In July 1889 Thomas Corwin Mendenhall was appointed Superintendent of the U.S. Coast and Geodetic Survey. His predecessor, Frank M. Thorn, was a lawyer with no scientific training who had been appointed four years earlier to reform the Survey. In contrast, and to the relief of many government scientists, Mendenhall was a trained scientist and was expected to restore the Survey’s leadership in scientific research; certainly that was Peirce’s hope. Peirce’s career had been dedicated to advancing the theoretical foundations of geodetic science and his field work had always been conducted with the greatest care, using the most refined instruments, so that his results could contribute not only to the immediate practical needs of economic and social life but also to the growth of the science. Under his leadership, American gravity research took its place alongside the best gravity research in Europe. But the turn away from pure research that the Survey had taken under Thorn could not be reversed in the political and economic climate of the times and Peirce and Mendenhall soon reached an impasse.8
Peirce had good reasons for being discontented with the Survey’s administration, especially under Thorn, but his unveiled discontent got him off to a bad start with Mendenhall, who regarded Peirce as uncooperative and set in his ways. It did not help that Peirce had been working for over three years to prepare the results of extensive field operations conducted from 1882 through 1886 for publication in what was expected to be his second major gravity report. This report had been a major source of conflict between Peirce and Thorn and it is certain that Thorn told Mendenhall that it was long overdue. Mendenhall would also have been aware that Peirce was working as a major contributor to the Century Dictionary project, then in its most demanding production phase, and that Peirce may have had too many irons in the fire. And Mendenhall would have known Thorn’s reservations about the quality of the overdue report and read about Peirce’s decision to reverse “the usual order of presentation in a scientific memoir by stating the conclusions before the premises.” When Peirce finally submitted his completed report on 20 November 1889, Mendenhall decided to have it reviewed for “form, matter, meaning and suitability for publication.” When Peirce and Juliette returned to Milford the following spring, Peirce had still heard nothing back from Mendenhall about plans for publication.
An exchange of letters between Mendenhall and Peirce in July illustrates the impasse they had reached. On 30 June, Mendenhall wrote to Peirce asking him for a definite value for “the force of gravity” for Ithaca, the place of one of the four main gravity stations dealt with in the report that was under review. Physics students at Cornell needed this figure as a constant for their laboratory work. All of relevance that Mendenhall could find in Peirce’s report was a “nearly unintelligible use of the so-called ‘logarithmic second’ which … renders the discussion uselessly and unnecessarily obscure.” Peirce replied quickly to explain how to derive the desired value from the data in his report; he lamented that the result would be at least one ten thousandth too small because he had not received the new pendulums he had requested for flexure corrections (3 July 1890), and wrote later to criticize Mendenhall’s conception of gravity as a force “calling for expression in dynes” (22 July 1890). Peirce argued that gravity should really be understood as a measure of acceleration and strongly defended his use of logarithmic seconds. Mendenhall replied that his disagreement with Peirce was not one that could be easily settled and gave Peirce a warning: “When acting for the public … one must be guided by the general consensus of opinion of those generally admitted to be the highest authorities; personal preferences and especially any weakness 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