Daniel Henry Gottlieb --- January 10, 1996
In "Math, Logic, and Lawyers" we advanced the thesis that Law Schools train Lawyers to apply general principles without training them to critically examine whether the application is correct. In "Math, Logic, and Lawyers" we saw how this led to the "water torture paradox" which resulted in severe riots and racial division in this country. In this article we examine the threat to the academic world which is posed by the Lawyers' present lack of critical reasoning.
This threat is augmented by two trends: The rapid increase of Law School graduates since the late 60's which absorbed most of the brightest young Americans; and the weakness of the influence over them by the core studies of academia, which are precisely those studies devoted to Truth and the methods of discovering it and explaining it.
This diversion of the nation's talent into Law was bemoaned by Chief Justice Warren Burger, who foresaw that this talented and superficially trained army of young people would press themselves into positions of power and influence. For the core of the academic world, it means that Lawyers will become chairwomen of congressional education committees and Secretaries of Education and Presidents of Universities. And that means that decisions will be made by people whose vision of academic studies is Law School. So it is no wonder that we have the chairwoman of a Senate committee who thinks that teaching is the only purpose of a University, and it is not surprising to have the Secretary of Education assert that there are parts of the curriculum which have not changed in 2000 years and it is high time to update it. So much for Euclidean Geometry, without which, according to Polya, the student misses his best opportunity to obtain the idea of strict reasoning and so acquire "a true standard with which to compare alleged evidence of all sorts aimed at him in modern life".
So let us consider a smart, good man. of about 45, who trained in the Law achieves a position in which he can influence the academic world. Say he becomes the Secretary of Education, or more likely, the president of an important university. His only serious study is in a subject which encourages clever misleading arguments and thoughtless applications of general principles. He is unexposed to the careful quest for truth of Mathematics or Physics or History. His general view is the egalitarian one taken over from the ideal relation among citizens. He regards all Subjects as equal.
Suppose a single number comes to his attention, a number which purports to show that his Mathematics Department is ranked lower in prestige than he thinks is desirable. This number and his standard become objective facts to him. The will be no critical examination of the statistics on which this number is based, even as there was no critical examination of the flawed statistics of the Coleman Report by the Law School trained judges in the school bussing cases. Just as the Coleman Report became the basis of the enforcement of school bussing, so does this number become the basis of our president's opinion of his Mathematics Department. And just as Coleman's repudiation of his own report failed to disturb its application in the Law, so nothing whatever can drive this president from his reliance on this sacred number and his artificial standard. It is settled, it is the Law, the Mathematics Department is substandard!
Since all Subjects are equal, he might reason, if he reduces Mathematics to a symbolic size and farms out its teaching duties to adjunct professors and other departments, he would save enough money to improve the "prestigious" departments. There would be no thought that the body of the university is more like that of live organism, than that of an egalitarian society, and that a weakness in Mathematics, its heart, should be regarded not as a signal to cut out the heart but rather as a warning to improve it.
Even if the rival view of universities as an organism is brought to his attention, he would regard it only as a self serving argument. He knows no History, so he does not know how the first Academy demanded of its students the knowledge of Geometry. Many Subjects; Astrology, Philosophy, Classical studies have waxed and waned in importance during the long centuries. When Mathematics receded in importance, Civilization declined, when Mathematics gained, Art, Science, even Politics flourished.
But History was Then, this is Now, he might argue. But Now the influence of Mathematics is even greater. The vast social movements of the current era were founded by mathematicians. The Computer was conceived by mathematicians and nurtured by mathematicians until it dominates the present day. The Quality Revolution was founded by Demming, a mathematician. To understand the universe we live in, one must think like a mathematician. The winners of Noble prizes in sundry fields, Chemistry, Economics, are mathematicians.
Yet in spite of all this evidence, someone trained only in Law School might assert in all sincerity that there are no links between Mathematics and the other disciplines in his University. He may even think that Mathematics can be taught by less expensive teachers from High School or engineering with as much quality as by the professional mathematician. Maybe it can be, if it is the cookbook courses we are talking about. But what happens if we begin to teach what we really should be teaching, Topology and Set Theory to Freshmen, so that the great clarifying point of view given by functions and category and Topology which dominates recent times can be spread to physicists and engineers. Will these non-professional teachers rise to the occasion, or will they fail to understand the brilliant new viewpoint much as the Math teachers of elementary schools could not understand the concepts of sets some years ago?
Sooner or later these ideas will spread out to a large class of people, just as the old university subjects of Arithmetic and Algebra spread out. I think it will be sooner than later. One thing is for sure. Those Universities led by Lawyers will not be leading the way. Lawyers never heard of Topology.
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