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Kathleen Hull The Inner Chambers of his Mind: Peirce's "Neglected Argument" for God as Related to Mathematical Experience1 Bertrand Russell liked to say that there are just two types of philosopher: those who think of the world as a bowl of jelly and those who think of it as a bucket of shot. Either the world is a jelly-like, indivisible whole, he believed, or it consists of discrete (logical and physical) atoms. Russell, of course, claimed to have abandoned the jelly for the shot.2 His pellet-like metaphysics became associated with a philosophic method whose influence on twentieth-century philosophy has yet to be fully assessed. This method involves distinct mental acts of parsing: step-by-step analysis using a particular kind of logic. Russell's theoretic vision acquired a status nearly akin to moral force in Anglo-American philosophy, setting the standard for right thinking. This vision has, in turn, influenced interpretations and evaluations of C. S. Peirce's philosophy. In Peirce studies, Peirce's worldview has been considered both jelly and shot. While his work on logic is often considered "the good stuff" (that is, in the masculine, "shot" camp), his writings on religion and cosmology have often been dismissed as gobbledygook "jelly." So we find critics like Hookway and Nagel suggesting that Peirce, in his analysis of God, has departed from the standards of clarity he employs in his logic and science. Perhaps such criticism of Peirce's God-talk is a hang-over from the bad-old days of logical positivism, for most positivists in the history of philosophy have been anxious to annihilate all metaphysics and to show that metaphysics is meaningless and nonsensical. Or, as Peirce put it, there is "a tendency to pooh-pooh at things unseen" (CP 6.431). What I'd like to do here is to "save" Peirce from such critics by showing that his quite limited work in religious philosophy may be connected to his work in philosophy of mathematics. Metaphysically speaking, the Peircean world may turn out to be a bowl of jelly after all; but at least the man is consistent, and he thought carefully about how one ought to reason about it. As early as 1859, at the age of 19, Peirce wrote three short pieces, one after the other, on God and Infinity; he argued that we can reason upon both.3 His philosophical life expresses his passion to articulate systematically a vision of Transactions of the Charles S. Peirce Society Summer, 2005, Vol. XLI, No. 3 484 Kathleen Hull the world as an intelligible whole. It is at least partly in connection with his metaphysics, I suggest, that Peirce took an interest in the question of whether reasoning could be reduced to a mechanical process. His metaphysical system, called Synechism, viewed continuity as of prime importance in philosophy — and Peirce concerned himself with determining the form of rationality appropriate to it. His objections to mechanical models of thinking are illustrated in his writings on logical machines and his criticisms of Babbage's Analytic Machine.4 A full discussion of this interesting aspect of Peirce's scholarship is beyond the purview of this paper. However, in relation to the thesis under discussion: Peirce believed that all genuine mathematical work, along with all creative work in metaphysics (and the sciences), involves originality, invention, and imagination that not only cannot be performed by machines, but cannot be accounted for by models of human reasoning that seek to confine our reasoning to symbol manipulation according to a rule or within the bounds of logical, formal rules. In this sense, mathematics cannot be reduced to logic; and here Peirce butts heads with Russell and the Logicists. The pervasive role of the continuum (both mathematical and metaphysical) in Peirce's Weltanschauung necessitated his development of non-mechanical, "intuitive" forms of reasoning that allowed for generalization, or growth in systems of thought, applicable to both mathematics and religion. Peirce is not alone in presenting connections between religious and mathematical knowledge. Indeed, following a long line of thinkers interested in the nature of infinity, a number of nineteenth-century philosophers and mathematicians linked theology with mathematics. In particular, Peirce...

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