Alfred North Whitehead's treatise Universal Algebra classifies algebras as either non-numerical or numerical according to whether they satisfy the law of idempotency, a + a = a. We undertake a technical critique of this classification scheme and examine how its flaws may reflect certain mathematical and philosophical biases in Whitehead's outlook. We argue further that Whitehead's presumption of immutable foundations for mathematics and his early commitment to the priority of objects over relations may in part account for his relative obscurity as a mathematician.

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