is human”⁠—then the various values of f ⁡ x form a set of propositions. We may extend the idea “not- p and not- q ” so as to apply to the simultaneous denial of all the propositions which are values of f ⁡ x . In this way we arrive at the proposition which is ordinarily represented in mathematical logic by the words “ f ⁡ x is false for all values of x ”. The negation of this would be the proposition “there is at least one