At the risk of introducing new terminology, does this definition of a statistic includes a “conditional expectation”? I guess it does, but conditional expectations are defined to possess certain properties as well as being functions of the data.

I appreciate the compliments, although do I detect a hint of sarcasm?

Anyway, I’m not sure I like this definition of statistics. The general intuition is that algebra is not statistics, but your definition overlaps both strata.

Also, I would point out that probability distributions are not unique in being abstract. *All* mathematical statements are abstract, however obvious.

That one?

Found at Jeff Miller’s Earliest Known Uses of Some of the Words of Mathematics page:
http://jeff560.tripod.com/s.html

Alex — Probability theory (as represented,say, by the axioms of Kolmogorov) provides one basis for the formal representation of uncertainty, and, subsequently, a basis for decision-making under uncertainty. But, contrary to the beliefs of many bayesian statisticians, probability theory is not the only way to fomally represent uncertainty, nor even necessarily the most appropriate in any given application domain. Because, historically, statisticians mostly failed to consider other formalisms, it was left to people outside statistics (in law, in medicine, and latterly, in AI) to consider non-probabilistic formalisms for uncertainty. These alternative formalisms (eg, Dempster-Shafer Theory, possibility theory) also provide a basis for decision-making under uncertainty.

Including notedscholar, who had the better question about irrationality of infinity and irrationality of imaginary numbers.