Mathematics and ethics

Summary: Since the time of Plato, mathematicians have been analyzing and confronting ethical problems.

Mathematics and ethics have a long and tangled history. Philosophy has nurtured mathematical forms of thought that, in turn, have had a profound influence on ethical theorizing. For example, mathematics served as a model for Jeremy Bentham (1748-1832) whose goal in utilitarianism was to develop a calculus of pleasure and pain.

Several contemporary ethical theories are tied to the mathematics of game theory, especially the work of John Rawls (1921-2002). Ethical issues arise in mathematics teaching, research, industry, and government work. Mathematicians such as Lee Lorch challenge discriminatory practices and fight for human rights, justice, and equality. Other mathematicians have refused to work on projects they find ethically problematic. Ethical norms often change over time and for various contexts, leading to controversial applications of mathematics research, like the atomic bomb. In the face of increasing marketability of mathematical results, some have questioned the disparity between the academic tradition of making knowledge freely available and personal ownership of intellectual property. Many professional associations have developed, maintained, and revised ethical guidelines for their members, and mathematicians who wish to perform experiments must submit a proposal to an institutional review board for ethical review. In 2010, the National Science Foundation issued a program solicitation for an Ethics in Science, Mathematics, and Engineering Online Resource Center.

Mathematics and Ethics in Plato (429-347 b.c.e.)

Plato’s Republic is the first systematic treatment of ethics. The best preparation for acquiring ethical knowledge is a firm foundation in mathematics. However, the connection between mathematics and ethics is much deeper. Methodologically, Plato develops his argument by building a simplified model of the state in the same manner in which a study of any geometrical figure is done in mathematics. Justice in the state is merely justice in the individual writ large. Thus, Plato appeals to similarity transformations. The argument is that, as a result of a uniform scaling operation, justice in the individual is similar to justice in the state. Further, within the Platonic tradition, mathematical and ethical knowledge have the same formal characteristics. They are both examples of purely intelligible objects grasped entirely by reason in an intellectual intuition and known as a result of a process of recollection. Thus, they are examples of immutable and unchangeable truths, which could not be other than what they are. Plato’s very definition of justice contains a mathematical element, because justice is a type of equality. Justice is a matter of treating equal individuals equally and unequal individuals unequally. According to Plato, different political orders arise from the different conceptions of equality.

Mathematics and Ethics in Aristotle (384-322 b.c.e.)

For Aristotle, mathematics does not provide a model for ethics. However, mathematical concepts function in an analogical sense. Aristotle used a distinction between arithmetic and geometric proportion in his discussion of justice. Distributive justice is based on geometrical proportion, while rectificatory justice is based on arithmetical proportion. Issues of rectificatory justice arise when a judge must rectify a situation by attempting to restore equality to someone who has been injured. Issues of distributive justice arise when something has to be divided among two individuals.

Modern Moral Euclidian Philosophers

Both Thomas Hobbes (1588-1679) and Baruch Spinoza (1632-1677) incorporated the mathematical method of Euclid of Alexandria into their treatment of ethics. Hobbes thought that mathematical modes of thought could produce clarity in ethics and politics. However, it was Spinoza who most rigorously and consistently imitated Euclid’s method. He begins each section of his Ethics with a set of definitions and axioms, which he then uses to demonstrate a series of propositions about the universe, human nature, and basic ethical precepts.

Mathematical Ethics

The guidelines of professional mathematical associations cover a wide range of topics. Creation, attribution, publication, and presentation of research, especially with regard to falsification and plagiarism, as well as skewed interpretations and one-sided “advertising” style arguments, are commonly addressed. These guidelines extend into the classroom, along with data sharing or loaning and responsible group work. Attention is also given to the nature of teacher-student and colleague relationships in which one individual has some level of authority over the other, especially when they involve professional decisions like hiring, granting tenure, issuing promotions, and conferring degrees.

Mathematician Philip Davis noted that ethics are typically derived from past experiences and so may do little good in addressing many future or even current dilemmas. Further, judging the past based on current criteria leads to additional difficulties. Arguments abound, for example, about whether statistical data gathered from Nazi medical experiments should be used or destroyed, or whether mathematicians can be held responsible for any future unanticipated uses of their work, such as computer viruses or code-breaking algorithms usurped by data thieves. The Manhattan Project exemplifies many of the moral dilemmas faced by mathematical scientists. Many participants have expressed profound regrets; others have not, citing the undeniable advances made in numerous fields and the need at the time to bring an end to the greater destruction of World War II. For example, the cyclotron was invented by Ernest O. Lawrence in 1931, who received the Nobel Prize in 1939 for this invention.

Bibliography

Ernest, Paul. “Values and the Social Responsibility of Mathematics.” Philosophy of Mathematics Education Journal 22 (2007).

Hersh, Reuben. “Mathematics and Ethics.” The Mathematical Intelligencer 12, no. 3 (1990).

Huff, Darrell. How to Lie With Statistics. New York: W. W. Norton, 1993.