One of the things that I have been reading recently is a very interesting paper by John N. Crossley, the Anglo-Australian logician and historian of mathematics, about the reception and adoption of the Hindu-Arabic numbers in medieval Europe.Here I came across this wonderful footnote:
It is interesting to note that Richard Lemay in his entry “Arabic Numerals,” in Joseph Reese Strayer, ed., Dictionary of the Middle Ages(New York, 1982–89) 1:382–98, at 398 reports that in the University of Padua in the mid-fifteenth century, prices of books should be marked “non per cifras sed per literas claras.” He gives a reference to George Gibson Neill Wright, The Writing of Arabic Numerals(London, 1952), 126. Neill Wright in turn gives a reference to a footnote of Susan Cunnigton, The Story of Arithmetic: A Short History of Its Origin and Development(London, 1904), 42, n. 2. She refers to Rouse Ball’s Short History of Mathematics, in fact this work is: Walter William Rouse Ball, A Short Account of the History of Mathematics, 3rded. (London, 1901), and there one finds on p. 192: “…in 1348 the authorities of the university of Padua directed that a list should be kept of books for sale with the prices marked ‘non per cifras sed per literas claras’ [not by cyphers but by clear letters].” I am yet to find an exact reference for this prohibition. (There is none in Rouse Ball.) Chrisomalis Numerical Notations, p. 124, cites J. Lennart Berggren, “Medieval Arithmetic: Arabic Texts and European Motivations,” in Word, Image, Number: Communication in the Middle Ages, ed. John J. Contreni and Santa Casciani (Florence, 2002), 351–65, at 361, who does not give a reference.
Here we have Crossley the historian following a trail of quotes, references and footnotes; his hunt doesn’t so much terminate in a dead-end as fizzle out in the void, leaving the reader unsure whether the university of Padua really did insist on its book prices being written in Roman numerals rather than Hindu-Arabic ones or not. What we have here is a succession of authors writing up something from a secondary, tertiary, quaternary source with out bothering to check if the claim it makes is actually true or correct by looking for and going back to the original source, which in this case would have been difficult as the trail peters out by Rouse Ball, who doesn’t give a source at all.
This habit of writing up without checking original sources is unfortunately not confined to this wonderful example investigated by John Crossley but is seemingly a widespread bad habit under historians and others who write historical texts.
I have often commented that I served my apprenticeship as a historian of science in a DFGfinanced research project on Case Studies into a Social History of Formal Logic under the direction of Professor Christian Thiel. Christian Thiel was inspired to launch this research project by a similar story to the one described by Crossley above.
Christian Thiel’s doctoral thesis was Sinn und Bedeutung in der Logik Gottlob Freges(Sense and Reference in Gottlob Frege’s Logic); a work that lifted him into the elite circle of Frege experts and led him to devote his academic life largely to the study of logic and its history. One of those who corresponded with Frege, and thus attracted Thiel interest, was the German meta-logician Leopold Löwenheim, known to students of logic and meta-logic through the Löwenheim-Skolem theorem or paradox. (Don’t ask!) Being a thorough German scholar, one might even say being pedantic, Thiel wished to know Löwenheim’s dates of birth and death. His date of birth was no problem but his date of death turned out to be less simple. In an encyclopaedia article Thiel came across a reference to c.1940; the assumption being that Löwenheim, being a quarter Jewish and as a result having been dismissed from his position as a school teacher in 1933, had somehow perished during the holocaust. In another encyclopaedia article obviously copied from the first the ‘circa 1940’ had become a ‘died 1940’.
Thiel, being the man he is, was not satisfied with this uncertainty and invested a lot of effort in trying to get more precise details of the cause and date of Löwenheim’s death. The Red Cross information service set up after the Second World War in Germany to help trace people who had died or gone missing during the war proved to be a dead end with no information on Löwenheim. Thiel, however, kept on digging and was very surprised when he finally discovered that Löwenheim had not perished in the holocaust after all but had survived the war and had even gone back to teaching in Berlin in the 1950s, where he died 5. May 1957 almost eighty years old. Thiel then did the same as Crossley, tracing back who had written up from whom and was able to show that Löwenheim’s death had already been assumed to have fallen during WWII, as he was still alive and kicking in Berlin in the early 1950s!
This episode convinced Thiel to set up his research project Case Studies into a Social History of Formal Logic in order, in the first instance to provide solid, verified biographical information on all of the logicians listed in Church’s bibliography of logic volume of the Journal of Symbolic Logic, which we then proceeded to do; a lot of very hard work in the pre-Internet age. Our project, however, was not confined to this biographical work, we also undertook other research into the history of formal logic.
As I said above this habit of writing ‘facts’ up from non-primary sources is unfortunately very widespread in #histSTM, particularly in popular books, which of course sell much better and are much more widely read than academic volumes, although academics are themselves not immune to this bad habit. This is, of course, the primary reason for the continued propagation of the myths of science that notoriously bring out the HISTSCI_HULK in yours truly. For example I’ve lost count of the number of times I’ve read that Galileo’s telescopic discoveries proved the truth of Copernicus’ heliocentric hypothesis. People are basically to lazy to do the legwork and check their claims and facts and are much too prepared to follow the maxim: if X said it and it’s in print, then it must be true!