Re: wittgensteins Tractarian logic any suggestions.?

On 20 Mar 2007 10:25:42 -0700, "translogi" <wilemien@xxxxxxxxxxxxxx> wrote:


I am not sure if Wittgenstein invented the truth tables, around the
same time Post published about them, probably they were independent.

Yes. General wisdom is that they developed them independently. Actually,
Peirce was the first to come up with truth tables --- but this only was
discovered much later.

I guess, Quine's statements (if not taking into account Peirce's early
usage of truth tables) are quite reasonable:

"The pattern of reasoning that the truth table tabulates was Frege's,
Peirce's, and Schröder's by 1880. The tables have been prominent in
literature since 1920 (Lukasiewicz, Post, Wittgenstein)." (W. V. O. Quine).

"Truth tables, and the graphic method of calculation which they
provide, came only in 1920-21 (Lukasiewicz, Post, Wittgenstein); but much
the same technique in non tabular form was made known by Peirce in 1885, an
is indeed implicit in Boole's <<general rule of development>> (_Laws of
Thought_, p. 75 f)."

(W. V. Quine, Mathematical Logic)

Concerning Peirce, see:
http://www.digitalpeirce.fee.unicamp.br/lane/trilan.htm

Quote:

"Peirce's Three-valued Connectives

Charles Peirce was the first logician to define logical operators for a
many-valued system of logic. In February 1909, on three pages of a notebook
in which he recorded his thoughts on logic (MS 339), he defined several
three-valued connectives using the truth-table, or matrix, method. The
system of triadic logic that Peirce envisioned employs the values "V", "F",
and "L". He interpreted "V" and "F" as "verum" ("true") and "falsum"
("false"), respectively, and he interpreted the third value, "L", as "the
limit."

Peirce's work on many-valued logical connectives was first brought to light
by Max Fisch and Atwell Turquette (1966). As Fisch and Turquette describe,
it had long been thought that Jan Lukasiewicz (1920, 1930) and Emil Post
(1921) had developed the first operators for three-valued logic. But Peirce
is now recognized as the first to use the truth-table method to define
three-valued operators. Subsequent to the publication of Fisch and
Turquette's paper, the formal aspects of Peirce's three-valued connectives
were explored extensively by Turquette (1967, 1969, 1972, 1973, 1976, 1978,
1981/4)."


F.


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