Paradox

Date: 05/07/2001 at 17:31:55
From: Ariel Klugman
Subject: Paradox

What is a paradox? How does it work? Is it right?

Date: 05/08/2001 at 14:33:33
From: Doctor Twe
Subject: Re: Paradox

Hi Ariel - thanks for writing to Dr. Math.

According to the Merriam-Webster OnLine Dictionary at:

   http://www.m-w.com/home.htm   

a paradox is:

   1:  a tenet contrary to received opinion

   2a: a statement that is seemingly contradictory or opposed to 
       common sense and yet is perhaps true

    b: a self-contradictory statement that at first seems true

    c: an argument that apparently derives self-contradictory 
       conclusions by valid deduction from acceptable premises

   3:  one that possesses seemingly contradictory qualities or phases

In math, we usually use the term in the context of definition 2a. The 
key is that a paradox *seems* to be contradictory, but is in fact true 
or valid. 

Here is an entry from our Ask Dr. Math archives that discusses the 
difference between a paradox and a fallacy:

   Paradox and Fallacy
   http://mathforum.org/dr.math/problems/lee.01.25.01.html   

Some famous math paradoxes include:

   Russell's Paradox
   http://mathforum.org/dr.math/problems/weibel7.2.96.html   
   http://mathforum.org/dr.math/problems/mcallister3.25.98.html   

   Zeno's Paradox
   http://mathforum.org/dr.math/problems/bearclaw.8.22.96.html   
   http://mathforum.org/dr.math/problems/gut10.19.html   

   The Infinity Hotel Paradox
   http://mathforum.org/dr.math/problems/evening.9.15.99.html   

   The Unexpected Exam Paradox
   http://mathforum.org/dr.math/problems/mcdaniel3.26.98.html   

   Bertrand's Paradox
   http://mathforum.org/dr.math/problems/krasik.05.09.99.html   

I hope this helps. If you have any more questions, write back.

- Doctor TWE, The Math Forum
  http://mathforum.org/dr.math/