Fri Sep 20, 2013
60 Evans Hall, 4:10–6 PM
Lotfi A. Zadeh (UC-Berkeley)
Truth and Meaning
The theory which is outlined in my lecture, call it RCT for short, is a departure from traditional theories of truth and meaning, including correspondence theory, coherence theory, possible-world semantics and truth-conditional semantics. The principal objective of RCT is construction of a procedure which on application to a proposition, p, drawn from a natural language leads to: (a) a mathematically well-defined meaning of p; and (b) truth value of p.
The centerpiece of RCT is the concept of a restriction. Informally, a restriction, R(X), on a variable, X, is a limitation on the values which X can take. Typically, a restriction is described in a natural language. Simple example. Usually X is significantly larger than a, where a is a real number. The canonical form of a restriction is: X isr R, where X is the restricted variable, R is the restricting relation, and r is an indexical variable which defines the way in which R restricts X.
There are two key postulates in RCT. First, the meaning postulate, MP. MP asserts that the meaning of p is a restriction, X isr R, in which X, R and r are implicit in p. This restriction is referred to as the canonical form of p. Second, the truth postulate, TP, which asserts that the truth value of p is the degree to which X satisfies R.
In RCT, a proposition, p, is associated with two truth values—internal truth value and external truth value. The internal truth value modifies the meaning of p. The external truth value relates to the degree of agreement of p with factual information. In the definition of truth value which was stated earlier, the truth value is internal. In RCT, truth values are numerical, taking values in the unit interval, or linguistic, e.g., very true, not quite true, more or less true, usually true, etc.