Speculative as opposed to analytical philosophy is centrally concerned with the concept of activity, understood as the activity of actualization which makes things what they are. Moreover, speculative philosophy has characteristically maintained that the activity of actualization is self-explanatory in the sense that it is defined in terms of a distinct kind of entity (substance, God, the Absolute) which has necessary existence or whose existence is not derived from anything except itself. It will be argued here that the hitherto unrecognized significance of Alfred North Whitehead (1861-1947) [1] resides in the fact that he fuses together a speculative philosophy of activity and logical analysis by drastically reinterpreting the nature of the mathematical function and redefining the self-explanatory in terms of the applicability or descriptive adequacy of his functional analysis to the nature of things.