I wondered whether ET Jaynes ever wrote or expressed an opinion about Lindley’s famous statistical paradox? I would be curious about his take on it, and imagine he must have done since he wrote prolifically on foundational issues.
I didn't know the answer, so I asked on Twitter. A very well respected Bayesian statistician Eric-Jan Wagenmakers replied stating that, although (obviously) he hasn't checked all Jaynes' work for an answer to your query, Jaynes does mention the 1957 paper of Lindley in Section 5.2 of his book Probability Theory: The Logic of Science, but the paradox itself is not really discussed in any detail.
Jaynes writes at length about Lindley's paradox in the commentary at the end of Bernardo (1980), A Bayesian analysis of classical hypothesis testing.
I found it more or less by chance after I'd stopped searching for anything Jaynes wrote about it and carried on reading generally about Lindley's paradox. I'm not sure if the paper or the comments are well known (there are other interesting comments including from Lindley himself, so maybe it is).
Jaynes doesn't cite work by himself about Lindley's paradox, which suggests he did not write about it elsewhere.