Kenneth Rosen Edition 6th Exercise 1.1 Question 42 (Page No. 20)

Question

Fuzzy logic is used in artificial intelligence. In fuzzy logic, a proposition has a truth value that is a number between 0 and 1, inclusive.A proposition with a truth value of 0 is false and one with a truth value of 1 is true. Truth values that are between 0 and 1 indicate varying degrees of truth. For instance, the truth value 0.8 can be assigned to the statement “Fred is happy,” because Fred is happy most of the time, and the truth value 0.4 can be assigned to the statement “John is happy,” because John is happy slightly less than half the time. Use these truthvalues to solve below exercise.

Is the assertion “This statement is false” a proposition?

Answer 1

The statement is a paradox. It is not possible to assign a consistent truth value to the statement because it contradicts itself. For example, lets assume it is a proposition and it is true. This statement is false leads one to conclude that the statement itself is false, which is in contradiction with the assumption. If it was assumed the proposition is false, then this statement is false is false which means this statement must be true, which is also a contradiction.