4 Feb 2011 21:20

## Re: [] Re: Truth Tables (was Boolean Expansions)

It may be possible to push the date back a little farther than The Laws of Thought (1854).

In the chapter on hypotheticals in The Mathematical Analysis of Logic (1847), Boole writes,

"Thus is we associate the Propositions X and Y, the total number of conceivable cases will be found as exhibited in the following scheme.

1st X true, Y true . . . xy
2nd X true, Y false . . . x(1-y)
3rd X false, Y true . . . (1-x)y
4th X false, Y false . . . (1-x)(1-y)"

The cases in the above "scheme" are arranged in what Post would later call a "truth table."

My edition of The Mathematical Analysis of Logic was published by the Thoemmes Press in 1998. The passage I cite above is on p. 50 of this edition.

G.

Graham R. SHUTT
Voice: 206.726.9491
Email: grshutt <at> gmail.com
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On Fri, Feb 4, 2011 at 10:18 AM, John F. Sowa wrote:
Jon,

That is a good reference:

JA
There is a lot of preliminary discussion in ''The Laws of Thought''
where Boole may have telegraphed the basic principle ahead of his
main discussion, but I think what we're looking for can be found
in Chapter V, Proposition II, "To expand or develop a function
involving any number of logical symbols", pages 73-78 in the
Dover edition.  There is even a tabular display on page 76.

I agree that Boole states a procedure for taking an arbitrary
Boolean expression, assigning all combinations of values (0 for false)
or (1 for true) to its logical symbols (variables), and displaying
the results in a table-like form.

On page 73, Boole states Proposition II.

pp. 73 to 78 describe the method, and p. 76 shows an example
in a form that isn't as clearly a table as one would like,
but it could be called a table.

Therefore, I believe that the Wikipedia article should be
corrected as follows:

1. Boole (pp. 73-78) presented a method for enumerating
all possible truth values of a Boolean expression
and displayed the results of a sample evaluation
in a table on p. 76.

2. Other logicians, including Jevons, Peirce, Russell,
Wittgenstein, and Post developed variations of Boole's
method with more clearly drawn tables.  But the basic
idea was invented by Boole.  The name 'truth table'
was coined by Post.

I suggest that somebody take the trouble of updating Wikipedia
with appropriate citations.

John

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