Process philosophy (or ontology of becoming) identifies metaphysical reality with change and dynamism. Since the time of Plato and Aristotle, philosophers have posited true reality as "timeless", based on permanent substances, whilst processes are denied or subordinated to timeless substances. If Socrates changes, becoming sick, Socrates is still the same (the substance of Socrates being the same), and change (his sickness) only glides over his substance: change is accidental, whereas the substance is essential. Therefore, classic ontology denies any full reality to change, which is conceived as only accidental and not essential. This classical ontology is what made knowledge and a theory of knowledge possible, as it was thought that a science of something in becoming was an impossible feat to achieve .
In opposition to the classical model of change as purely accidental and illusory (as by Aristotle), process philosophy regards change as the cornerstone of reality–the cornerstone of the Being thought as Becoming. Modern process philosophers include Henri Bergson, Charles Peirce, John Dewey, Alfred North Whitehead, Charles Hartshorne, Martin Heidegger, Friedrich Nietzsche, Nicholas Rescher, and Gilles Deleuze. In physics Ilya Prigogine distinguishes between the `physics of being' and the `physics of becoming'.
In Ancient Greek thought
The formal development of this theory begins with Heraclitus's fragments in which he posits the nous, the ground of Becoming, as agon, or "strife of opposites" as the underlying basis of all reality defined by change. That balance and conflict were the foundations of change and stability in the flux of existence.
In early twentieth century philosophy of mathematics, it was undertaken to develop mathematics as an airtight axiomatic system, in which every truth could be derived logically from a set of axioms. In the foundations of mathematics, this project is variously understood as logicism or as part of the formalist program of David Hilbert. Alfred North Whitehead and Bertrand Russell attempted to complete, or at least greatly facilitate, this program with their seminal book Principia Mathematica, which purported to build a logically consistent set theory on which to found mathematics. This project may have been ultimately defeasible, and afterwards Whitehead intuited that the entire venture was an organ of an overarching ontological mistake. He saw that science and mathematics were struggling to overcome an ontology of substances, and thus could not engage phenomena whose nature are more properly understood as 'process'. This resulted in the most famous work of process philosophy, Alfred North Whitehead's Process and Reality, a work which continues that begun by Hegel but describing a more complex and fluid dynamic ontology. While process thought does describe truth as "movement" in and through determinates (Hegelian truth), and not these determinates as fixed concepts or "things" (Aristotelian truth), process thought since Whitehead is distinguished from Hegel in describing complexes of occasions of experience that arise or coalesce in becoming, rather than being simply dialectically determined from prior posited determinates. It is also distinguished in being not necessarily conflictual or oppositional in operation. Process may be integrative, destructive or both together, allowing for aspects of interdependence, influence, and confluence, and addressing coherence in universal as well as particular developments, which aspects are not condign to Hegel's system. Additionally, instances of determinate occasions of experience, while always ephemeral, are nonetheless seen as important to define the type and continuity of those occasions of experience that flow from or relate to them.
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