Put another way, it is objectionable to insist that a function exists based on the Axiom of Choice, and then to derive results based on the existence of that function, when in fact there is no known example of such function and no algorithm for identifying it. This objection to use of the Axiom of Choice is analogous to the objection to the use of non-[[falsifiable]] claims in science. It strains logic to insist that something is true when it cannot be verified, and if it were false no one would even know. | Put another way, it is objectionable to insist that a function exists based on the Axiom of Choice, and then to derive results based on the existence of that function, when in fact there is no known example of such function and no algorithm for identifying it. This objection to use of the Axiom of Choice is analogous to the objection to the use of non-[[falsifiable]] claims in science. It strains logic to insist that something is true when it cannot be verified, and if it were false no one would even know. |