# Is there any evidence De Morgan abandoned probability theory due to it being "too tricky/non-intuitive/difficult"?

During a brief conversation in Ten Fold, whuber pointed out:

I recall reading long ago that Augustus DeMorgan abandoned probability theory after much study, finding it too tricky/non-intuitive/difficult; but I have been unable to find an authoritative reference in any of his works.

I searched in his bio of Augustus De Morgan, but at least I couldn't catch anything conspicuous.

So, I am curious whether there is any written account of any possible rendezvous with probability by De Morgan.

It depends on what "abandoned" means. De Morgan did write his main works on probability in 1837-38 and then turned his primary attention to logic. In his lengthy 1837 review of Laplace's Théorie analytique des probabilités, he did characterize the book as

"the Mont Blanc of mathematical analysis; but the mountain has this advantage over the book, that there are guides always ready near the former, whereas the student has been left to his own method of encountering the latter".

In 1853 De Morgan mused in a letter to Hamilton that "everybody makes errors in probabilities, at times, and big ones", and in 1861 confessed one of his own, see Rice, ‘Everybody makes errors’: The intersection of De Morgan's Logic and Probability, 1837 – 1847.

So perhaps one can make the inference. Rice does:"read in the light of the above discussion, [the 1853 quote] seems to give a reasonable explanation for his later neglect of the subject". Still, De Morgan continued to use and promote probability in his logical works.

When De Morgan talked about making errors, he was speaking from personal experience. His major contribution to probability in 1837 was to spot a mistake in works of Laplace and Poisson, but... in his supposed "correction" he himself made several mistakes, see Rice, De Morgan in the prehistory of statistical hypothesis testing. And he missed that Poisson corrected the mistake later in the same work. To top it off, the next year De Morgan made the same mistake in two other works. The mistake was to confuse $$p(X|Y)$$ with $$p(Y|X)$$, a typical rookie mistake by modern standards and the "thundering error", as he put it years later. Here is humbled De Morgan of 1861 (quoted from Rice):

"There are no questions in the whole range of applied mathematics which require such close attention, and in which it is so difficult to escape error, as those which occur in the theory of probabilities … and, of all subjects, there is no one in which writers of every grade have so frequently or so strangely made mistakes of mere inadvertence. One was pointed out about twenty years ago (‘Camb. Phil. Trans.’) into which both Laplace and Poisson had fallen, one after the other; but the discoverer of their slip proved himself signally liable to greater ones a very little while after."

"The discoverer of their slip" is De Morgan himself, as he intimated in a letter to Hamilton:

"I see you did not notice, in the part you have read, a thundering error, on the simplest point possible. Nor has anyone else noticed it, except myself, who have printed a sarcasm against ‘a recent writer’ that I may be able to prove I found it out before anybody."

Hamilton did not notice the "thundering error" even after that, so De Morgan had to give him a page reference.

• Thanks Conifold, as always, for the extensive research. +1. I would go through the details a bit and then hopefully would accept it. Apr 21 at 19:46
• I never could have imagined De Morgan was suffering that much rummaging through those texts. Amazing account. Apr 21 at 19:49