facebook Twitter RSS Feed YouTube StumbleUpon

Home | Forum | Chat | Tours | Articles | Pictures | News | Tools | History | Tourism | Search

 
 


Go Back   BanglaCricket Forum > Miscellaneous > Forget Cricket

Forget Cricket Talk about anything [within Board Rules, of course :) ]

Reply
 
Thread Tools Display Modes
  #1  
Old October 3, 2003, 09:48 AM
oracle oracle is offline
Cricket Legend
 
Join Date: July 25, 2003
Location: U.A.E
Posts: 3,750
Default "A new way to analyse self-referential and contradictory sentences" (2003 thread)

This thread is dedicated to the valiant debaters of the previous thread @ international topics, i.e " Comparing batsmen in an objective approach".
Spread the word of fuzzy logic in cricket.


SOURCE: http://www.economist.com/science/dis...ory_id=2099851

A new way to analyse self-referential and contradictory sentences

EPIMENIDES the Cretan, a philosopher of the 6th century BC, is said to have uttered the sentence, All Cretans are liars. As he himself was a Cretan, this gave rise to a paradoxif he were telling the truth, then he would be a liar. Depending on how one defines a liar, the paradox is resolvable; he could have been a habitual liar who was telling the truth in this one instance. However, a stronger version of the paradox, known as the Liar paradoxthis sentence is falseis not resolvable in conventional logic systems.

Indeed, the circular loop that the sentence inducesif it is false, it must be true, and if true, falsehas been used more than once in science-fiction movies to cause marauding computers to lose their sanity and explode. But in a new paper, Kostis Vezerides of the American College of Thessaloniki, and Athanasios Kehagias of the Aristotle University of Thessaloniki, in Greece, show that, in almost all cases, paradoxes such as the Liar are resolvable with the use of fuzzy logic.
Traditionally, logicians have made a stark distinction between truthhood and falsity. A statement was considered to be either true (given a truth value of one) or false (a value of zero). In the 1960s, Lotfi Zadeh of the University of California at Berkeley came up with the catchy innovation of fuzzy logic. In this system, things could be sort-of true, or only partially false. A truth value of 0.5 meant that a statement was half-true, and so forth.

In 1979, Dr Zadeh was the first to apply fuzzy logic to self-referential sentences, which can give rise to paradoxes like the ones above. (Not all self-referential sentences are paradoxicalconsider this sentence is true.) He reasoned that the Liar sentence is exactly half-true. But more complicated self-referential paradoxes are trickier to resolve. One example is the inconsistent dualist, which can be thought of as a pair of brothers, one of whom asserts the other is lying, while the other says his brother is telling the truth.

Earlier work had shown how assigning fuzzy values to self-referential sentences could give rise to mathematical chaos. This is because the systems of equations that must be solved to determine the truth-values are often non-linearso attempts to find a solution can rarely be found in the general case, but must be found numerically, closing in on the answer through several iterations of trial and error.

Dr Kehagias and Mr Vezerides, though, set out to find consistent solutions to fuzzy truth equations without chaotic oscillations. The first part of their insight is simple. Using an existing result from calculus called Brower's Fixed-Point Theorem, they proved that at least one solution could be found. They then tried several different numerical algorithms for finding that solution. The simplest is an extension of an idea that Isaac Newton himself had, which uses approximations to the non-linear equations to find their solutions. The method that seems to work best is borrowed from control theory, the science of how to operate complicated systems (such as aircraft or chemical plants).

For the comparatively simple case of the Liar, these methods all agree with Dr Zadeh's proof that the sentence is exactly half-true. The two brothers of the inconsistent dualist are also each telling exactly a half-truth. Indeed, the pair show that any set of self-referential sentences that assert complete truth or falsity about one another are exactly half-true. (Though other solutions are possible as well.) Other fractional truth-values arise when the sentences themselves make fuzzy assertions.

Dr Kehagias suggests two directions for further research. The first is to examine the various mathematical algorithms of fuzzy logic from the point of view of psychological authenticity. Since there might be more than one logically consistent solution to a problem, the idea would be to enable a computer to arrive at the same truth value that a human would, by reasoning in a similar fashion. The second possibility is to devise a form of logic that is in between fuzzy logic and normal, true-or-false binary logic. Rather than the infinite choices of fuzzy logic, or the two in binary logic, this would have options for false, true, sort of true, sort of false, and exactly half-way. Epimenides the Cretan would surely have approved, or disapprovedor, most likely, something in between.:P:P
Reply With Quote

  #2  
Old October 3, 2003, 02:54 PM
Arnab Arnab is offline
Cricket Legend
 
Join Date: June 20, 2002
Location: BanglaCricket.com
Posts: 6,069

I always wanted to learn about fuzzy logic. May be I should pick up a book or two from the library.
Reply With Quote
  #3  
Old September 29, 2010, 07:03 PM
Zeeshan Zeeshan is offline
Banned for 2 weeks
 
Join Date: March 9, 2008
Location: Ω
Posts: 31,128

Wow! And only 1 reply??? I believe this can do more talking. Reading Kosko's book.
Reply With Quote
  #4  
Old September 29, 2010, 07:43 PM
Nasif's Avatar
Nasif Nasif is offline
Administrator
BanglaCricket Development
 
Join Date: October 4, 2002
Location: USA
Favorite Player: Mashrafe Mortaza
Posts: 9,048

Quote:
Originally Posted by ZeeshanM
Wow! And only 1 reply??? I believe this can do more talking. Reading Kosko's book.
There were only 40/50 members back then. There are many threads with 1 or 0 response
__________________
They said, "After we turn into bones and fragments, we get resurrected anew?!" Say, "Even if you turn into rocks or iron.[17:49-50] |Wiki: Cold Fusion occurring via quatum tunnelling in ~101500 years makes everything into iron.
Reply With Quote
  #5  
Old September 29, 2010, 09:11 PM
Ajfar's Avatar
Ajfar Ajfar is offline
Cricket Sage
 
Join Date: February 27, 2006
Location: Connecticut
Posts: 17,780

Quote:
Originally Posted by Nasif
There are many threads with 1 or 0 response
hey that sounds very much like Zeeshan bhai's threads lol
__________________
"I was the happiest man in the world, happier than Bill Gates"- Tamim Iqbal
Reply With Quote
  #6  
Old September 29, 2010, 10:13 PM
Zeeshan Zeeshan is offline
Banned for 2 weeks
 
Join Date: March 9, 2008
Location: Ω
Posts: 31,128

Can anyone suggest me some books on this topic in the line of popular books like those of Hofstadter or Smullyan's Forever Undecided?
Reply With Quote
  #7  
Old September 30, 2010, 12:51 PM
auntu's Avatar
auntu auntu is offline
Cricket Guru
 
Join Date: March 7, 2007
Location: elsewhere
Favorite Player: ZAR
Posts: 9,882

Quote:
Originally Posted by bangladesh_sy
hey that sounds very much like Zeeshan bhai's threads lol
*Like it*
__________________
﴾اَلَاۤ اِنَّ اَوۡلِيَآءَ اللّٰهِ لَا خَوۡفٌ عَلَيۡهِمۡ وَلَا هُمۡ يَحۡزَنُوۡنَ ۖ ۚ‏ ﴿۶۲
"Listen, the friends of Allah shall have no fear, nor shall they grieve" (Yunus: 62)
Reply With Quote
  #8  
Old September 30, 2010, 01:29 PM
Habib's Avatar
Habib Habib is offline
Cricket Guru
 
Join Date: August 30, 2007
Location: Dhaka, Bangladesh
Favorite Player: A few
Posts: 9,938

Quote:
Originally Posted by Nasif
There were only 40/50 members back then. There are many threads with 1 or 0 response
I feel like opening a thread called- 'Ice age of BC'.
__________________
Don't be a blind fan, be rational
Reply With Quote
Reply


Currently Active Users Viewing This Thread: 1 (0 members and 1 guests)
 
Thread Tools
Display Modes

Posting Rules
You may not post new threads
You may not post replies
You may not post attachments
You may not edit your posts

BB code is On
Smilies are On
[IMG] code is On
HTML code is On



All times are GMT -5. The time now is 10:46 AM.



Powered by vBulletin® Version 3.8.7
Copyright ©2000 - 2017, vBulletin Solutions, Inc.
BanglaCricket.com
 

About Us | Contact Us | Privacy Policy | Partner Sites | Useful Links | Banners |

© BanglaCricket