David Henige’s Reply^*

I would like to thank Dr. Zambardino for commenting on my paper concerning the size of the contact population of Hispaniola and contributing another voice to this colloquy. His remarks are especially welcome since they speak directly and eloquently to the larger issue of the role of quantitative methods in historical investigations where the data are exiguous and indirect. In this regard, he urges that my arguments be “firmly resisted.” He believes, too, that I have been unfair in suggesting that Borah and Cook’s analysis of the pre-Spanish population of central Mexico is exceptionable. Zambardino feels that the methods used by Borah and Cook for central Mexico are very similar to those which they used for Hispaniola after 1508.

Would that this were so. In fact, though, whereas Borah and Cook were able, when discussing post-1508 Hispaniola, to base themselves on specific numbers directly applied, the materials they have used for aboriginal central Mexico nowhere discussed numbers of people. The only population figures are Borah and Cook’s own. Under the circumstances it may not be inappropriate to address directly, though very briefly, the work of Borah and Cook as it relates to central Mexico. In doing so, I will devote attention to discussing why I believe that there is little more reason to accept their methodology (as Zambardino would) or their figures (as Zambardino would not) than there is for Hispaniola.¹

On the grounds that the burden of proof always lies with the framer of an argument and that it is reasonable to judge the extent to which the argument is persuasive without recourse to external evidence, I confine my comments to Borah and Cook’s The Aboriginal Population of Central Mexico on the Eve of the Spanish Conquest,² This work, the classic exposition of the authors’ argument for a population of approximately twenty-five million, was the last of several studies which they devoted to the population of parts of New Spain during the sixteenth century. It is based almost entirely on tribute information found in the Matrícula de tributos and the Codex Mendoza, early post-conquest records which, the authors argue (pp. 36-40), were independently derived copies of a preconquest source.³

Whatever their provenance, these sources’ information relating to tribute is confined to products, provinces, and periodicity; people are not mentioned. This forces Borah and Cook to work their way through a series of exercises designed to overcome this defect: attempting to determine absolute and relative values of the goods pictured by adjudicating discrepancies, striking averages, and determining periodicity of payment; suggesting an average family size; speculating on the proportion of the population that was exempt from tribute; and identifying those areas not subject to the Triple Alliance. Although it is true that none of their conclusions taken individually can be considered impossible, it is equally true that none of them is historically verifiable or, for that matter, even enjoys very much evidential support, being derived from the odd Spanish source or from problematical extrapolations from conditions during Spanish rule.⁴

The result is in effect a minefield of “perhaps,” “probablys,” “must have beens,” and “seems likelys.” One or more of these expressions can be found on nearly every page, sometimes (for example, p. 68) occurring twice in a single sentence. Certainly it is wise and necessary that any exercise of the historical imagination be controlled rather than unleashed by the deficiencies in the data, but the sum of verbal caution expressed in this instance is clearly detrimental to the success of the inquiry.

Even so it might have been tolerable, if only a number of these caveats had not occurred at the crucial juncture (pp. 60-66) in the argument. Here the authors attempt to establish “some estimate of the probable average quota assessed against the individual family” (p. 62), even though they had already conceded that such a standard quota was “unlikely” to have been imposed throughout the tributary area (p. 60). Inevitably they fail in their attempt to establish the existence of that which never was. By their own testimony, the available sources fail to establish unequivocally (or even suggestively) a widespread and direct relationship between amount of tribute and size of population. From all accounts, tribute was negotiated, a matter of realpolitik and not of numbers of people (pp. 60-61).

Undoubtedly the burden of taxation ultimately fell on the smallest social unit, but the ways in which it did so were not uniform and were adventitious over time and space. This can be illustrated by the problem of the relationship between rebellion and the amount of tribute imposed. Since tribute was allegedly doubled after an unsuccessful revolt, a given province which rebelled, say, three times during its period of subservience would eventually pay a tribute equal to eight times that of another province of equal original levy which had remained quiescent. By this argument, there would be an inverse relationship between numbers of people and incidence of revolt, but none at all between numbers of people and amount of tribute assessed.

The inability to demonstrate a direct relationship between tribute and people is a fatal flaw in the web of Borah and Cook’s argument. Having failed to establish that the tribute system of the Triple Alliance was based on a per capita principle, any attempt to proceed in their chosen methodology is necessarily fruitless and meaningless. That they did proceed, and that their conclusions have been widely accepted, amply illustrates the seductive qualities of apparently sophisticated numerical procedures. Borah and Cook must be given high marks for industry, ingenuity, and candor, but rather lower marks for failing to recognize the crippling effect of the problems they themselves raise. Instead, they too often attempt to prove one hypothesis by advancing another, exhibiting a tendency to move lightly from conjecture to argument to assertion.⁵

Unlike Zambardino, then, I find the methods adopted by Borah and Cook for central Mexico even less acceptable than their results. Partly, this is because I disagree that in practice it is very easy to divorce assumptions from methods; partly it is because the data, like those for Hispaniola (albeit in different ways) cannot support the overload of inference thrust on them in an effort to demonstrate the efficacy of the quantitative approach. Simply put, the lack of satisfactory evidence blunts the cutting edge of the techniques adopted, and no amount of numerical sophistication, however it is deployed, can compensate for the hopelessly numerous imponderables that result.

We have probably now reached a point of irreducible philosophical and methodological antithesis. Those who will quantify at all costs may regard those who are unwilling to do so as mere conventional historians who, content to be tethered by orthodoxy, plod along missing insight after insight. Conversely, the non-quantifier may take the position that, after all, it is the evidence which really matters and which must govern the extent to which quantitative techniques can be successfully applied. If so, perhaps many of them will be puzzled by the recent rush to numbers in historical scholarship and left slightly breathless by what seem to them unjustified leaps of faith of the kind that allowed Borah and Cook to proceed untouched and unimpeded by the detonations of numerous mines of their own making. It may well be that eventually evidence will emerge suggesting that the population of central Mexico actually was of the magnitude argued by Borah and Cook, or which would at least permit some sort of quantitative analysis to be applied to it. If so, such evidence will, I am sure, be gladly received and promptly put to use. Until then, though, aprioristic reasoning characterized by simple assertion and sanguine assumption cannot be allowed to stand as surrogate.