's a door you can open you can stand outside and paint the last piece. But it's not inconsistent - that means something else entirely. A logical system may be inconsistent (because some of the axioms - the assumptions - and the rules contradict others). That means you can generally "prove" the same hypothesis to be both true and false depending on how you construct your proof from those axioms & rules - which isn't very useful (unless perhaps you are Schrödinger's cat - but that entity has other problems...) Gödel was talking about consistent logical systems - where anything that can be proved is known for sure, and all valid reasoning about the same hypothesis must lead to the same conclusion. IIRC prior to his work the belief amongst mathematicians was that mathematics was complete - everything that was true about a system could be proved from within if only you were clever enough. His Incompleteness Theorem came as a great shock to the mathematics world. And never say "incomplete equates to inconsistent" when there's another maths/comp sci nerd around But perhaps we should keep the volume down before the philosophy nerds are attracted by the apparent paradoxes...

thank you for the correction. i did intend to say "incomplete." i am however working on a problem that involves extending a closed system to be both incomplete and inconsistent at the same time and i think that that is where the word inconsistent crept in. let me also add that i have gotten nowhere in the past 3 weeks since i started working on this problem. soooooooooooo...any ideas?

oh and not to worry. i represent the philosophy nerds as well. i just like talking about paradoxes in mathematical terms. they seem more drastic.

 

[ingwe]

Quote:

Originally Posted by Mazz /img/forum/go_quote.gif But perhaps we should keep the volume down before the philosophy nerds are attracted by the apparent paradoxes...

I post. Therefore I spam.

 

[immtbiker]

^

 

[crappyjones123]

Descartes to a tavern was drawn;
Took a table outside, on the lawn.
Said the serving wench, 'Dear,
Would you care for a beer?'
'I think not.' And like that, he was gone.
(Nester Macavity)

i think there was a cartoon of that joke as well but i cant seem to find it =/