Whitehead as Mathematician

Mathematicians work in a world between Science and Metaphysics, between proximal and ultimate causes. Whitehead worked as a scientist, mathematician and philosopher, finding commonality between these fields.

Mathematics is the tool specially suited for dealing with abstract concepts of any kind and there is no limit to its power in this field.— Paul A.M. Dirac (1902-1984), English physicist.

Whitehead's work in the second book of Principia Mathematica (Principles of Mathematics), a seminal work on the foundations of all mathematics, is indicative of the expression of his thought throughout his works. One deceptively simple but powerful entry ties together the abstract (the number "1") with the reality of a singular unity in the real world in the equation 1+1=2. This connection of the propositional and the actual provided the ground for all ideas and actualities, rendering them all 'forms' of process, tying them all into a continuum and ending the need for dualism.

Extending this work, the actual and the propositional are dynamic elements of the same process, one an instantaneous and the other a derivative expression, linked by a calculus of changes as experienced in the real world. Everything flows through states of balance, a punctuated equilibrium, yet never divided in time.

Whitehead joined the sensible and transcendent -- the pragmatic and aesthetic -- sign and referent -- past, present and future into a cohesive unity. He asks us, "How many realities can there be?"