Paradoxes

Originally posted by FabianFnas
But Russels paradox isn't a paradox anymore if you use modern logic definitions, is it?

I say that there are no paradoxes in a well defined logic.

Depends on your definition of "well defined". You can certainly define a logic system in a way that eliminates all paradoxes, but in doing so you will also eliminate some valid results that can be proven in stronger systems. Whether this is acceptable depends on what you are trying to do. (See also, for mathematical logics, Gödel.)

Richard

Originally posted by Shallow Blue
Depends on your definition of "well defined". You can certainly define a logic system in a way that eliminates all paradoxes, but in doing so you will also eliminate some valid results that can be proven in stronger systems. Whether this is acceptable depends on what you are trying to do. (See also, for mathematical logics, Gödel.)

Richard

I don't have the deep knoledge enough to understand the leaglity of the Russel paradox within the modern logic - I read it in a mathematical magazine once - but a logic system who accepts flaws is not a good one, and that is my opinion.

Never mind - it is just an academic question after all.

Originally posted by FabianFnas
I don't have the deep knoledge enough to understand the leaglity of the Russel paradox within the modern logic - I read it in a mathematical magazine once - but a logic system who accepts flaws is not a good one, and that is my opinion.

Never mind - it is just an academic question after all.

Different systems of logic are appropriate for different tasks .. for instance, quantum physics can make use of the ambiguity of a logic state as it more accurately reflects reality. Newtonian physics on the the other hand abhors the paradox .. it all depends on ones perspective 😉

Originally posted by HandyAndy
I think you're missing the point. When you copy something from a book or another source, unless it's obvious who the author is, you need to credit that source so people won't think the words are yours. Otherwise, it's plagiarism.

Are you a teacher? That's all our English teacher talked about for a week...plagiarism, plagiarism, plagiarism (even though I don't think this instance was)... 😉

Originally posted by FabianFnas
But Russels paradox isn't a paradox anymore if you use modern logic definitions, is it?

I say that there are no paradoxes in a well defined logic.

exactly, but human mathmatitions did not develop a perfect system for sets that's why this kind of errors occur.

Originally posted by wittywonka
Are you a teacher? That's all our English teacher talked about for a week...plagiarism, plagiarism, plagiarism (even though I don't think this instance was)... 😉

e.x.a.c.t.l.y

accually there is a class in my school called "LACA" for the stupid media things. if i post something onn the web, i don't mind people taking credict of it, because i post it. and so what? you combine the knowledge everybody give you and make it into your own.

Originally posted by wittywonka
What about the paradox: "Can an almight God (creator/force/God/etc.) make a rock so big that he couldn't move it?"

-If God is omnipotent, he should be able to make a huge rock big enough that he can't move it, but he should still be able to move it because he can do anything...

the answer is no...hehe lol

Yogi Berra (I think):

"I go to other people's funerals so they'll come to mine."

Originally posted by Ason Pigg2
e.x.a.c.t.l.y

accually there is a class in my school called "LACA" for the stupid media things. if i post something onn the web, i don't mind people taking credict of it, because i post it. and so what? you combine the knowledge everybody give you and make it into your own.

Would you publish a book with your name on it and fill it with material lifted verbatim from other books without giving credit to the other authors?

Originally posted by HandyAndy
Isn't this a fragment from Wikipedia? You should give credit.

Where did that story from the barber come from?

Originally posted by wittywonka
Are you a teacher? That's all our English teacher talked about for a week...plagiarism, plagiarism, plagiarism (even though I don't think this instance was)... 😉

Clearly teachers don't go on about it enough, because plenty of students keep doing it!

Originally posted by gonnawhoopyourass
Where did that story from the barber come from?

Probably from a recreational math collection or puzzle book. It's a version of Russell's Paradox, which is mentioned earlier in the thread. For the most part, questions come from websites, books, newspapers, magazines, memory and the creative minds of members.

Originally posted by Ason Pigg2
the answer is no...hehe lol

If God is omnipotent then yes he could be able to make a rock that he couldnt lift and lose his omnipotnce (now the rock is the god lol) so the rock after that (the new god) would be able to raise itself 😛
so then answer is YES and YES :p
second (if god is a spirit he cant lift anything ) 😛 🙂

i am goooood!!!

man i know u guys must be college students or somethin but with all this talk about mathamatical logic and stuff im completely confused. is there such thing as overusing wikipedia?

This paradox concerns numbers. Each number is expressed as words with a certain number of syllables (e.g. "four" has one syllable, "se-ven" has two). Imagine the smallest number which cannot be expressed in less than twenty syllables.

This expression "the smallest number which cannot be expressed in less than twenty syllables" however contains only nineteen syllables.

Hence the smallest number which cannot be expressed in less than twenty syllables can indeed be expressed in less than twenty syllables.