Logic and Foundations of Mathematics Commons^™

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 …