Whitehead is well known for saying that much of Western philosophy is a series of footnotes to Plato. In "Mathematics and the Good," published in 1941,* he is explicitly inspired by Plato as he discusses the connections between mathematics and the good. The essay begins: "About two thousand three hundred years ago a famous lecture was delivered. The audience was distinguished: among others it included Aristotle and Xenophon. The topic of the lecture was The Notion of The Good. The lecturer was competent: he was Plato." Plato's subject, he adds, was mathematics, and Plato's general idea, too often ignored by his successors, is that mathematics and the Good are inseparable. Whitehead agrees.
Whitehead proposes that mathematics is the exploration of patterns abstracted from their exemplifications in nature and human life and argues that these patterns have their value and place as embodied in the experience of the world. When embodied in experience, he adds, they can be considered "good" or, in words, "bad." Therefore, the good he speaks of is not moral goodness, as exemplified in Greek virtues (temperance, courage, wisdom, and justice) or Christian virtues (faith, hope, and love), but rather the goodness of experience as intense and harmonious, or as, in the case of triviality, maladaptive. Value is, in Whitehead's philosophy, richness of experience as enjoyed by human beings, other animals, and actual entities of any size and scale.
One of his key points, in support of Plato who believed the same, is that mathematics and the concept of the good, as understood in this context, are inseparable, and that the subsequent separation of the two in Western history was a mistake. In discussing geometry, arithmetic, and algebra, he highlights that the activity of abstraction itself, as exemplified in mathematics, is a remarkable achievement of the human imagination. It gives rise to consciousness. However, he also emphasizes that patterns themselves, in abstraction, are not where value or goodness lies; instead, goodness lies in the activity of experience itself, as it both exemplifies and discerns patterns. Additionally, he argues that the universe revealed in abstraction and in experience is nested within an "unbound" infinity of actuality and potentiality. He also suggests that this unbound infinity, in which everything is connected to everything else in myriad ways, is "awakened" by the creativity of the actual world itself.
Whitehead is impressed with the fact that the Good itself (with an upper case G) can be considered in abstraction from its instances, just as mathematical patterns can be thus considered. The question emerges: Does the Good exist even apart from its instances? Does it exist, for example, as an ideal in the mind of the universe, by which human beings are somehow lures or beckoned? Does it exist in God? He does not say. Another related question is: Do the mathematical patterns themselves, when considered in abstraction from their instances, also exist apart from those instances? Here, too, he does not say. But he is clear that the mathematical patterns are neither good nor evil. "Every abstraction derives its importance from its reference to some background of feeling, which is seeking its unity as one individual complex fact in its immediate present. In itself, a pattern is neither good nor bad." He is most interested in the process of abstraction itself, as a supreme achievement of the human mind, but also as incomplete without other dimensions of life, including feeling. It is when the mathematical patterns are conjoined with feeling, in the actual process of experience, that they have value. When embodied or actualized, they find their place in the creativity of the universe, a creativity which surpasses even the patterns. In their very finitude, creative entities in the universe awaken the infinite. Nagel E. Alfred North Whitehead. Mathematics and the good. The philosophy of Alfred North Whitehead, edited by Paul Arthur Schilpp, Northwestern University, Evanston and Chicago1941, pp. 666–681. Journal of Symbolic Logic. 1942;7(2):101-101. doi:10.2307/2266317
Here are some excerpts. The entire essay can be purchased from Cambridge University Press by clicking here.
"The notion of the importance of pattern is as old as civilization. Every art is founded on the study of pattern. Also, the cohesion of social systems depends on the maintenance of patterns of behavior, and advances in civilization depend on the fortunate modification of such behavior patterns. Thus, the infusion of pattern into natural occurrences, the stability of such patterns, and the modification of these patterns are the necessary conditions for the realization of the Good. Mathematics, being the most powerful technique for understanding patterns and analyzing their relationships, plays a fundamental role in this process. This understanding of patterns is the fundamental justification for Plato's lecture topic."
"But this notion [of triviality in experience] is meaningless except as a reference to the background of feeling—namely emotional and analytic experience—within which that total pattern arises. Every abstraction derives its importance from its reference to some background of feeling, which is seeking its unity as one individual complex fact in its immediate present. In itself, a pattern is neither good nor bad. But every pattern can only exist in virtue of the doom of realization, actual or conceptual. And this doom consigns the pattern to play its part in an uprush of feeling, which is the awakening of infinitude to finite activity."
"Abstraction involves emphasis, and emphasis vivifies experience, for good, or for evil. All characteristics peculiar to actualities are modes of emphasis whereby finitude vivifies the infinite. In this way Creativity involves the production of value-experience, by the inflow from the infinite into the finite, deriving special character from the details and the totality ofthe finite pattern. This is the abstraction involved in the creation of any actuality, with its union of finitude with infinity. But consciousness proceeds to a second order of abstraction whereby finite constituents of the actual thing are abstracted from that thing. This procedure is necessary for finite thought, though it weakens the sense of reality. It is the basis of science. The task of philosophy is to reverse this process and thus to exhibit the fusion of analysis with actuality. It follows that Philosophy is not a science."