Contemporary students of the social sciences are well-acquainted with two claims about the role of quantitative techniques in those fields. One is that quantification is essential for an objective and rigorous investigation of the social no less than the "natural" domain; another is that no description of a social world or an aspect of one can be complete without some qualitative appreciation of relevant properties of the territory. Our purpose here is not to rehearse the several arguments and accounts that could be given in support of or in opposition to one or the other of these not incompatible claims, but rather to show how their familiarity tends to conceal a vast array of presuppositions that can be felicitously displayed through an historical and philosophical analysis of their content.