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In October 1909 Alfred North Whitehead and Bertrand Russell had to hire "an old four-wheeler" (instead of a hansom) to transport the colossal manuscript of Principia Mathematica to the Cambridge University Press. (Russell 1967:152) It had taken them approximately eight years of Herculean efforts to produce the huge manuscript, and its typesetting, proofreading and publishing dragged on for another four years. The first volume of Principia Mathematica was published in 1910, the second in 1912, and the third in 1913. The aim of this paper is to make sure that the celebration of the 100th anniversary of the publication of the first volume of Principia Mathematica is not merely a Russell celebration, but also puts Whitehead on stage. Principia Mathematica is usually presented as part and parcel of Russell's intellectual development, while conceived as out of place in Whitehead's overall oeuvre. With regard to Whitehead's oeuvre, for example, Granville C. Henry and Robert J. Valenza (1993) argue that the formalism of Whitehead's Universal Algebra (1898) was rejected by him when he embraced the logicism of Principia Mathematica; that Whitehead was of two minds in the 1910s, a Platonist mind expressed in Principia Mathematica, and an empiricist mind in An Introduction to Mathematics (1911); and that as a professional mathematician he never scented a relational approach, whereas he became a famous process philosopher for just this kind of approach. Contrary to Henry and Valenza, I hold that Whitehead's logicism is a logical update of his earlier algebraic formalism; that he conceived both algebra and logic as symbolic tools to support the mathematician's essential activities of recognizing, entertaining, and applying relational patterns; and that both led Whitehead to disentangle pure and applied mathematics, and to illuminate that the essential pure-applied interplay of mathematics and physics is a high-level expression of the potential-actual dialectics of human thought. Moreover, I hold that Whitehead's later relational structuralism is a philosophical enrichment of his logicism, and that Principia Mathematica's ontology of individuals and propositional functions is just as relevant to Whitehead's metaphysics of actual occasions and pure potentials as it was to Russell's so-called analytical philosophy. |
