towards ‘eccentricity’ must often give way” (24 July 1890). In the coming months, Mendenhall would weigh Peirce’s obvious strengths as a physical scientist against his “weakness toward eccentricity.”
One of Peirce’s first compositions after returning to Milford, possibly finished just prior to his return, was “Familiar Letters about The Art of Reasoning” (sel. 1). It is not certain what Peirce had in mind for this paper, dated 15 May 1890, but, given the title of the piece, it might have been intended as a lesson for his correspondence course in logic, a course in the “art of reasoning” he planned to resume after his return to Milford. Peirce may have had something else in mind, perhaps a series of letters on logic for a newspaper or magazine or maybe a new kind of arithmetic textbook that would use pedagogical methods anchored in a more sophisticated understanding of reasoning processes at work in counting, adding, and multiplying. His reference to Thomas Murner, famous for his success in teaching logic to weak students through the use of cards, would seem to bear that out. For two years Peirce had been surveying arithmetic textbooks with the idea of writing one of his own.9 And, spurred by his research at the Astor Library, he had begun amassing an ample collection of old arithmetics. By 1893 he would work out a deal with Edward Hegeler, the owner of the Open Court Company, to finance an innovative arithmetic textbook. “Familiar Letters” is an example of a writing that can hardly be appreciated unless readers perform the operations they are called on to perform. Even though Peirce was teaching card tricks, he intended to be teaching something more general about reasoning and a modern reader is likely to notice that the mechanical operations of multiplying and adding with cards are suggestive of early computing operations. Peirce’s admonition that “one secret of the art of reasoning is to think” where he seems clearly to regard “thinking” as an activity, like manipulating cards according to general rules, is reminiscent of the “new conception of reasoning” expressed in his 1877 “Fixation of Belief” as “something which was to be done with one’s eyes open, by manipulating real things instead of words and fancies” (W3: 243–44).
Some other writings from this period seem clearly to have been intended as lessons for Peirce’s correspondence course; sels. 17 and 18 derive from lessons Peirce used in his correspondence course three years earlier (see especially W6, sels. 1 and 6). Precisely when Peirce resumed working with them is not certain but we know that he had not given up the idea that he could make this course pay and that within a few months he would again advertise for students. There are a number of related manuscripts, at least two of which, with sel. 18, were composed as opening chapters for a book on logic, probably intended as a text for Peirce’s course but plausibly also as a general logic text to parallel what his “Primary Arithmetic” would do for teaching arithmetic.10 In “Boolian Algebra. First Lection” (sel. 18), Peirce gives Boole a rare compliment, namely, that Boole’s idea for the algebra of logic “sprang from the brain of genius, motherless” so far “as any mental product may.” Before taking up the elements and rules of his algebra of logic, Peirce reviewed some of the deficiencies of ordinary language for exact reasoning: its “deficiency of pronouns,” its “feeble marks of punctuation,” and its inadequacy for diagrammatic reasoning. Peirce’s modification of “the Boolian calculus,” what he here calls a “propositional algebra,” was intended to overcome these deficiencies of ordinary language. It is noteworthy that Peirce has the idea of expressing the truth of propositions in degrees “as temperatures are expressed by degrees of the thermometer scale,” although he goes on to say that there are only two points on this scale, true and false.
In Peirce’s 19 June “Review of Théodule Ribot’s Psychology of Attention” (sel. 2), his third book review of 1890 to appear in the Nation and the first during the period covered by this volume, Peirce drew together ideas that would tie several lines of thought from his philosophical work of the W6 period to the systematic philosophy he was about to take up for the Monist. Born like Peirce in 1839, Ribot became the leading French psychologist of his time. He argued for the separation of psychology from philosophy and introduced his compatriots to the “new psychology” then emerging in both Germany and England. Ribot was instrumental in promoting an experimental approach in psychology, and though Peirce could not but approve of this modern trend, he saw in Ribot’s enthusiasm for it the workings of a metaphysical confusion. In offering his critical assessment, Peirce previews a number of important ideas that will be developed especially in his third Monist paper, “The Law of Mind” (sel. 27). Casting doubt on Ribot’s emphasis on a physiological conception of mental association, Peirce objects that it is the “welding together of feelings” that “seems to be the only law of mental action” and he argues that instead of focusing on “attention” (an “unscientific word”), which Ribot wrongly viewed as principally inhibitory, Ribot would have done much better by recognizing the centrality of the positive role played by “emotional association, aided in certain cases by acts of inhibition.” Peirce rejects Ribot’s monism, the monism of the “physiological psychologists” which is put forward as a psycho-physical double-aspect theory, “a happy compromise between materialism and spiritualism,” though it is really a materialism that makes mind “a specialization of matter.” Peirce objects that “common sense will never admit that feeling can result from any mechanical contrivance,” insisting that “sound logic refuses to accept the makeshift hypothesis that consciousness is an ‘ultimate’ property of matter in general or of any chemical substance.” The school of physiological psychologists, in “forever exaggerating the resemblances of psychical and physical phenomena, forever extenuating their differences,” remains blind to the distinction between the law of mechanics and the law of mind. Still, this is not an absolute distinction, and the road toward a more balanced metaphysics is to acknowledge that there are physical phenomena “in which gentle forces seem to act” and others “which seem to violate the principle of energy,” such appearances being due to the action of probability.
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
