The Nation carried three brief book notices in Peirce’s hand in May: on the 12th, Frank N. Cole’s translation of Eugene Netto’s Theory of Substitutions—an improvement over the German original—and Joseph Edwards’s Elementary Treatise on the Differential Calculus; on the 19th, a highly critical oneparagraph notice of Robert Grimshaw’s Record of Scientific Progress for the Year 1891—blind to real scientific progress, especially in astronomy; and a somewhat longer review of W. W. Rouse Ball’s Mathematical Recreations, appearing also on 12 May. Peirce’s notice of Ball was not one an author would have hoped for: an entertaining book with “as good a notion of a fourth dimension … as could be acquired without serious study,” but scrappy throughout, with a bad sketch of non-Euclidean geometry and with the results of Klein and Riemann misstated.
Peirce travelled to Cambridge around 17 May and stayed for about a week. He spoke at the Philosophical Club on the 21st and a day or two later he gave what William James described as “a godlike talk at Royce’s.” Much of what we know about the Philosophical Club talk comes from Frank Abbot’s diary. He recorded that some twenty graduates and friends, including Peirce’s brother Jem, attended the talk on synechism, Peirce’s “new system of philosophy.” The paper Peirce read was his “Law of Mind” (sel. 27), which he was about to submit to the Monist. Royce was probably also at the Philosophical Club talk, possibly occasioning a little tension in light of the recent battle between him and Abbot. James did not see Peirce at all because he was too occupied with preparations to depart on the 25th for a fifteen-month trip to Europe with his family. James sent a note to Peirce probably on the 23rd: “It has been a great chagrin to me to have you here all this time without meeting or hearing you. I especially wanted to hear you on Continuity, and I hear of a godlike talk at Royce’s. But Continuity will appear in Monist. Talks can never come again!!” James added a friendly remark about Peirce’s recent paper “The Doctrine of Necessity Examined”: “I meant to write you long ago to say how I enjoyed your last paper in the Monist. I believe in that sort of thing myself, but even if I didn’t it would be a blessed piece of radicalism.”
It is unclear what the “godlike talk” was that James had heard about. Peirce may have given a talk at Royce’s home or lectured in Royce’s seminar, “several séances” of which had been devoted to a discussion of Peirce’s “Doctrine of Necessity” prior to his visit, as Peirce wrote to Carus on 24 May, adding that Royce intended to attack the paper in the Philosophical Review.101 But one of Royce’s students, Dickinson S. Miller (1868–1963), reminiscing about Peirce’s Cambridge visit many years later, told Max Fisch that he and Sheffield had been allowed to attend silently a long informal conversation between Peirce and Royce in Royce’s study, and this might have been all that the “talk” amounted to.102 While in Cambridge, Peirce probably followed Francis Russell’s suggestion to rally support for his candidacy for the University of Chicago philosophy professorship, and he may have tried to learn more about it from Palmer. With his note mentioned above, James enclosed “a scrap for Harper which you can send with your other ‘credentials,’” and promised to write to Harper from the steamer. Carus also wrote to recommend Peirce to Harper, and others must have as well. But when Palmer learned that James had written, he wrote to Harper to warn him about Peirce: “I am astonished at James’s recommendation of Peirce. Of course my impressions may be erroneous, and I have no personal acquaintance with Peirce. I know, too, very well his eminence as a logician. But from so many sources I have heard of his broken and dissolute character that I should advise you to make most careful inquiries before engaging him. I am sure it is suspicions of this sort which have prevented his appointment here, and I suppose the same causes procured his dismissal from Johns Hopkins.”103 Palmer’s letter took Peirce out of the running.
With his 24 May letter to Carus Peirce had enclosed “The Law of Mind” (sel. 27). This article plays a crucial role in his Monist series since it is an examination of the general law of mental action, which was claimed by Peirce to be fundamentally distinct from mechanical action. Peirce’s main objective in “The Law of Mind” was to argue for the importance of continuity for mental operations and to examine the law of mind guided by a mathematically informed understanding of continuity. Peirce’s ideas about the “prime importance” of continuity for understanding mental processes, and for philosophy in general, were brought together in the theory or doctrine he called “synechism.” About a year later, Peirce wrote an article for the Open Court, “Immortality in the Light of Synechism” (W9, sel. 54), in which he stated, concisely, that he “proposed to make synechism mean the tendency to regard everything as continuous.” Peirce said that this third Monist paper was “intended chiefly to show what synechism is, and what it leads to,” and he connected his work for the Monist to his 1868–69 Cognition Series (W2, sels. 21–23) where his study of mind was explicitly based on semiotic principles.
Peirce’s key challenge is to explain what makes mental or psychical processes fundamentally irreversible, in contradistinction to physical processes, which, when they are irreversible, are so only in a statistical sense owing to their inherent complexity (such as with the behavior of gases). As seen before, Peirce hypothesizes that the general law of mental action is that “ideas tend to spread continuously and to affect certain others which stand to them in a peculiar relation of affectibility.” In spreading, ideas lose intensity as they gain generality. Ideas must not be supposed to be fleeting events in consciousness that come and go abruptly but, rather, to be states of consciousness occupying infinitesimal intervals of time. In this infinitesimal interval “we directly perceive the temporal sequence” and are thus able to immediately perceive relations between emerging and passing, but temporally overlapping, ideas. “We are thus brought to the conclusion that the present is connected with the past by a series of real infinitesimal steps.” Through inference, or mediate perception, a train of thought can be built up and comprehended.
The “peculiar relation of affectibility” is what gives the movement of thought (and mental time) its forward direction. Ideas can only be affected by ideas that have preceded them, not by ideas yet to come: “The present is affectible by the past, but not by the future,” but the present affects the future. Affectibility is a non-associative transitive relation like the copula of Peirce’s algebra of logic, a point stressed in the earlier versions of “The Law of Mind” (sels. 25 and 26). According to Peirce, we “encounter three elements” in considering how ideas affect other ideas: their intrinsic qualities as feelings, their energy, and “the tendency of an idea to bring along other ideas with it.” As ideas spread, their intrinsic quality remains “nearly unchanged,” but their energy dissipates quickly while their tendency to affect other ideas increases. As more and more ideas are affected they become “welded together in association,” which results in a general idea. The feeling associated with a general idea is that of “a vague possibility of more than is present.”
Peirce says that the law of mind follows the forms of logic. By the “hypothetical process” (abduction), sensations somehow “suggest” general ideas; by induction, habits become established (“a number of sensations followed by one reaction become united under one general idea followed by the same reaction”); and by deduction, the mind functions under the domination of habit (by “calling out certain reactions on certain occasions”). But a telling difference between the law of mind and physical law is that the mental law is not “rigid” and allows for some spontaneity in mental action: “the uncertainty of the mental law is no mere defect of it, but is … of its essence.” If the law of mind acted with the rigidity of physical law, intellectual life would come to “a speedy close.”
Peirce’s introduction of infinitesimals into his philosophy of mind required support from mathematics. Peirce held that the “spread-out” feeling in a moment