Modern mathematics as religion

[...] Most (but not all) of the difficulties of Set Theory arise from

the insistence that there exist `infinite sets', and that it is the

job of mathematics to study them and use them.

In perpetuating these notions, modern mathematics takes on many of the

aspects of a religion. It has its essential creednamely Set Theory,

and its unquestioned assumptions, namely that mathematics is based on

`Axioms', in particular the Zermelo-Fraenkel `Axioms of Set Theory'.

It has its anointed priesthood, the logicians, who specialize in

studying the foundations of mathematics, a supposedly deep and

difficult subject that requires years of devotion to master. Other

mathematicians learn to invoke the official mantras when questioned by

outsiders, but have only a hazy view about how the elementary aspects

of the subject hang together logically.

Training of the young is like that in secret societiesimmersion in

the cult involves intensive undergraduate memorization of the standard

thoughts before they are properly understood, so that comprehension

often follows belief instead of the other (more healthy) way around. A

long and often painful graduate school apprenticeship keeps the cadet

busy jumping through the many required hoops, discourages critical

thought about the foundations of the subject, but then gradually

yields to the gentle acceptance and support of the brotherhood. The

ever-present demons of inadequacy, failure and banishment are however

never far from view, ensuring that most stay on the well-trodden

path.

The large international conferences let the fellowship gather together

and congratulate themselves on the uniformity and sanity of their

world view, though to the rare outsider that sneaks into such events

the proceedings no doubt seem characterized by jargon, mutual

incomprehensibility and irrelevance to the outside world. The official

doctrine is that all views and opinions are valued if they contain

truth, and that ultimately only elegance and utility decide what gets

studied. The reality is less ennoblingthe usual hierarchical

structures reward allegiance, conformity and technical mastery of the

doctrines, elevate the interests of the powerful, and discourage

dissent.

There is no evil intent or ugly conspiracy herethe practice is held

in place by a mixture of well-meaning effort, inertia and self-

interest. We humans have a fondness for believing what those around us

do, and a willingness to mold our intellectual constructs to support

those hypotheses which justify our habits and make us feel good.

[Set Theory: Should You Believe?

N J Wildberger

School of Maths UNSW Sydney NSW 2052 Australia

webpages:

http://web.maths.unsw.edu.au/~norman]

http://web.maths.unsw.edu.au/~norman/views2.htm

Gruß, WM

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