Writings of Charles S. Peirce: A Chronological Edition, Volume 8. Charles S. Peirce

Чтение книги онлайн.

СКАЧАТЬ have been pleased with the promise of Schröder’s book for the future of his line of logical thought. It would not be until 1893, after Peirce had received three more letters from Schröder, that they finally resumed a regular correspondence (by then Peirce had also received the second volume of Schröder’s Logik).

      In the spring of 1891 Peirce resumed work on his own “exact logic,” specifically on the algebra of the copula (sels. 31–35). This work was the successor to Peirce’s well-known treatment of the algebra of the copula in his famous American Journal of Mathematics papers of 1880 and 1885,³⁶ papers that had much influenced Schröder. Peirce might have been working up a presentation paper, possibly stimulated to resume his study of the copula because of Schröder’s rejection of the copula as the preferred logical connective. Peirce may also have been working toward a logic book; his 1894 “How to Reason,” more commonly known as his “Grand Logic,” would include a substantial chapter on “The Algebra of the Copula.” It is noteworthy that Peirce began sel. 32 with what is in effect the truth table for the copula of inclusion—or the copula of consequence, as he called it in sel. 33. In these selections, Peirce showed some movement toward a graphical approach that would gain momentum with his recognition in his summer 1892 “Critic of Arguments” papers that there are significant diagrammatic features in logical algebras. Peirce’s attention to operations with parentheses and rules for inserting or omitting propositional variables into or from parenthetical spaces bears some resemblance to later existential-graph operations.³⁷

      It was likely in March 1891 that the Peirces decided to name their estate Arisbe. In December 1890, they had settled a claim made against their property by Levi Quick and at last gained clear title to all of their estate. They had finished a first round of home renovations the previous year and now that Charles had begun construction of his philosophical mansion in the pages of the Monist, he and Juliette returned to making grand designs for their house and their estate. They made a survey of Wanda Farm, they unsuccessfully petitioned the township to reroute the public road that passed nearby, and they received confirmation that they held the timber and quarry rights to their property. With the return of hope for the possibilities of life in their Milford home, and perhaps with the idea of symbolizing that the estate was ready to assume a new character, they must have felt that the time was right to settle on a new name. How they came to choose the name “Arisbe” is unknown and has given rise to a lot of speculation. Max H. Fisch for example suggested that Peirce named his Arisbe after the Milesian colony northeast of Troy along the Hellespont in ancient Greece,³⁸ because Miletus was the home of the first Greek philosophers, and the scientific philosophy they aspired to was of a kind with the philosophical program Peirce had inaugurated with his “Guess at the Riddle.” Or perhaps it was because Peirce was familiar with Book IV of Homer’s Illiad, which tells the story of Axylus, whose home on the road through Arisbe was known as a place of welcome to all who passed by. Whatever the source of the inspiration (other explanations exist), the estate became known as “Arisbe” in 1891 and by the fall, the Peirces had begun using “Arisbe” regularly in their correspondence.

      The fifth volume of the Century Dictionary was published in May, so sometime before that Peirce turned to the proofs for the sixth and final volume. Under much work pressure, he arranged in mid-May for the Century Company to hire Allan Risteen to help him with the research for his remaining definitions. Risteen worked as a safety engineer for an insurance company in Hartford, Connecticut, but he was able to spend much of June and July helping Peirce, often traveling to New York or Cambridge for library research. Surviving correspondence indicates that Peirce used Risteen to help with specialized mathematical or scientific terms, working up material for the constellations in the S to Z letter range, for example, but much of Risteen’s effort focused on three words given encyclopedic treatment: theorem, transformation, and triangle. By the middle of July, Risteen had finished his work as Peirce’s special assistant and Peirce must have concluded his work by the end of August. The 18 September 1891 issue of Science carried a notice that the Century Dictionary “is at last completed; the sixth and concluding volume will soon be brought out, the final pages being now on the press.”

      In early June, Peirce asked Risteen to add “trees” to his research list of mathematical subjects. It had occurred to Peirce that Arthur Cayley’s diagrammatic method of using branching trees to represent and analyze certain kinds of networks based on heritable or recurrent relations would be useful for his work on the algebra of the copula and his investigation of the permutations of propositional forms by the rearrangement of parentheses. In “On the Number of Dichotomous Divisions: A Problem in Permutations” (sel. 35), Peirce sought to determine how many propositional forms there were given a certain number of copulas (or any other non-associative connective) and a continuous supply of parentheses, and used Cayley’s method of trees to work out his solution.³⁹ When Risteen wrote back on 10 June, his report, illustrated with diagrams, dealt fairly extensively with Cayley’s 1875 article, “On the Analytical Forms called Trees, with Application to the Theory of Chemical Combinations.” This may have given Peirce the idea that Cayley’s tree method for analyzing propositional forms could help him improve on the brief treatment of slime-molds and protoplasm he had given in “Architecture of Theories.” Cayley’s analytical treatment of chemical combinations had the potential to produce a “molecular theory of protoplasm” that was more in tune with the current physics and more straightforwardly subject to a mathematical treatment of continuity. In his fourth Monist article, “Man’s Glassy Essence” (sel. 29), when discussing the “enormous rate” of increase of the numbers of chemical varieties as the number of atoms per molecule increases, Peirce remarked that “Professor Cayley has given a mathematical theory of ‘trees,’ with a view of throwing a light upon such questions.”⁴⁰

      One of the writings in this volume that might puzzle readers is Peirce’s two-part unsigned Nation review of William James’s Principles of Psychology (sel. 37), not so much for its content as for its tone. The content itself is not surprising, for it reflects Peirce’s practice of zeroing in on logical inconsistencies committed by authors who should know better, and of displaying and criticizing the hidden metaphysics that underlies naïve anti-metaphysical claims. But Peirce and James were friends of long standing, and Peirce knew that James had spent many hard years writing his first major work. Peirce was one of five persons whom James expressed gratitude to in his preface for intellectual companionship. So it might be surprising that Peirce took James rather severely to task (merciless Royce, on the other hand, would have appreciated the deed, as we shall soon see). After calling into question James’s inexact writing style, Peirce wrote that James’s thought “is highly original, or at least novel,” but it is “originality of the destructive kind,” and that “the book should have been preceded by an introduction discussing the strange positions in logic upon which all its arguments turn.” James, Peirce found, “seems to pin his faith” on “the general incomprehensibility of things,” and he is “materialistic to the core … in a methodical sense”—according to James, once psychology “has ascertained the empirical correlation of the various sorts of thought and feeling with definite conditions of the brain,” it can go no farther. This is part and parcel of the mechanistic philosophy that Peirce had taken it upon himself to refute. Peirce accused James of employing the “principle of the uncritical acceptance of data,” which “would make a complete rupture with accepted methods of psychology and of science in general.” To illustrate his case, Peirce chose in the second part of his review to examine with some care one section of James’s book: “Is Perception Unconscious Inference?” Peirce went to some length to explain in what sense he believed perception to involve unconscious inference and challenged James’s claim that although there is inference in perception there is nothing unconscious about it. According to Peirce, James failed to understand that what was meant by “unconscious inference” was only that “the reasoner is not conscious of making an inference,” and, furthermore, James “forgets his logic” in assigning the inference in perception to “immediate inference,” because it has no middle term, when, in fact, modus ponens is the form it takes in that sort of analysis (which Peirce thinks is wrong, having long concluded that the inference is hypothetical in form). СКАЧАТЬ