Open Access. Powered by Scholars. Published by Universities.®
Logic and Foundations of Mathematics Commons™
Open Access. Powered by Scholars. Published by Universities.®
Articles 1 - 2 of 2
Full-Text Articles in Logic and Foundations of Mathematics
What Do We Mean By Logical Consequence?, Jesse Endo Jenks
What Do We Mean By Logical Consequence?, Jesse Endo Jenks
Summer Research
In the beginning of the 20th century, many prominent logicians and mathematicians, such as Frege, Russell, Hilbert, and many others, felt that mathematics needed a very rigorous foundation in logic. Many results of the time were motivated by questions about logical truth and logical consequence. The standard approach in the early part of the 20th century was to use a syntactic or proof-theoretic definition of logical consequence. This says that "for one sentence to be a logical consequence of [a set of premises] is simply for that sentence to be derivable from [them] by means of some standard system of …
A Foundation For Arithmetic, Kevin Halasz
A Foundation For Arithmetic, Kevin Halasz
Summer Research
This paper contains a proof of Frege's Theorem: the statement, first discovered by George Boolos, that Gottlob Frege's failed proof of the analyticity of arithmetic could be slightly altered so as to provide an axiomitization of arithmetic with just one proposition. After an expository treatment of the mathematical work in Frege's 'Foundations of Arithmetic,' the work in which Frege presented his failed proof, a novel, and particularly succinct, proof of the Theorem is provided.