The Logic of Is

Bertrand Russell adopted Frege’s predicate logic as his primary philosophical method, a method he thought could expose the underlying structure of philosophical problems. For example, the English word “is” has three distinct meanings by predicate logic:

• For the sentence ‘the cat is asleep’, the is of predication means that “x is P” (denoted as P(x))
• For the sentence ‘there is a cat’, the is of existence means that “there is an x” (∃x);
• For the sentence ‘three is half of six’, the is of identity means that “x is the same as y” (x=y).