Mathematics, ethics and purism: an application of MacIntyre’s virtue theory

A traditional problem of ethics in mathematics is the denial of social responsibility. Pure mathematics is viewed as neutral and value free, and therefore free of ethical responsibility. Applications of mathematics are seen as employing a neutral set of tools which, of themselves, are free from social responsibility. However, mathematicians are convinced they know what constitutes good mathematics. Furthermore many pure mathematicians are committed to purism, the ideology that values purity above applications in mathematics, and some historical reasons for this are discussed. MacIntyre’s virtue ethics accommodates both the good mathematician (and good pure mathematics) and the ethics of the social practice of mathematics. It demonstrates that purism is compatible with acknowledging the social responsibility of mathematics. Four aspects of this responsibility are mentioned, two concerning the impact of mathematics via education, and two concerning explicit and implicit applications of mathematics. The last of these opens up the performativity of mathematical and measurement applications in society, which change the very processes they are supposed to measure. Although these applications are not explored in detail, they illustrate the importance of considering the ethics and social responsibility of mathematics in society. MacIntyre’s virtue theory opens a broad approach to the controversial topic of the ethics of mathematics encompassing purism, and absolutist and social constructivist philosophies of mathematics, but still enabling ethical critiques of the impact of mathematics on society.

Mathematics, College

In my own undergraduate experience I took so many courses as a student where I sat in class writing as fast as I could to get the material down—I wasn’t talking at all—I wrote it down in order to take it back to my room and work on it. That doesn’t seem like a human way to utilize a classroom. I didn’t get as much out of undergraduate studies as I should have. I was getting A’s in my math courses and hence assumed I was learning all that was necessary at the time. I memorized too much for exams and remembered too little afterwards. That’s why I can’t forget Bill Transue at Ohio State. Students called him “Smiling Bill.” A gentle man, he taught a two-term class in “Topology and Functional Analysis.” He didn’t use the standard lecture mode, but made us students learn from each other. Every day he would assign a section of the text along with the corresponding problems. The next day he would ask us, “Which ones did you get?” He took your word for that, and then he’d ask a person to go to the board and present one of those problems he thought he had solved. Transue sat in the back, smoking his ever-present pipe, and didn’t say much. Maybe someone in class would find errors or misdirections. When Transue found something wrong, he never announced it in a way that put a student down. He was a good teacher, who got us to do our best work, and a good mathematician himself. But I must also mention Allan Ziebur, with whom I had five courses. He was a man of incredible energy and great warmth. He had, and still has, a broad grin that could disarm Attila the Hun. He used to love standing in front of his 8 A.M. class (he always taught at 8 A.M.), his eyes twinkling, and exclaim that it was a wonderful day and he would give anyone of us an A if we would blow up the smokestack down the road that was polluting the air and ruining the view.

Thomas Harriot's reputation for impiety

The bishop of Sarum (Seth Ward) told me that one Mr Haggarn (a country man of his), a gentleman and good mathematician, was well acquainted with Mr Thomas Hariot, and was wont to say, that he did not like (or valued not) the old storie of the Creation of the World. He could not beleeve the old position ; he would say ex nihilo nihil fit . But sayd Mr Haggar, a nihilum killed him at last : for in the top of his nose came a little red speck (exceeding small), which grew bigger and bigger, and at last killed him. I suppose it was that which the chirurgians call a noli me tangere.

II. Account of levellings carried across the Isthmus of Panamá, to ascertain the relative height of the Pacific Ocean at Panamá and of the Atlantic at the mouth of the river Chagres; accompanied by geographical and topographical notices of the Isthmus

In November 1827 I received a special commission from General Bolivar to make a survey of the Isthmus of Panamá and Darien, in order to ascertain the best and most eligible line for a communication (whether by road or canal) between the two seas. On my arrival in Panamá in March 1828 I was joined by a brother officer of Engineers, a Swede in the Colombian service, a good mathematician and of habits of great correctness in observation. Upon consulting together, we found that we could combine the particular object of the commission with a second object in which we both felt a deep interest, namely, the determination of the relative height of the ocean on either side of the Isthmus; and that we could best accomplish both, by taking a part of the present line of road between Porto Velo and Panamá, until we should fall in with the river Chagres about twenty miles above Cruces, which village is the usual landing-place for all articles of commerce in their transit from the North Sea to Panamá.

XXIV. An observation of an eclipse of the Sun at the Island of New-found-land, August 5, 1766, by Mr. James Cook, with the longitude of the place of observation deduced from it: Communicated by J. Bevis, M. D. F. R. S

Mr. Cook, a good mathematician, and very expert in his business, having been appointed by the Lords Commissioners of the Admiralty, to survey the sea coasts of New-found-land, Labradore, &c. took with him a very good apparatus of instruments, and among them a brass telescopic quadrant made by Mr. John Bird.

XXXI. Observations on the eclipse of the Sun at Chatham, April 1, 1764, by My. Mungo Murray: Communicated to Joseph Salvadore, Esq; F. R. S. in a letter from Dr. John Bevis

Sir, I Fancy I can now satisfy your curiosity as to a place in the northern limit of the path of the Moon's shadow, int he eclipse we observed at your house; that is, where the lower limbs of the Sun and Moon coincided, by the following abstract from a letter I received from my friend Mr. Mungo Murray of Chatham, a good mathematician, and author of an excellent work on ship-building.