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move from New York and his family troubles did not prevent Peirce from making some progress on the intellectual front. By mid-May 1887, he had finished his review of Phantasms of the Living, his first paper after arriving in Milford. Although Peirce did not believe that the postulation of telepathy and apparitions, Gurney’s “ghosts,” formed a good hypothesis for explaining the unusual phenomena recounted in Phantasms, that conviction was not why he devoted so much attention to that gigantic book. Gurney, Myers, and Podmore had put forward their results as a serious scientific study and had presumed to build their argument on the basis of probabilities, hoping to show that in an earlier investigation by Charles Richet the probability in favor of telepathic phenomena had been found to be too low.¹⁸ The critical use of probability theory in the design of scientific experiments and the analysis of results was relatively new, although not for Peirce, who was an expert in two sciences that were exceptions, astronomy and geodesy. In the preceding decade Peirce had devoted much thought to extending the use of statistical reasoning to new sciences, and in the 1883–84 experiments with Jastrow, he had introduced the first modern randomized experimental design for psychology.¹⁹ Peirce saw at once that the method of Gurney and his associates was inadequate to their task and that they had seriously misapplied the logic of probability. However well-intentioned, their work amounted to an attack on the logic of science, and Peirce could not let it go unanswered. It only made matters worse that William James had been impressed by the absurd claim made in Phantasms that the odds in favor of “ghosts” was about “a thousand billion trillion trillion trillions to one.”²⁰ In the first paragraph of his “Criticism” (sel. 16), Peirce alluded to this claim—“I shall not cite these numbers, which captivate the ignorant….”—and pointed out that “no human certitude reaches such figures as trillions, or even billions to one.” Gurney, Myers, and Podmore had presented thirty-one cases²¹ which they claimed established their hypothesis to this remarkable degree of certitude and Peirce’s aim was to show how their results were vitiated by inadequate sampling and control procedures; specifically, that in each of the thirty-one cases they had failed to meet one or more of sixteen conditions of an adequately designed experiment.

      Peirce’s review was forwarded to Gurney for a reply to be published along with it. These papers, together with a rejoinder by Peirce probably written in the late summer or fall, appeared in the December 1887 issue of the Proceedings of the American Society for Psychical Research. In his review (sel. 16) Peirce’s criticism of the thirty-one cases was somewhat casual and perhaps slightly derisive, containing a number of inaccuracies and exaggerations that Gurney, in his lengthy “Remarks” (sel. 17), pounced on. He answered Peirce point for point, often with an impatience that matched Peirce’s swagger. He did admit that perhaps he and his colleagues fell “far short of Mr. Peirce’s standard in respect of caution, shrewdness of observation, and severity of logic,” but he supposed that his deficiencies were not so great as to override the weight of the evidence. Peirce, stung a bit by some of Gurney’s rebuttals, wrote a “Rejoinder” (sel. 18) almost as long as Gurney’s “Remarks” and more technical and precise than his original criticism. He reiterated why he had felt the need to take a stand against Gurney, namely, that “to admit the existence of a principle, of which we certainly only meet with manifestations in very exceptional observations, is to rashly set the prosperity of scientific progress at hazard.” He then answered all of Gurney’s rebuttals and attempted to show that once the suspicious or problematic cases were weeded out there really was no “weight of evidence” at all. Peirce praised Gurney for adopting a statistical method “with a view of putting this question to rest,” but his badly designed study “leaves the question where he found it.” In response to Gurney’s claim that any bias he might have in favor of the supernatural was no greater than Peirce’s bias against it, Peirce agreed, but he added that “a bias against a new and confounding theory is no more than conservative caution; while a bias in favor of such a theory is destructive of sound judgment.” Gurney set about answering Peirce’s “Rejoinder,” but had not finished his remarks when, in 1888, he apparently took his own life. It is thought that the impetus for his apparent suicide was the revelation that his assistant, George Albert Smith, had manufactured evidence (annotation 61.23). Gurney’s final but unfinished answer to Peirce appeared posthumously in 1889 as “Remarks on Mr. Peirce’s Rejoinder,” with a concluding “Postscript” by Myers (sel. 19). In his final “Remarks” Gurney wanted to make it clear that he was really not an advocate for the supernatural and that, in fact, he agreed with Peirce “in professing ‘a legitimate and well-founded prejudice against the supernatural.’” The entire controversy had been acrimonious, with both parties sometimes verging on the scornful. Ian Hacking says “It is Peirce at his crankiest (but none the less sound for that),” and he suspects “that many of the Boston skeptics were egging him on.”²² On his side, Gurney had the resources and encouragement of the Psychical Research Society behind him, along with his co-editors and assistants. But, all in all, one senses that the disputants did not lose respect for each other and even understood that they were in a curious way working together in an effort to advance human knowledge. About a dozen years later, when Peirce revisited this subject for a paper he was writing on “Telepathy and Perception,” he reminisced: “I had a somewhat prolonged controversy with Edmund Gurney which was only interrupted by his death; and this brought me into fine touch with the spirit of the man. I was most strongly impressed with the purity of his devotion to truth” (CP 7.612).

      After returning to Milford in October, following his mother’s funeral, Peirce finished the year working on the theory of hydrodynamics, concerned with the effects on pendulums of the viscosity of air, and he worked on other matters related to his Coast Survey investigations, including his postponed report on the construction of a practical standard of length calibrated against a specified wave length of sodium light (W4:269–98). Peirce was probably stimulated to resume that work by three papers on wavelengths that appeared in 1887, one of them a study by Michelson and Morley precisely on the point of Peirce’s own research. Michelson and Morley’s paper, and the others by Louis Bell and Henry Rowland, made reference to Peirce’s work.²³ Peirce also resumed work on his “Guess” and continued to write his definitions for the Century Dictionary. Possibly in connection with his dictionary work or his study of hydrodynamics, or his interest in mathematical pedagogy, and stimulated by an 1887 article in the Journal fur die reine und angewandte Mathematik,²⁴ Peirce began a systematic study of curves that he would carry on for at least two more years (see sel. 42; also see c. 1888.4 and 1889.3, 20–22 in the Chronological Catalog). Apparently in response to an invitation from Peirce to join in this study, Survey computer and occasional aid to Peirce, Allan Risteen, replied on 4 August: “It has often occurred to me that a collection ought to be made of these properties that are common to all curves of given kinds—say, closed curves—and that perhaps the close examination of such a set of general propositions might lead to others equally general, so that after a time we should have a general geometry in the truest sense.” Sometime during the year Peirce also returned to his work on the theory of number and applied quantification theory to his 1881 axiomatization (sels. 20 and 21).²⁵ It is noteworthy that in “Logic of Number” (sel. 21), Peirce gives a technical definition of the “hereditary character” for number that brings to mind Frege’s “hereditary property” (see annotation 156.11), but Peirce’s regrettable inattention to Frege, probably because of Schröder’s dismissal of him,²⁶ argues that Peirce’s innovations arose from an independent course of thought. It is not definite when or how Peirce’s interest in number theory was rekindled; perhaps it was in connection with his study of number for his Century definition. A few years later, in 1896, he would present a lecture on number to the mathematics department at Bryn Mawr College (probably R 25), and number theory would periodically occupy him for the rest of his days.

      In the latter months of 1887, Peirce began a correspondence with Francis C. Russell, a Chicago attorney who had taken a sudden interest in Peirce’s logic. Russell soon became something of a disciple of Peirce and, after he became associated with the Open Court Press, was instrumental in paving the way for Peirce to publish in The Monist. Peirce also resumed correspondence with William James, writing to him in October about his “admirable work on Space.”²⁷ This was Peirce’s first letter to James after moving to Milford, and it may have

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