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

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СКАЧАТЬ and had concluded that the Survey could no longer afford the traditional European-style pendulum operations Peirce had introduced to U.S. science. Under the influence of Robert von Sterneck, a geodesist from Austria-Hungary, Mendenhall decided to reprogram the Survey’s gravity operations by basing them on the use of short half-seconds invariable pendulums of his own design that could be easily transported from station to station and operated at a fraction of the cost of Peirce’s operations.²⁴ On October 1st, Mendenhall wrote to Peirce to let him know that he was “contemplating a renewal of activity in Gravitation work with field operations under the direction of Assistant Preston” and that “to reduce greatly the time and expense” he would make use of the new half-seconds pendulums.

      Peirce was not pleased. Not only was Mendenhall indirectly giving him notice that his leadership of gravity research would not be restored, but also that the world-class research operation Peirce had built up over the years would be abandoned. The radical change of apparatus and technique would inevitably tend to disconnect the results of future research from those of the past—Peirce’s for the most part. Peirce might have suspected that this decision would influence Mendenhall’s judgment about the value of the long report he had submitted the previous November. In fact, Mendenhall had heard back from at least one reviewer: Simon Newcomb. Newcomb acknowledged that the report was “a careful and conscientious piece of work” but he advised that Peirce’s “inversion of the logical order” of the presentation made it impossible to comprehend. He recommended that the report not be published unless Peirce reconstructed it “in logical order” (28 April 1890). Of course Peirce did not know how things stood with his report; what he knew was that his leadership and his legacy were being threatened by Mendenhall’s changes.

      Peirce held little back. He replied at once (2 Oct. 1890) that “[t]o go back to a non-reversible bar pendulum would be an unintelligent and ostrich-like policy,—a way of concealing from oneself any source of constant error.” He insisted that there were factors more important than time and money relevant to “the economy of the subject”: “One of these is accuracy; for if this is not attained, the work is useless; and the time and money, however little, are thrown away. The other is assurance of accuracy; for however accurate the work may be, if we do not positively know that it is so, it is little better than if it were not so.” Peirce added that more than a year earlier he had shared his own plan for conducting pendulum operations quickly and inexpensively (occupying three stations a week), and that that plan should be adopted and he should be in charge. Mendenhall asked in reply to see the details of Peirce’s plan but reminded him that it was not accuracy that he wanted to sacrifice but unnecessary refinement.²⁵

      The inaugural issue of the Monist was published in October without Peirce’s “Architecture” article, but Peirce celebrated the event with an appreciative note in the Nation (sel. 11): “the establishment of a new philosophical quarterly which may prove a focus for all the agitation of thought that struggles today to illuminate the deepest problems with light from modern science, is an event worthy of particular notice.” He wrote that the first number opened “with good promise,” the articles having been authored by reputed European and American psychologists, biologists, and physicists with a keen interest in the philosophical questions of the day. Peirce questioned what the editors meant by “monism.” Referencing Carus’s explanation in his Fundamental Problems where monism was offered in opposition to a two-substance dualism and as an alternative to both idealism and materialism, Peirce warned that “metaphysicians who call themselves Monists are usually materialists sans le savoir.” Here was already a public intimation that Hegeler’s program might be based on a philosophical misconception.

      As 1890 drew toward a close, Peirce knew that the coming year would bring an end to his work for the Century Company and that his Coast Survey position was not secure. It was critical to find alternative means for his and Juliette’s livelihood, and he would launch himself into various pursuits, many of them seemingly haphazard or short-lived. It appears, for instance, that he began to develop an investment scheme that involved rapid transit out of New York City. On 12 November 1890, Samuel Dimmick Mott, an inventor who had worked for Thomas Edison, wrote to say that he was sorry to have missed Peirce when he tried to see him to discuss the “rapid transit matter.” Mott then explained expected costs and gains for a project to construct a rapid transit rail line between New York and Philadelphia and told Peirce that if he could “succeed in doing anything in my behalf with good parties I will cheerfully make it worth your while, by agreeing to give you 10%.” This railroad scheme, which ultimately went nowhere, was only one of several investment or marketing ideas that Peirce pursued around this time. On 22 November, his brother Herbert wrote: “With regard to your inventions I am immediately in the way of taking them up and doing the best possible with them and should be glad to do so—I have a good patent lawyer …” Among those inventions there was a barrel head, which Herbert recommended that Peirce tried to sell to a barrel maker, and there was a table of logarithms (see sel. 14), which Herbert believed could be marketed through a publisher and was more likely to yield “immediate returns.” Except for a brief discussion of his experiments with logarithmic scales in a letter from Peirce to Mendenhall (4 Feb. 1891), there is no further record concerning these inventions until 1894 when Peirce unsuccessfully tried to get Ginn and Company to publish his logarithmic table.²⁶

      During the years of Peirce’s most intensive work for the Century Dictionary, his research on definitions would frequently carry over into other writings. As a result, it is sometimes difficult to determine whether some of the shorter, often fragmentary, manuscripts of this period are preparatory to a definition or are independent studies stimulated by his lexicographical research.²⁷ “Note on Pythagorean Triangles” (sel. 13), is a good example. This short selection might be a variant form of Peirce’s definition of “Pythagorean triangle” for the dictionary or it might be only the beginning of a paper based on the research for that definition.

      During the first half of the 1890s, Peirce undertook quite a number of textbooks, often simultaneously, but because of lost manuscripts and reorganizations on Peirce’s part, a precise recounting of his textbook projects may no longer be possible. Among the books mentioned by Peirce in his correspondence are a primary arithmetic, a practical arithmetic, a vulgar arithmetic, an arithmetic for young readers, a geometry, a projective geometry, a revision and expansion of his father’s 1873 Elementary Treatise on Plane and Solid Geometry, a trigonometry, and a topology—much of which would be reshaped into two books, the “New Elements of Geometry” (1894–95) and the “New Elements of Mathematics” (1895–96). Peirce also worked on several different logic books during the same period, including “The Light of Logic,” “The Short Logic,” and volume two of his proposed “Principles of Philosophy” on the “Theory of Demonstrative Reasoning.” And there were other book projects not aimed at the classroom. It is evident that Peirce turned to writing as one of his main hopes for increasing his annual income to a sufficient level and that textbooks fit centrally into his plans.

      Several manuscripts listed in the Chronological Catalog for 1890, including two W8 selections, may belong to one of these book projects.²⁸ In “Logical Studies of the Theory of Numbers” (sel. 15), a short document that continues earlier work on number theory,²⁹ Peirce plans to investigate whether a proof procedure can be found for “higher arithmetic, so that we can see in advance precisely how a given proposition is to be demonstrated.” This is equivalent to asking whether there is an algorithm for finding solutions to equations in number theory, and in raising that question Peirce anticipates, in a more general way, David Hilbert’s “Tenth Problem,” posed in 1900 at the International Congress of Mathematicians in Paris, of determining whether there is an algorithm for solutions to Diophantine equations.³⁰ Peirce probably aimed to translate such equations into Boolean algebra, but the paper stops a long way short of showing how he would have actually proceeded. In writing it, Peirce was perhaps stimulated by his recent work on the definition of “number” for the Century Dictionary, or he might have conceived it as preliminary work toward a foundational chapter for a mathematics textbook. “Promptuarium of Analytical Geometry” (sel. 16), on the other СКАЧАТЬ