The speculative generalization of the function: A key to Whitehead

In Process and Reality (1929) and subsequent writings, A.N. Whitehead builds on the success of the Frege-Russell generalization of the mathematical function and develops his philosophy on that basis. he holds that the proper generalization of the meaning of the function shows that it is primarily to be defined in terms of many-to-one mapping activity, which he terms 'creativity'. This allows him to generalize the range of the function, so that it constitutes a universal ontology of construction or 'process'. He analyzes the concept of God in terms of functional mapping to structure, and he defines finite entities as iterative 'occasion' of mapping activity. He thus challenges the widespread logical-analytical view that the connectives and variables of a function in its different instantiations are merely numerically different, and he develops a fallibililst theory of activity as essentially serial in nature.