Why p and q?

Date: 11/29/2001 at 09:59:31
From: Laurie Schroeder
Subject: Logic

Dr. Math:

I am teaching a unit of logic to my seniors and also cover it briefly 
in geometry. We are wondering why the letters p and q are used to 
abbreviate statements. We understand it's simpler that way, but why 
were these letters chosen? I have looked in the books where I get my 
information on logic - but can't find an answer. Thank You.

Laurie Schroeder

Date: 11/29/2001 at 10:09:24
From: Doctor Tom
Subject: Re: Logic

Hi Laurie,

"p" stands for "proposition" -- a statement that's either true or 
false. Then when you talk about a second proposition, people just tend 
to use nearby letters. Just as "x" was used for a generic unknown in 
algebra, where if you need two or three unknowns, "y" and "z" are 
usually chosen.

Jeff Miller's Earliest Uses of Symbols of Set Theory and Logic at 
http://members.aol.com/jeff570/set.html    says that

   "p, q, and r were used as "propositional letters" in 1910 
    by Alfred North Whitehead and Bertrand Russell in the 
    first volume of Principia mathematica."

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

Date: 11/29/2001 at 10:14:10
From: Doctor Achilles
Subject: Re: Logic

Hi Laurie,

That's a good question. I don't know for certain, but I have a couple 
of suspicions.

First, P is the first letter of the word "proposition". Old logic 
texts sometimes say something like "assume a proposition P" and then 
go on to prove something about P. Q is just the next letter after P, 
so when you need another proposition to assume, it's an easy and 
convenient letter to use.

Second, P and Q are in the middle of the alphabet and weren't really 
being used anywhere else.  u, v, w, x, y, and z are usually used for 
variables.  a, b, c, and d are usually used for generic constants 
(like the constants in a quadratic equation: ax^2 + bx + c).  f, g, 
and h are used for functions, as in f(x).  i, j, and k are used in 
coordinate systems and sometimes with imaginary numbers.  m and n are 
used for integers. That leaves p, q, and r as convenient letters to 
use for logic.

I think that these two reasons are more or less jointly responsible 
for the convention.

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