Whitehead and Process Philosophy
Alfred North Whitehead (1861–1947) was an accomplished mathemetician and philosopher. It is believed by many that the most significant of his contributions to philosophy was his effort to formalize process philosophy by constructing a thorough metaphysical framework and vocabulary based on process.
I am not as yet convinced of the efficaciousness of his metaphysics. Unfortunately, much of Whitehead's rigorous, formal approach is difficult to interpret and internalize, and it also overlies some fairly transparent personal biases of Whitehead.
A process-based world view is intrinsically relational. It recognizes no discrete stuff or annihilation thereof, but only processes that may sometimes take the form of discrete things.
By virtue of this fluid perspective, death loses some of its sting because everything is part of a flow: nothing every really "is" but is ever in a state of "becoming". This kind of deathlessness is referred to as "objective immortality" in process circles.
For similar reasons, process thinking lends itself to panpsychism, or more precisely, what process philosopher David Ray Griffin has termed "panexperientialism". I am partial to such a doctrine because I consider the more modern alternative of "vacuous actuality" psychologically unpalatable, but what really motivates me to defend panexperientialism is existentialist logic.
The suggestion that subjective experience somehow emerges from the objective at some level of complexity is—frankly—absurd. I am utterly convinced that experience must be universal. Process thought is allied with this conviction, but I reject the notion that panexperientialism must depend upon Whitehead's metaphysics. Rather, I consider it a simple matter of logic: the subjective is more fundamental to human experience than the objective. If either is derivative of the other, the derivative is the objective. I do not propose pure subjectivism here, nor any basis for free will or vitalism, but simply that experience is fundamental to existence.
The primary physicalist objection to panexperientialism is that it doesn't actually explain how consciousness emerges. I would simply reply that it is easier to explain the emergence of consciousness from experience than to explain the emergence of consciousness from the void of non-subjectivity that pure objectivism posits.
References
Whitehead Special Relativity and Simultaneity, by Villard Alan White
Physicalism and Panexperientialism: Response to David Ray Griffin, by Jaegwon Kim
The Principles of Psychology, by William James.