t least two authors of historical importance.Bertrand Russell and Alfred North Whitehead in their Principia Mathematica (1910–1913) use the word matrix in the context of their Axiom of reducibility. They proposed this axiom as a means to reduce any function to one of lower type, successively, so that at the “bottom” (0 order) the function is identical to its extension:“Let us give the name of matrix to any function, of however many variables, which does not involve any apparent variables. Then any possible function other than a matrix is derived from a matrix by means of generalization, i.e., by considering the proposition which asserts that the function in question is true with all possible values or with some value of one of the arguments, the other argument or arguments remaining undetermined”.[97]For example a function Φ(x, y) of two variables x and y can be reduced to a collection of functions of a single variable, e.g., y, by “considering” the function for all possible values