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Russell, extending the work of Gottlob Frege, who had similar thoughts, proposed according to his 'theory of definite descriptions' that when we say "the present king of France is bald", we are making three separate assertions: 1.) there is an x such that x is the king of France 2.) there is no y, y not equal x, such that y is the king of France (ie. x is the only king of France) 3.) x is bald. Since assertion 1. is plainly false, and our statement is the conjunction of all three assertions, our statement is false. Similarly, for "the present king of France is not bald", we have the identical assertions 1. and 2. plus 3.) x is not bald so "the present king of France is not bald", because it consists of a conjunction, one of whose terms is assertion 1. ("there is a king of France") is also false. The law of the excluded middle is not violated because by denying both "the king of France is bald" and "the king of France is not bald," we are not asserting the existence of some x which is neither bald nor not bald, but denying the existence of some x which is the king of France. |
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