Quotations in Context: Plato – 2

“Mathematics is like checkers in being suitable for the young, not too difficult, harmless, amusing and without peril to the state.”

For quite some time, I had been unsuccessfully trying to track down the original source of this quotation, which is attributed to Plato in many modern publications. So I was surprised and relieved to find the correct citation in the online archives for the Canadian Society for History and Philosophy of Mathematics, on the last page of the September 1988 CSHPM/SCHPM Bulletin, which contained a column of “Citations/Quotes.” No author of the column is listed, so the material may have been collected by that issue’s editor, Roger Herz-Fischler; in any case, I was very grateful to finally discover the correct source and wanted to give full credit to the Society’s archived Bulletin for showing me the way.

Bust representing Plato, Roman copy of earlier Greek sculpture, 4th-century BCE. Public domain, Wikimedia Commons.

In 1951, the article “A Mathematical Reappraisal of the Corpus Platonicum” appeared in the journal Scripta Mathematica. The author, Domhnall A. Steele, began the article by expressing deep concern over the “danger of trivialization” [Steele 1951, p. 173], specifically the tendency to reduce or oversimplify the works of Greek mathematicians, robbing their work of important context and translating them into something “trite and obvious” [Steele 1951, p. 173]. The author stated that this is particularly a problem with modern assessments of Plato, and he provided several examples of mathematical terms and phrases from Plato’s work, arguing that the original context supports a more meaningful and robust English translation than is usually given.

Steele argued that correct interpretation of Plato requires that we “know into what kind of mathematical world he was born” [Steele 1951, p. 176], and he explored examples of mathematics from Hippocrates, Eudoxus and Euclid to illustrate the kinds of mathematics that Plato would have seen and the level of understanding and expertise of his culture. Steele followed this with fifteen brief examples of mathematics from Plato’s own works.

The final portion of the article presented Plato’s overall views on mathematics by synthesizing statements on the subject from his many works. While this section of the article provides numerous endnotes to meticulously indicate the sources from which the views originated, this material was paraphrased rather than directly quoted, and Steele stated clearly that he would “speak for a while in Plato’s name” [Steele 1951, p. 184]. It was in this section of the article that we find this column’s quotation:

Mathematics is like checkers in being suitable for the young, not too difficult, harmless, amusing, and without peril to the state. The citizens of the ideal state, our Callipolitans, cannot be allowed to neglect mathematics, for there is an immense chasm between a man who has grasped it and a man who has not. The holders of high office must proceed to its advanced stages and master at least the theory of the multiplicative composition of numbers.

When we look to the future activity of the young in industry or affairs public or private, no subject is more suitable for their training than the science of number, for it wakes up the intellectually somniferous and confers even upon them an adroitness in excess of their natural capacity. The born arithmeticians turn out sharpwitted in other studies as well [Steele 1951, p. 185].

The endnotes in the article indicated that the sentence containing this column’s quotation was based on material from Plato’s Laws. For the sake of comparison, below is an English translation of the relevant section of Laws by Benjamin Jowett:

Athenian: The natures of commensurable and incommensurable quantities in their relation to one another. A man who is good for anything ought to be able, when he thinks, to distinguish them; and different persons should compete with one another in asking questions, which will be a far better and more graceful way of passing their time than the old man’s game of draughts.

Cleinias: I dare say; and these pastimes are not so very unlike a game of draughts.

Athenian: And these, as I maintain, Cleinias, are the studies which our youth ought to learn, for they are innocent and not difficult; the learning of them will be an amusement, and they will benefit the state. If anyone is of another mind, let him say what he has to say [Plato 1892, pp. 203–204].

I suspect that Steele’s paraphrase of Plato has proven popular in modern works because it seems to give a negative (or at least not very positive) impression of mathematics; after all, calling something “harmless” and “without peril to the state” is not usually a way of indicating that a subject is highly valued or useful. However, when the quotation is viewed in the surrounding context of Steele’s article (and also considering the original text of Plato on which it was based), it is clear how much higher of a value is really being assigned to mathematics.

References

Plato. 1892. The Dialogues of Plato. Translated by Benjamin Jowett. 3rd ed. Vol. 5. Oxford: Clarendon Press.

Steele, Domhnall A. 1951. “A Mathematical Reappraisal of the Corpus Platonicum.” Scripta Mathematica 17: 173–189.

“Quotations in Context” is a regular column written by Michael Molinsky that has appeared in the CSHPM/SCHPM Bulletin of the Canadian Society for History and Philosophy of Mathematics since 2006 (this installment was first published in May 2017). In the modern world, quotations by mathematicians or about mathematics frequently appear in works written for a general audience, but often these quotations are provided without listing a primary source or providing any information about the surrounding context in which the quotation appeared. These columns provide interesting information on selected statements related to mathematics, but more importantly, the columns highlight the fact that students today can do the same legwork, using online databases of original sources to track down and examine quotations in their original context.