Sometime in the spring of 1890, Peirce composed the short paper (possibly a fragment), “The Non-Euclidean Geometry Made Easy” (sel. 6), likely in connection with his plan to produce textbooks in logic and mathematics, or perhaps to summarize for expository purposes the theoretical advantages afforded by a clarified non-Euclidean perspective. As with Peirce’s review of Ribot, much of the substance of this paper would soon find its way into his Monist articles, especially, in this case, the first one, “Architecture of Theories” (sels. 22 and 23). Peirce had noticed early in his career that philosophical logic tends to be modeled after the example of geometry and by 1865 he had pointed out that a functioning geometry requires the introduction of a “purely arbitrary element,” a “point of view,” and that although one point of view may be “more natural than another,” given human capacities, that is not the case for pure mathematics (W1: 268) where, as he would say later, “the great democracy of may-bes” holds sway (W6: 251). By 1870, Peirce would appeal to non-Euclidean geometry in support of his revolutionary logic of relatives (W2: 416–17). While teaching at Johns Hopkins, Peirce lectured on non-Euclidean geometry (W4: 486), and in his pivotal JHU Metaphysical Club lecture, “Design and Chance” (17 Jan. 1884), he announced that the Darwinian turn had started a new “epoch of intellectual history” marked by a “tendency to question the exact truth of axioms,” and he suggested that non-Euclidean geometry might be relevant for interstellar measurements (W4: 544–46).
During the decade following his Metaphysical Club lecture, Peirce became increasingly interested in the theory of space. In 1885, in his review of William Kingdon Clifford’s Common Sense of the Exact Sciences, Peirce wrote that to form “clear ideas concerning the non-Euclidean geometry” we must understand that “the geometrical conception of space itself is a fiction”—that there is no definite meaning to the conceptions “absolute position” and “absolute velocity” and that “space only exists under the form of general laws of position” (W5: 255). It was up to the philosophers of science to question why our “natural idea” of space came to be what it was and to consider whether observations could be made that were better explained by alternative geometries. In his “Logic and Spiritualism” essay of 1890, Peirce, marveling at the clarity, beauty, and incomparable scientific significance of the common sense conception of space, mused that if some of the principles of the geometry defining it could be shown to be measurably erroneous, it “would be the most remarkable [discovery] ever made by science” (W6: 388).
So we find Peirce, in sel. 6, entertaining doubts about the exact correctness of our “a priori or natural idea of space,” and of any other natural ideas, and emphasizing the need for correction “by comparison with observations.” This fallibilistic stance gives warrant to non-Euclidean approaches to geometry, of which Peirce considers two: that space is immeasurable, or infinite, but limited (hyperbolic) or that it is measurable, or finite, but unlimited (spherical or elliptic). These two alternatives, along with Euclidean geometry—that space is both immeasurable and unlimited (parabolic)—will be taken up again in “Architecture of Theories” (sels. 22 and 23) as conceptual “materials” for the construction of systematic philosophy.
Two other short working pieces included in this volume were probably composed during the first half of 1890: “Notes on the Question of the Existence of an External World” (sel. 19) and “Note on Kant’s Refutation of Idealism” (sel. 20). Both of these selections revisit Kant’s famous “refutation of idealism,”11 and sel. 20, which glosses on Kant’s claim that “his argument beats idealism at its own game,” suggests a more direct and simpler method of refutation. In sel. 19, Peirce states that if the idealists were right to assume that only the inner present can be immediately perceived, then the impossibility of perceiving the external immediately would indeed entail, “as a matter of logic,” that the existence of anything external was inadmissible.12 The problem, however, is that the idea that we can only immediately perceive what is present in the mind is “a vulgar prejudice” parallel to the idea that “a thing cannot act where it is not.” For Peirce, this idea, by appealing to a naïve view of space and time, helps underscore how misleading inductions from ordinary experience can be. In sel. 20, he adds that we can only apprehend our own ideas as flowing in time, and since neither the past nor the future are immediately present, our perception of the internal can be no more immediate than our perception of the external. If idealism is so easily beaten at its own game, then, it is because its conception of the present fails to grasp the continuity of experience.
Why Peirce took up Kant’s refutation of idealism at this time can only be guessed at, but just two years earlier Peirce had been engaged with related theories of Kant’s for his “Guess at the Riddle,” and his reflections on space and time had been invigorated by William James’s 1887 paper in Mind on “The Perception of Space” (see W6: xliv) and probably also by James’s 1886 paper in the Journal of Speculative Philosophy, “The Perception of Time,” which developed E. R. Clay’s idea of “the specious present.” Perhaps also of relevance is that in 1889 Edward Caird published in Glasgow his two-volume work on The Critical Philosophy of Immanuel Kant, which included a thorough treatment of Kant’s refutation of idealism that would likely have caught Peirce’s eye. Caird’s book was reviewed by A. Seth in Mind in April 1890 with specific mention of Kant’s refutation—discussions of Kant’s refutation of idealism were not uncommon in the literature of the day. Any of the above could have rekindled Peirce’s interest in Kant’s ideas about the present and his refutation of idealism. Soon after composing these notes, Peirce would again take up his Kant-inspired cosmology project, and the nature of the present would again play an important role.
On 1 July 1890, Francis C. Russell, a Chicago judge and an admirer of Peirce, wrote to him a letter that was more consequential for the remaining course of his life than anyone could have foreseen. Russell wrote at the request of Paul Carus to invite Peirce to contribute an article on logic for Edward C. Hegeler’s new philosophy journal, The Monist: “It is the intention of the management of the journal to make it the vehicle of such utterances only as shall be competent to the topics treated and they expect to pay for their articles after a measure in some degree fitted to the dignity of the writers and the customary recognition of the value of their productions.” Hegeler was a wealthy industrialist with a zeal for reconciling religion with science. He was an evolutionist who rejected what he regarded as Spencer’s hedonism and who embraced a quasi-Platonic idea that the process of growth is a teleological movement toward the fulfillment of higher forms. He was a fervent monist who believed that “God and the universe are one … the continuous ALL of which man is a limited part and phenomenon.”13 Hegeler supported religiously radical groups, including the