Once upon a time, a certain mathematics professor, one William Dilworth, joined the ranks of those purporting to rebut Cantor’s diagonal argument and aiming to show that that set theory (as we know and love it) is founded on mistake — indeed “Logicians’ axiomatic set theory is meaningless in mathematics. They have been working in wrong mathematics and exerting their efforts in vain over the past sixty years.” Underwood Dudley gave Dilworth a mention in his entertaining squib Mathematical Cranks. Dilworth sued for defamation. [HT to a FOM posting …]
The case was dismissed, then went to appeal. The dismissal was upheld on appeal in a decision written by Richard Posner. From the decision:
A crank is a person inexplicably obsessed by an obviously unsound idea—a person with a bee in his bonnet. To call a person a crank is to say that because of some quirk of temperament he is wasting his time pursuing a line of thought that is plainly without merit or promise … To call a person a crank is basically just a colorful and insulting way of expressing disagreement with his master idea, and it therefore belongs to the language of controversy rather than to the language of defamation.
That seems to me an excellent characterisation of a crank! But it does prompt the thought that, by that token, an awful lot of philosophers are either cranks or expend a great deal of ink on cranks …
Or am I just getting cranky in my old age?
Emile Borel observed in 1905 that in Cantor’s assumption of a numbering of the reals, it is not specified how the numbering is given. He added a little word: Assume an effective numbering… and arrived at the conclusion that no such effective numbering exists. Was he a crank?
The court documents identify Dilworth as an engineer rather than a mathematics professor.
On FOM, Alexander Lemberg seems to have conflated Dilworth (cited as “D.” and discussed on pages 44-45 of _Mathematical Cranks_) with “H.N.” (discussed on page 322).