According to Wikipedia, "The theorems, proven by Kurt Gödel in 1931, are important both in mathematical logic and in the philosophy of mathematics." It further reports that "The first incompleteness theorem states that no consistent system of axioms whose theorems can be listed by an 'effective procedure' (e.g., a computer program, but it could be any sort of algorithm) is capable of proving all truths about the relations of the natural numbers (arithmetic)."
Does this not hold for performance attribution? Recall that I recently touched on the question as to whether or not attribution answers the questions we wish it to. Perhaps even the best model will leave something out. Might Gödel's theorem hold here, too?
You know the saying, "a little knowledge is dangerous," and it definitely applies here, as I've only lightly scratched the surface of this topic, and would need to devote several hours to have any real understanding of it. But the brief statement above seems to hold some truth.
Perhaps this might be a good topic for Jose Menchero, PhD to address, given that his PhD is in physics, and he is no doubt familiar with Gödel. Interesting subject, I think.
By the way, Gödel is an interesting subject, himself.
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Dave, what fun! And "great minds," as they say: I published a piece on the paradox of the liar and Gödel’s theorem in my blog, Middle Office, a few months ago (December 16, 2011). It is called "Pants on Fire," and here is the address: http://middle-office.com/2011/12/16/unclassifiable/.
ReplyDeleteBest regards,
Philip
Philip, thanks for your thoughts; I look forward to reading your piece.
ReplyDeletePhilip,
ReplyDeleteI loved your piece.
And beyond its impressive intelligence, I learned the source for the Cretan Liar.
Thanks
Dave,
One point in all this is that it is always possible to expand any system to make what was an unprovable statement in one system provable in the expanded system. So if our performance measurement system “leave(s) something out” that we need and which is undecidable, the system can always be expanded to incorporate what we need. What would be problematic is if there were an infinite list of such theorems that we would want to include, as there might be in formal mathematics. Thus, I do not think that Godel poses a problem for financial performance measurement where we have a limited intent and are pretty much in control of our foundations, even if practitioners tend to give them insufficient consideration.
Andre