Friday, March 25, 2005

Intro to the math chapter

Here is the rough draft of the introduction to my chapter in my thesis about mathematics:

It is not the results but methods that can be transferred with profit from the sphere of the special sciences to … philosophy. – Bertrand Russell

Although Bertrand Russell’s idealist philosophy in the massive Principia Mathematica of a complete codification of the universally acceptable modes of human reasoning (that is, those modes without contradictions), at least as they applied to mathematics, came crashing down with Kurt Godel’s tiny “On Formally Undecidable Propositions in Principia Mathematica and Related Systems I” (1932), his methodology is still useful and pertinent today in literary criticism. The gap between the sciences (whether “hard sciences,” such as mathematics, physics, chemistry, biology, or the social sciences, such as political science, sociology, economics, linguistics) and the humanities (literature, philosophy, art theory) has seemed impassable for ages given the stereotype of scientists as the kings of the temple of objective truth and knowledge and humanists as jesters entertaining others in flights of fancy and make-believe. Every year at the time of the MLA conference, there is a mocking article in the New York Times about the fanciful ideas humanists have come up with. Perhaps some of the mocking is justified. Of course, such stereotypes are not true, but one discovers a kernel of truth given the Alan Sokol affair. Sokol played a famous hoax on the postmodern academic world when he submitted a pseudoscientific paper to Social Text entitled “Transgressing the Boundaries: Toward a Transformative Hermeneutics of Quantum Gravity” with the goal of seeing whether a humanities journal would “publish an article liberally salted with nonsense if (a) it sounded good and (b) it flattered the editors’ ideological preconceptions.” The footnotes contain even more obvious jokes:
Just as liberal feminists are frequently content with a minimal agenda of legal and social equality for women and 'pro-choice', so liberal (and even some socialist) mathematicians are often content to work within the hegemonic Zermelo-Fraenkel framework (which, reflecting its nineteenth-century liberal origins, already incorporates the axiom of equality) supplemented only by the axiom of choice. (242-243).
The Zermelo-Fraenkel axioms with the addition of the axiom of choice, which states that given any set of mutually exclusive non-empty sets, there exists at least one set that contains exactly one element in common with each of the non-empty sets, are the standard axioms of axiomatic set theory, and hence, are unrelated to political questions of equality and choice. In the end, the Sokol affair demonstrated that some humanities scholars lack a basic understanding of science and mathematics. Of course, the converse is also true: some scientists and mathematicians lack a basic understanding of literary criticism and theory, so we must return to the divide between the physical and human sciences.


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