The two cultures of logic

Abstract

In his famous Rede Lecture of 1959, the physicist, novellist and polymath C.P.Snow put forward his thesis of the Two Cultures [13]. Snow observed that a gulf had appeared between two academic cultures, with engineers and scientists on one side, and scholars in the humanities on the other. Snow lamented that little communication went on across the gulf, so that most representatives of each of the two academic cultures lacks the most basic understanding, and appreciation, of the other. My thesis, in this written homage to Lotfi Zadeh, is that something akin to Snow's gulf runs through mathematical logic. For even though logic is a science, there are two types of logicians: on one side of the gulf are those who insist on using True and False (and, possibly, Indeterminate or Undefined) as the only possible truth values; on the other side are those logicians who embrace a wealth of different truth values, with True and False as the extremes of a continuum; to denote the latter area of work, which covers a large variety of approaches including (but not limited to) Fuzzy Logic, we shall loosely use the term multi-valued logic. © 2013 Springer-Verlag Berlin Heidelberg.