Fully agree with every single word in this article. Particularly the bit about "identity statistics". Also, regarding failure of notation: I've been arguing fo

Fully agree with every single word in this article. Particularly the bit about "identity statistics". Also, regarding failure of notation: I've been arguing for a while that the notation we use for probability is highly problematic and effectively eggregious abuse of notation. And not just the whole "belief vs frequency of hypotheticals", but even the simple fact of what it represents. Does p(x) denote an event? The whole distribution? The distribution over a particular space? An apologist might rightly point out that p(x) is actually shorthand for p(x=X), where x is the event and X is the distribution. But even this screams confusion. For me the ideal notation would have been something that makes it explicit that the probability describes a set of 'sampling events' from a 'pool', e.g. Prob_{x}(X), where x is the set of events, and X is the nature of the distribution (i.e. a function which returns frequencies/beliefs over a domain). And probability density functions would be denoted as actual derivatives, e.g. d/dx P_x (Cum.Normal)