Suhhhhhweet! I am so taking that.
I was just looking for the money shot from the Jaynes paper EY refers to, and one of the links brought me here. Long time no see.
Since I’m here, here’s the money shot:
ET Jaynes—CHAPTER 15 PARADOXES OF PROBABILITY THEORY
How to Mass Produce Paradoxes
Having examined a few paradoxes, we can recognize their common feature. Fundamentally, the procedural error was always failure to obey the product and sum rules of probability theory. Usually, the mechanism of this was careless handling of infinite sets and limits, sometimes accompanied also by attempts to replace the rules of probability theory by intuitive ad hoc devices like B2′s ‘reduction principle’.
Indeed, paradoxes caused by careless dealing with infinite sets or limits can be mass produced by the following simple procedure:
(1) Start from a mathematically well-defined situation, such as a infinite set or a normalized probability distribution or a convergent integral, where everything is well behaved and there is no question about what is the correct solution.
(2) Pass to a limit—infinite magnitude, infinite set, zero measure, improper pdf , or some other kind without specifying how the limit is approached.
(3) Ask a question whose answer depends on how the limit was approached.
...
Our conclusion based on some forty years of mathematical efforts and experience with real problems is that, at least in probability theory, an infinite set should be thought of only as the limit of a specific (i.e. unambiguously specifed) sequence of finite sets. Likewise, an improper pdf has meaning only as the limit of a well defined sequence proper pdfs. The mathematically generated paradoxes have been found only when we tried to depart from this policy by treating an infinite limit as something already accomplished, without regard to any limiting operation. Indeed, experience to date shows that almost any attempt to depart from our recommended infinite sets’ policy has the potentiality for generating a paradox, in which two equally valid methods of reasoning lead us to contradictory results.
*****
David Wolpert of “No Free Lunch” Theorems and Stacked Generalization had something similar, a Declaration of Independence from Infinite Sets, roughly “This works for finite sets. The extension to infinite sets is left as an exercise to the interested reader.”
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I protest against the use of infinite magnitude as something accomplished, which is never permissible in mathematics. Infinity is merely a figure of speech, the true meaning being a limit.
-- C. F. Gauss
“more likely caused by a lab accident (aka lab leak) or zoonotic spillover”
False dichotomy.
One thing you can be sure of in Establishment “debate”: the truth is not among the proffered options.