Patrick O'Donnell on the quantitative and the postmodern

Herewith Patrick O'Donnell's response to Quantitative Postmodernism:

My acquaintance with the natural and social sciences leads me rather to think that a belief in mathematical analysis is a recurrent positivist fantasy, the latest of which is incarnate in a misplaced faith in the application of Bayesian reasoning to all sorts of problems and areas in which it may not be appropriate or sufficiently informative or explanatory. As Richard Miller points out in Fact and Method: Explanation, Confirmation and Reality in the Natural and Social Sciences (1987), this faith in Bayesian reasoning is emblematic of “an excess of formalism in which truisms about likelihood (plausibility, simplicity, and so forth) are given one-sided readings and abstract results are developed at too far a remove from the problems to be solved.” And belief in the power of mathematical analysis (what we once pejoratively dubbed ‘numbers crunching’) is a by-product of its prominence in several natural sciences, especially (thus not only) physics, and may be a trickle-drown or spillover effect of the prestige of naturalized epistemology. Such formalism is indicative of what Nicholas Rescher calls a “penchant for quantities,” a “fetish for measurement”:

People incline to think that if something significant is to be said, then you can say it with numbers and thereby transmute it into a meaningful measurement. They endorse Lord Kelvin’s dictum that "When you cannot express it in numbers, your knowledge is of a meager and unsatisfactory kind." But when one looks at the issue more clearly and critically, one finds there is no convincing reason to think this is so on any universal and pervasive basis.

Rescher reminds us that “the things you cannot quantify in the context of an inquiry may well turn out to be the most important.” Bayesianism may have been elected the post-positivist prom queen of induction, but there are other princesses and their retinue deserving jeweled pieces of the crown: inductive generalization (e.g. enumerative induction) and hypothetical induction (e.g. hypothetico-induction) for two, a sum of three paradigmatic inductive principles, three archetypes, and the respective families they engender in the quest to formalize, naturalize, or mathematize explanation in the social sciences. Although applicable to stochastic systems (as probabilistic analysis of games of chance), Bayesianism has been stretched in application to belief, “based on the principle that belief comes in degrees, usually numerical, and is governed by a calculus modeled more or less closely on the probability calculus” (John D. Norton). Bayesianism has all the formalist pretensions of deductive reasoning, for “if there is one account of induction that does aspire to be the universal and final account, it is the Bayesian account.”

Richard Miller, John D. Norton, John Earman, and the late L. Jonathan Cohen provide, I think, sufficient reason to be skeptical of this latest adventure in “scientific imperialism,” that is, “the tendency for a successful scientific idea to be applied far beyond its original home [cf. the fate of ‘rational-choice theory’], and generally with decreasing success, the more its application is extended” (John Dupré). Hilary Putnam credits Nelson Goodman with a knockdown argument that demonstrates “inductive logic is not formal in the sense that deductive logic is,” yet the endeavor to formalize inductive reasoning, largely through mathematics, persists. Putnam himself argues that “a purely formal method cannot be hoped for in inductive logic,’ while Norton makes a compelling case for what he calls a “material theory of induction,” wherein “all inductions ultimately derive their license from facts pertinent to the matter of the induction.” In the letter if not spirit of Stephen Toulmin’s several briefs on behalf of practical reasoning over the past fifty years, Norton proclaims, “It is high time for us to recognize that our failure to agree on a single systematization of inductive inference is not merely a temporary lacuna. It is here to stay.

None of this is meant to be utterly dismissive, if you will, of a modest application of mathematical reasoning. For example, from Nicolas de Condorcet to Amartya Sen, we see the indispensable and important value of mathematical reasoning in “social choice” analysis and theory. And in domains of finance, for instance, we can readily ascertain its necessity and applicability. Computer modeling relying on complex algorithmic formulas and mathematics has demonstrated its value in a wide array of fields, especially in the natural sciences (including ecology, as Daniel B. Botkin has well argued). So the cautionary sentiment above is just that: in “looking for ways to quantify things heretofore characterized, perhaps even dismissed, as ‘behavioral’ and therefore not worthy of or susceptible to mathematical analysis,” I ask only that you keep in mind the possibility that in this quest to quantify many things heretofore not quantified (perhaps for good reason), the explanatory and illuminative scope of such quantification may, in the end, be rather disappointing, at least if history is a reliable guide for such matters. To be sure, the proof of the pudding is in the eating so, as always, I anticipate with relish the fruits of your labors here.

References and Further Reading:

• Brown, Harold I. Rationality. London: Routledge, 1988.
• Cohen, L. Jonathan. An Introduction to the Philosophy of Induction and Probability. Oxford, UK: Oxford University Press, 1989.
• Dupré, John. Human Nature and the Limits of Science. Oxford, UK: Clarendon Press, 2001.
• Earman, John. Bayes or Bust: A Critical Examination of Bayesian Confirmation Theory. Cambridge, MA: MIT Press, 1992.
• Elster, Jon. Explaining Social Behavior: More Nuts and Bolts for the Social Sciences. Cambridge, UK: Cambridge University Press, 2007.
• Hausman, Daniel M. and Michael S. McPherson. Economic Analysis and Moral Philosophy. Cambridge, MA: Cambridge University Press, 2nd ed., 2006.
• Horst, Steven. Beyond Reduction: Philosophy of Mind and Post-Reductionist Philosophy of Science. New York: Oxford University Press, 2007.
• Kitcher, Philip. Science, Truth, and Democracy. Oxford, UK: Oxford University Press, 2001.
• McCloskey, Deirdre (formerly ‘Donald N.’). The Rhetoric of Economics. Madison, WI: University of Wisconsin Press, 1985.
• McCloskey, Deirdre. If You’re So Smart: The Narrative of Economic Expertise. Chicago, IL: University of Chicago Press, 1990.
• McCloskey, Deirdre. Knowledge and Persuasion in Economics. Cambridge, MA: Cambridge University Press, 1994.
• Miller, Richard W. Fact and Method: Explanation, Confirmation and Reality in the Natural and Social Sciences. Princeton, NJ: Princeton University Press, 1987.
• Norton, John D. “A Material Theory of Induction,” Philosophy of Science, 70 (2003): 647-670.
• Putnam, Hilary. Realism with a Human Face (James Conant, ed.). Cambridge, MA: Harvard University Press, 1990.
• Putnam, Hilary. Words and Life (James Conant, ed.). Cambridge, MA: Harvard University Press, 1994.
• Rescher, Nicholas. Objectivity: The Obligations of Impersonal Reason. Notre Dame, IN: University of Notre Dame Press, 1997.
• Rescher, Nicholas. The Limits of Science. Pittsburgh, PA: University of Pittsburgh Press, 1999 revised ed.
• Rescher, Nicholas. Nature and Understanding: The Metaphysics and Method of Science. Oxford, UK: Clarendon Press, 2000.
• Rescher, Nicholas. Cognitive Pragmatism: The Theory of Knowledge in Pragmatic Perspective. Pittsburgh, PA: University of Pittsburgh Press, 2001.
• Shapiro, Ian, Rogers M. Smith, and Tarek E. Masmoud, eds. Problems and Methods in the Study of Politics. Cambridge, UK: Cambridge University Press, 2004.
• Toulmin, Stephen. Cosmopolis: The Hidden Agenda of Modernity. Chicago, IL: University of Chicago Press, 1990
• Toulmin, Stephen. Return to Reason. Cambridge, MA: Harvard University Press, 2001.
• Toulmin, Stephen, Richard Rieke and Allan Janik. An Introduction to Reasoning. New York: Macmillan, 1984 ed.
• Toulmin, Stephen (2003 ed.). The Uses of Argument. Cambridge, UK: Cambridge University Press, 20003 ed.
• Williams, Michael. Problems of Knowledge: A Critical Introduction to Epistemology. Oxford, UK: Oxford University Press, 2001.