Thanks for the compliment.

"Given a set of observations, plenty of statistical distributions can correspond to the exact same realizations--each would extrapolate differently outside the set of events on which it was derived."

True obviously, but it does seem that he subscribes to the idea that theory building (and a model that isn't grounded on theory is numerology IMHO) is basically fitting curves to data points.

I think there's a more technical meaning underlying his viewpoint, which is also relevant to the turkey problem. A fundamental idea in probabilistic finance is the idea of the change of probability measure. This is the crucial idea which allows calculations to be done.

Normally, a probability model/distribution is a kind of encoding of degrees of belief. (There's a famous result due to Cox to the effect that the only consistent way (with conventional logic) of modelling belief with a single number leads to Bayesian probability theory). In particular, the exact values of the probabilities matter a lot.

If two models are only slightly different, then it's possible to mathematically reweigh one model in terms of another (via likelihood ratios, radon-nikodym derivatives, Girsanov's formula...), which means that you can work within one belief framework, and in the end adjust the numerical predictions so that it's as if you had computed entirely within another set of beliefs.

For some kinds of calculations, such as those used when replicating portfolios, the end result only depends on the equivalence class of the beliefs, so it's common for finance people to work in a "risk neutral" belief system. Even though they don't know a good numerical model for the truth, they argue (rightly or wrongly) that the best "true" model belongs to the equivalence class of a simpler model, such as geometric Brownian Motion. So they calculate with BM in the knowledge that, had they worked with the true best model, they would have ended up with the same hedging rules. This is a huge advance, because the true values of the probabilities don't need to be understood exactly. You still need to estimate some parameters, but only "implied" ones rather than true predictive ones. And of course, you can't calculate everything, just those things that are invariant under change of measure.

At this level, what Taleb is getting at I think is that it's still hard to be sure that the true model is in fact equivalent, in the above sense, to the simpler models which allow calculations. It's the structural properties which matter. For example, Brownian motion is a continuous process without jumps, and that's a structural property. As long as the best "true" model doesn't have jumps, it might be equivalent to the BM model, but if you observe rare kinds of events such as a spectacular crash, then the BM model becomes incompatible, and you really should be looking for another family of risk neutral measures to work with. The heavy tails idea is one of those: BM doesn't have heavy tails, although other processes do.

This attitude is evident in his opening paragraph. Surely a statistician's hubris is behind the claim that:

Statistical and applied probabilistic knowledge is the core of knowledge

I agree with you, although I think much of this can be traced back in this case also to Taleb wanting to connect with various other pop science books that his readers would know about and respect. Later in the essay, he mentions Mandelbrot and Barabasi, which brings to mind fractals and networks. I also wouldn't be surprised if his "logic of science" is just a hat tip to Jaynes.

Yet in exhorting the theories of rare events, he misses other approaches. In the 70s, the big thing was catastrophe theory, which is a fully deterministic approach to rare events, although it's now out of style.

The reason I described EVT in detail was that it's one of those things I would have expected to show up somewhere in his essay. It's like when you open a new book and look at the index first, just to be sure that it contains the right mix of keywords.

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$E(X_t|F_s) = X_s,\quad t > s$