All of that hinges on your 3rd bullet point.

And translating into plain English means that if you bet your life or your life saving on the outcome of a coin toss, you're an idiot.

That's not an effective critique of frequentist statistical theory. That's obvious.

The absolute best and most courteous interpretation of this is, "Don't be an idiot." Thanks, Taleb, for that most insightful piece of advice.

The problem here is that this series of thoughts ascribes an attribute to statistical theory that is absolutely non-existent: that there is any weight given to any individual trial of an outcome. No one thinks that. He, and now you, are arguing against a completely non-existent point.

Look, if you have anything approaching a decent model, you know the range of possible outcomes.

If you want to understand flipping a fair coin, the outcomes are that there's a heads and a tails and it has to land on one of them.

What Taleb and you are arguing is that there's a third possibility you didn't think of where the coin lands in an alternative universe, and Margaret Thatcher is the queen of the United States, and all the puppies die.

And if that's the real set of possibilities, I want to play that game. Because I would trade all of the puppies for Queen Thatcher right now. (No offense to you if you are actually a puppy. I just really don't like Trump.)

Saying that statistics is broken because infinity doesn't exist is like saying that basic arithmetic is broken if 1 equals 0.

No shit. Yeah, when you change the basic rules of how things work, things get broken really quickly.

I'm sorry if I'm being obtuse here, but I don't see anything even remotely worthwhile in his article, your post, or your link.

Trying to work backwards from a stochastic model to the outcome of an individual event will never work. And no one thinks that it will. If you want certainty, you have to use an entirely different model of logic.

Taleb is criticizing inductive logic for not being deductive, and then claiming that you'll get just as good a result by limiting the inductive model and using only a portion of what makes it work.

It's utter and complete bullshit, as far as I can tell.

Happy to be corrected, if you think I'm wrong.

Can we agree that a charitable plain english version of what he's trying to say is this:

Don't play the long odds if you aren't playing the long game. If you're playing the short game, don't risk more than you can afford to lose.

If he's saying more than that, please enlighten me. In my first post on this topic I said that he wasn't entirely wrong, but he is entirely useless. If you've made it past the age of 5 and haven't figured this out already, well, reading his book won't help you because you won't understand a goddamn word in it.

I will read his next book because it's unfair to criticize something you haven't exposed yourself to. But I can't imagine any possible way that it could comprise a collection of proofs.

Again, what is there to prove? That probability doesn't work good when you change the rules about how it works? That you can't take a distribution and apply it to a single point in time? That you can't take a collection of inductive data and use it to prove a universal truth?

No sane person has ever claimed that you can do any of those things. All I can tell is that Taleb is claiming to be both interesting and original by writing a book that says you can't do any of those things.

Welcome to the grown-up world, Taleb. We already knew that.

P.S. Santa Clause isn't real.
Maybe I should write a book about how not real Santa is. I bet Murray Gell-Mann would immediately grasp this concept.