“Whitehead’s theme, begun in the first chapter and maintained throughout the book and, in our judgment, for the rest of his philosophy, is that mathematics begins in experience and as abstracted becomes separated from experience to become utterly general. “We see, and hear, and taste, and smell, and feel hot and cold, and push, and rub, and ache, and tingle” (IM 4). These feelings belong to us individually. “My toothache cannot be your toothache” (IM 4). Yet we can objectify the tooth from the toothache and so can a dentist who “extracts not the toothache but the tooth,” (IM 4) which is the same tooth for both dentist and patient. Whitehead would give later in Process and Reality a metaphysical explanation of how we may objectify precisely an individual thing from vague feelings by his description of indicative feelings (PR 260).

Abstraction is objectification; that is, the activity of abstraction from our experiences produces ideal objects. In the process we “put aside our immediate sensations” and recognize that “what is left is composed of our general ideas of the abstract formal properties of things; . . . the abstract mathematical ideas” (IM 5). Mathematics applies to the physical world because of its abstraction. By abstraction we get to mere things. The configuration of abstract things in abstract space at different (abstract) times is the mathematical science of mechanics, “the great basal idea of modern science” (IM 31). “The laws of motion . . . are the ultimate laws of physical science” (IM 32). Mechanics is the foundation of science. How strange to hear these words from the philosophical anti-mechanist of Process and Reality.”

The above passage comes from an essay titled “Whitehead’s Early Philosophy of Mathematics” by Granville C. Henry and Robert J. Valenza. Knowing what I know about Whithead’s philosophical influences—his affinity for Plato and for empiricism—I always sort of assumed this carried over to his philosophy of mathematics, and it was nice to have this confirmed; Henry and Valenza, while discussing Whitehead’s book An Introduction to Mathematics, describe Whitehead as “an empiricist with a romantic streak of Platonism.” Sounds about right. And now there is certainly no way I can resist describing myself that way too 😁

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Painting above by Gudrun Åsling

Tags:empiricismphilosophy of mathematicsplatonismwhitehead