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/ |
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