Just Say No

Siger wished to remain a professing Catholic, and to safeguard his faith he had recourse to the celebrated theory of the two truths: what is true in philosophy may be false in religion, and vice versa.
—“Siger of Brabant” New Catholic Encyclopedia. 1914. 
If a thing can be done adequately by means of one, it is superfluous to do it by means of several; for we observe that nature does not employ two instruments where one suffices.
—Thomas Aquinas. Summa Contra Gentiles
“The Triumph of Thomas Aquinas Over Averroës”  Benozzo Gozzoli        (1420-1497)

Let no one,” read the sign over Plato’s Academy, the famed school of ancient Athens, “ignorant of mathematics enter here.” To Plato, understanding mathematics was prerequisite to the discussion of other topics, including politics. During the 1880s, however, some professors in the German university system (like Wilhelm Windelband and Wilhelm Dilthey) divided knowledge into what they called “geisteswissenschaften” (“human sciences”) and “naturwissenschaften” (“natural sciences”), so that where Plato viewed mathematics as a necessary substrate in a vertical, hierarchical relation with other fields, the Germans thought of that relation horizontally, as if they were co-equals. Today, that German conception is best exemplified by what’s known as “science studies”: the “institutional goal of” which, as Mark Bauerlein of Emory University observed some years ago, is “to delimit the sciences to one knowledge domain, to show that they speak not for reality, but for certain constructions of reality.” (Or, as one of the founders of “science studies”—Andrew Ross—began a book on the matter back in the early 1990s: “This book is dedicated to all of the science teachers I never had. It could only have been written without them.”) Yet, while it may be that the German horizontal conception (to use Plato’s famous metaphor) “carves nature at the joint” better than Plato’s vertical one, the trouble with thinking of the mathematical, scientific world as one thing and the world of the human, including the political, as something else is that, among other costs, it makes it very difficult to tell—as exemplified by two different accounts of this same historical event—the story of George Washington’s first veto. Although many people appear to think of the “humanities” as just the ticket to escape America’s troubled political history … well, maybe not.

The first account I’ll mention is a chapter entitled “The First Veto,” contained in a book published in 2002 called Political Numeracy: Mathematical Perspectives on Our Chaotic Constitution. Written by law professor Michael Meyerson of the University of Baltimore, Meyerson’s book is deeply influenced by the German, horizontal view: he begins his book by observing that, when he began law school, his torts teacher sneered to his class that if any of them “were any good in math, you’d all be in medical school,” and goes on to observe that the “concept of mathematics can be relevant to the study of law seems foreign to many modern legal minds”—presumably, due to the German influence. Meyerson writes his book, then, as an argument against the German horizontal concept—and hence, implicitly, in favor of the Platonic, Greek one. Yet Meyerson’s work is subtly damaged by contact with the German view: it is not as good a treatment of the first presidential veto as another depiction of that same event—one written long before the German distinction came to be dominant in the United States.

That account was written by political scientist Edward James of the University of Chicago, and is entitled The First Apportionment of Federal Representatives in the United States: A Study in American Politics. Published in 1896, or more than a century before Meyerson’s account, it is nevertheless wholly superior: in the first place because of its level of detail, but in the second because—despite being composed in what might appear to contemporary readers as a wholly-benighted time—it’s actually far more sophisticated than Meyerson on precisely the subject that the unwary might suppose him to be weakest on. But before taking up that matter, it might be best to explain just what the first presidential veto was about.

George Washington only issued two vetoes during his two terms as president of the United States, which isn’t a record—several presidents have issued zero vetoes, including George W. Bush in his first term. But two is a pretty low number of vetoes: the all-time record holder, Franklin Roosevelt, issued 635 vetoes over his twelve years in office, and two others have issued more than a hundred. Yet while Washington’s second veto, concerning the War Department, appears fairly inconsequential today, his first veto has had repercussions that still echo in the United States. That’s because it concerned what’s of tremendous political importance to all Americans even now: the architecture of the national legislature, Congress. But it also (in a fashion that may explain just why Washington’s veto does not receive the attention it might) concerned that basic mathematical operation: division.

The structure of the Congress is detailed in Article One of the U.S. Constitution, whose first section vests the legislative power of the national government in Congress and then divides that Congress into two houses, the Senate and the House of Representatives. Section Two of Article One describes the House of Representatives, and Clause Three of Section Two describes, among other things, just how members of the House should be distributed around the nation: the members should, the clause says, “not exceed one for every thirty Thousand” inhabitants. But it also says that “each state shall have at Least one Representative”—and that causes all the trouble.

“At the heart of the dispute,” as Meyerson remarks, is a necessarily small matter: “fractions.” Or, as James puts it in what I think of as his admirably direct fashion:

There will always be remainders after dividing the population of the state by the number of people entitled to a representative, and so long as this is true, an exact division on numerical basis is impossible, if state lines must be observed in the process of apportionment.

It isn’t possible, in other words, to have one-sixth of a congressman (no matter what we might think of her cognitive abilities), nor is it likely that state populations will be an easily-dividable number. If it were possible to ignore state lines it would also be possible to divide up the country by population readily: as James remarks, without having to take into account state boundaries the job would be “a mere matter of arithmetic.” But because state boundaries have to be taken into account, it isn’t.

The original bill—the one that Washington vetoed—tackled this problem in two steps: in the first place, it simply divided the country, whose population the 1790 Census revealed to be (on Census Day, 2 August 1790) 3,929,214, and divided by 33,000 (which does not exceed one per 30,000), which of course gives a product just shy of 120 (119.067090909, to be precise). So that was to be the total number of seats in the House of Representatives.

The second step then was to distribute them, which Congress solved by giving—according to the “The Washington Papers” at the University of Virginia—“an additional member to the eight states with the largest fraction left over after dividing.” But doing so meant that, effectively, some states’ population was being divided by 30,000 while others were being divided by some other number: as James describes, while Congress determined the total number of congressmen by dividing the nation’s total population by 33,000, when it came time to determine which states got those congressmen the legislature used a different divisor. The bill applied a 30,000 ratio to “Rhode Island, New York, Pennsylvania, Maryland, Virginia, Kentucky and Georgia,” while applying “one of 27,770 to the other eight states.” Hence, as Washington would complain in his note to Congress explaining his veto, there was “no one proportion or divisor”—a fact that Edmund Randolph, Washington’s Attorney General (and, significantly as we’ll see, a Virginian), would say was “repugnant to the spirit of the constitution.” That opinion Washington’s Secretary of State, Thomas Jefferson (also a Virginian) shared.

Because the original bill used different divisors, Jefferson said that meant that it did not contain “any principle at all”—and hence would allow future Congresses to manipulate census results for political purposes “according to any … crochet which ingenuity may invent.” Jefferson thought, instead, that every state’s population ought to be divided by the same number: a “common divisor.” On the one hand, of course, that appears perfectly fair: using a single divisor gave the appearance of transparency and prevented the kinds of manipulations Jefferson envisioned. But it did not prevent what is arguably another manipulation: under Jefferson’s plan, which had largely the same results as the original plan, two seats were taken away from Delaware and New Hampshire and given to Pennsylvania—and Virginia.

Did I mention that Jefferson (and Randolph and Washington) was a Virginian? All three were, and at the time Virginia was, as Meyerson to his credit points out, “the largest state in the Union” by population. Yet while Meyerson does correctly note “that the Jefferson plan is an extraordinarily effective machine for allocating extra seats to large states,” he fails to notice something else about Virginia—something that James does notice (as we shall see). Virginia in the 1790s was not just the most populous state, but also a state with a very large, very wealthy, and very particular local industry.

That industry was, of course, slavery, and as James wrote (need I remind you) in 1896, it did not escape sharp people at the time of Washington’s veto that, in the first place, “the vote for and against the bill was perfectly geographical, a Northern against a Southern vote,” and secondly that Jefferson’s plan had the effect of “diminish[ing] the fractions in the Northern and Eastern states and increase them in the Southern”—a pattern that implied to some that “the real reason for the adoption” of Jefferson’s plan “was not that it secured a greater degree of fairness in the distribution, but that it secured for the controlling element in the Senate”—i.e., the slaveowners—“an additional power.” “It is noticeable,” James drily remarks, “that Virginia had been picked out especially as a state which profited” by Jefferson’s plan, and that “it was […] Virginians who persuaded the President” to veto the original bill. In other words, it’s James, in 1896, who is capable of discussing the political effects of the mathematics involved in terms of race—not Meyerson, despite the fact that the law professor (because he graduated from high school in 1976) had the benefit of, among other advantages, having witnessed at least the tail end of the American civil rights movement.

All that said, I don’t know just why, of course, Meyerson feels it possible to ignore the relation between George Washington’s first, and nearly only, veto and slavery: he might for instance argue that his focus is on the relation between mathematics and politics, and that bringing race into the discussion would muddy his argument. But that’s precisely the point, isn’t it? Meyerson’s reason for excluding slavery from his discussion of Washington’s first veto is, I suspect at any rate, driven precisely by his sense that race is a matter of geisteswissenschaften. 

After all, what else could it be? As Walter Benn Michaels of the University of Illinois at Chicago has put the point, despite the fact that “we don’t any longer believe in race as a biological entity, we still treat people as if they belonged to races”—which means that we must (still) think that race exists somehow. And since the biologists assure us that there is no way—biologically speaking—to link people from various parts of, say, Africa more than people from Asia or Europe (or as Michaels says, “there is no biological fact of the matter about what race you belong to”), we must thusly be treating race as a “social” or “cultural” fact rather than a natural one—which of course implies that we must think there is (still) a distinction to be made between the “natural sciences” and the “human sciences.” Hence, Meyerson excludes race from his analysis of Washington’s first veto because he (still) thinks of race as part of the “human sciences”: even Meyerson, it seems, cannot escape the gravity well of the German concept. Yet, since there isn’t any such thing as race, that necessarily raises the question of just why we think that there are two kinds of “science.” Perhaps there is little to puzzle over about just why some Americans might like the idea of race, but one might think that it is something of a mystery just why soi-disant “intellectuals” like that idea.

Or maybe not.


Please let me know what you think! Also, if you are having trouble with posting a comment, please feel free to email me personally at djmedinah@yahoo.com. Thanks for reading!

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