In Greek, ‘to apeiron’ means ‘the infinite’: ‘a’ denotes privation and ‘peras’ the notion of ‘limit’ or ‘bound’. Etymologically, the English word ‘infinite’ comes from the Latin word ‘infinitas’: ‘in’ = ‘not’ and ‘finis’ = ‘end’, ‘boundary’, ‘limit’, ‘termination’, or ‘determining factor’. In contemporary English, there is a range of uses of the word ‘infinite’:
In a loose or hyperbolic sense, ‘infinite’ means ‘indefinitely or exceedingly great’, ‘exceeding measurement or calculation’, ‘immense’, or ‘vast’.
In a strict but non-mathematical sense that reflects its etymological history, ‘infinite’ means ‘having no limit or end’, ‘boundless’, ‘unlimited’, ‘endless’, ‘immeasurably great in extent (or duration, or some other respect)’. This strict, non-mathematical sense is often applied to God and divine attributes, and to space, time and the universe.
There is also a strict, mathematical sense, according to which ‘infinite’ quantities or magnitudes are those that are measurable but that have no finite measure; and ‘infinite’ lines or surfaces or volumes are measurable lines or surfaces or volumes that have no finite measure.
- Easwaran, Kenny, Alan Hájek, Paolo Mancosu, and Graham Oppy, "Infinity", The Stanford Encyclopedia of Philosophy (Winter 2021 Edition), Edward N. Zalta (ed.), URL = <https://plato.stanford.edu/archives/win2021/entries/infinity/>.
"Ever since people have been able to reflect, they've been captivated and puzzled by the infinite in its many varied guises. By the endlessness of space and time. By the thought that between any two points in space, however close, there's always another. By the fact that numbers go on forever. And by the idea of an all-knowing all-powerful God. People have been by turns attracted, fascinated, perplexed and disturbed by these various different forms of infinity".
In Whitehead's philosophy, God is both infinite and limited in different aspects.
a) God's Infinity in Actualization: According to Whitehead, God's ongoing life includes the entirety of past events. This means that God's existence comprehensively encompasses the historical unfolding. In this sense, God's infinity in actualization implies that nothing is excluded or lacking in God's understanding and inclusion of all that has happened.
b) God's Infinity in Potentiality: Whitehead also recognizes God's potential infinity. God's ongoing life is characterized by continuous process and becoming. As time progresses, God's existence expands to incorporate new experiences, events, and possibilities. This potential infinity suggests that God's ongoing life embraces a future that is ever-growing and evolving, encompassing more possibilities and potential than the present.
c) God's Infinity of Love and Empathy: Whitehead describes God's love and empathy for the world as qualitatively unique and infinite. This means that God's understanding, care, and connection with everything that transpires in the world surpass our finite comprehension. God's love is boundless in its depth, encompassing an extraordinary level of empathy for all beings.
On the other hand, Whitehead's philosophy acknowledges certain limitations regarding God:
a) God's Non-Infinite Power: In contrast to traditional conceptions of an all-powerful God, Whitehead's philosophy suggests that God is not infinitely powerful. Instead, power is understood to exist within the world itself. The entities and processes in the world possess their own agency, creativity, and ability to shape events. Whitehead views power as a shared responsibility, with various entities contributing to the unfolding of events.
In summary, in Whitehead's philosophy, God is considered infinite in actualization, potentiality, and love. God's ongoing life encompasses the entirety of the past, embraces an expanding future, and manifests boundless empathy. However, God is not regarded as possessing infinite power, as power is recognized as distributed among the entities and processes within the world.
History of the Infinite Part I: click here. History of the Infinite Part II: click here.
University of Oxford professor Adrian Moore explores the philosophical, mathematical and cultural history of the infinite through two and a half millennia. In this first of two episodes, Adrian discovers why the Ancient Greeks abhorred the notion of infinity and introduces us to the Greek philosopher, Aristotle. He describes how the church attempted to stamp its authority on the debate and how that led to some explosive disagreements amongst medieval thinkers, before bringing us to the verge of the modern world and the way we think now. Having looked at the infinite in philosophical and theological terms, Adrian then views it through the lens of mathematics, considering the pivotal role mathematics has played in the quest to understand the infinite.