Emil Post
“I study Mathematics as a
product of the human mind and not as absolute.” (Post – 1920)
Life:
Emil Leon Post was born in Augustów, a Russian city, in February 11
1897 and died April 21, 1954. His parents, a Jewish family, immigrated to
America in May 1904 when he was a kid. In his childhood his first love was
astronomy, after Post suffer an accident - a car crashed into other car, and he
was in the middle – he lost his left arm, and because of this, he could not
follow this profession. He started to show interest to math and attended to Townsend
Harris High School, graduated in City College of New York in Math and obtained
his Ph.D. in Math at Columbia University.
Work:
In his
first paper Post talked about the Principia Mathematica and proved the
consistency as well as the completeness of the propositional calculus as
developed in Whitehead and Russell’s Principia Mathematica. He did that using truth-tables (Introduced by C. S
Peirce and Schröder). From this paper
came general notions of completeness and consistency. For post, a system is
complete if every well-formed formula can be proved after introducing a
well-formed formula that is not provable. A system is consistent if well-formed formula
consisting of only a propositional variable is provable. He
also introduced in this paper multivalued systems of propositional logic and
introduced multivalued truth tables in analyzing them.
Post also created the “Post
production system” – cited in the MU-puzzle, GEB book – a system that work with
strings basically. Post production system is a string-manipulation system that
start with a string (A collection of characters) and then applying some rules
you can transform/modify this string – Like the MU-puzzle-, this system
generates what we call “Formal language”, and this language is composed by the
tokens, symbols or letters formed by the rules. From this, we can obtain the
recursively enumerable languages – If you have a set S and you have a recursive
function whose domain is exactly S then you have a recursively enumerable
language.
He also did some work in 1920
obtaining the same results that Kurt Godel obtained in his theory in 1930. Post
theory was fundamental to the progress of the theory of recursive functions.
References:
Web site:
http://www.ualberta.ca/~francisp/Phil428.526/UrquhartPost.pdf ; Accessed: 2/4/2015
http://www.encyclopedia.com/doc/1G2-2830903487.html ; Accessed: 2/4/2015
http://www-history.mcs.st-andrews.ac.uk/Biographies/Post.html ; Accessed: 2/4/2015
Image:
http://www.pucsp.br/~logica/Post.jpg ; Accessed: 2/4/2015
