How might the stock market react to about the forthcoming Pentagon report on UFOs?

boing
41

Of course, but when the truth really is complicated, the number of possible explanations increases exponentially with the complexity of the hypothesis. Most of the logical work that needs to be done comes from having enough data to even identify the hypotheses worth paying attention to within the space of possible hypotheses. You can make Occam’s Razor pretty darn rigorous in terms of Kolmogorov complexity and Solomonoff induction and various corollaries and more-computable-approximations thereof. It’s a tool of statistics and probability theory, not a tool of deductive logic, which means that if you ignore it, you’ll be wrong almost all of the time, and a smart enough observer would be able to calculate how often.

Now, if you claim to already have access to enough data to specify aliens as a likely enough category of explanations to be worth paying attention to, I would be thrilled to learn more. Until then, I’m going to apply Laplace’s Rule of Succession to the sequence of all prior claims of things-being-aliens whose truth value has since been determined, which evaluates to (1/(number of UFOs-being-aliens claims ever disproven + 2)).

42

There’ll be spandex jackets.
One for everyone.

1 Like
43

Lockheed didn’t seem to do much in direct reaction to Harry Reed’s pronouncements.

44

Excuse me? I was merely noting you shared a common misperception of Ockham’s Razor; I made no claims about aliens or UFOs at all.

45

What a beautiful world this will be!

2 Likes
46

It wasn’t me you initially replied to, and I have no idea whatsoever what misconceptions @Ericb may or may not have about Occam’s Razor. But in any case, UFOs aside, your claim that Occam’s razor “is not logically rigorous” is questionable at best, so I decided to sketch out some of the formal, rigorous mathematical underpinnings of which it is a convenient informal description.

Either you’re also familiar with those, and with the rules of probability theory, conditional probability, and statistical inference that they’re tangled up with, and there’s still a misconception you’re pointing to that I’m not seeing, which I’d love to know about, or else you may want to reconsider how well you understand Occam’s Razor’s logic and rigor.

47

“Questionable”…?

Ockham’s Razor isn’t logically rigorous, because it makes no claims at all re: logic, of course. Once again, it merely states that the most simple explanation of a given fact/phenomenon is most likely correct. Quite often, however, the truth of the matter isn’t so conveniently pigeonholed.

Statements of “likelihood” are the province of statistics, not formal logic, which does not deal well with “maybe” or “probably”. Using Ockham’s Razor as if it actually settles a given argument is deeply flawed. So is assuming I am arguing for “aliens” as the likely explanation of UFOs.

48

Well, this isn’t an argument, and we’re not discussing or deducing the logical implications of premises, so I don’t really see how that’s relevant. We’re hoping to understand and explain inconclusive data by selecting among a set of hypotheses, in advance of expected new data to come. Interpretation of data is a probabilistic/statistical matter.

49

You tried to use Ockham’s Razor as if it proves something, and it very much does not. Not even close.

https://nikhilsamuel.medium.com/understanding-occams-razor-6734c8888a31

Literally EVERY source mentions the simple fact that Ockham’s Razor proves nothing (you can even use it to “prove” blatantly false premises, such as the world being flat). It’s a tool meant to suggest fruitful avenues of research/debate, nothing more.

50

You tried to use Ockham’s Razor as if it proves something, and it very much does not.

I…honestly have no idea what you’re referring to. Occam’s Razor is an informal statement of a sound and formalizable principle of statistical inference, that if you have multiple hypotheses that explain a given data set, you will almost always do better to endorse those that are strictly simpler in an information-theoretic sense, until you get enough data to adequately single out which of the exponentially larger set of more complex hypotheses will be more accurate.

No one here is trying to prove anything: the original comment you replied to wasn’t, AFAICT, a positive claim of any sort, but just the observation that we should hold off postulating anything as complex as “aliens” as an explanation until after we have data that can overcome the prior improbability of that hypothesis. These aren’t theorems, and rigorous, deductive mathematical logic or proof are not available in this situation. Statements about how-the-real-world-is are always probabilistic and uncertain, never proven in the sense you’re describing, even if some of them are close enough that we all ignore the difference.

Obviously, sometimes, even most of the time, the truth is complicated because the world is complicated. Occam’s razor isn’t about proof, it’s about not prematurely jumping to conclusions about which of the vast set of complex hypothesis might be correct, and making useful predictions in the meantime by investigating the much smaller set of simpler-but-likely–to-be-partly-or-mostly-true hypotheses.

Edit to add: the links you gave are all about the informal philosophical principle of Occam’s razor, not the (unknown to William of Occam of anyone else prior to the discovery of information theory) formal probability-theoretic rules of inference for how to reach accurate conclusions from data sets. If that’s the limit of your understanding of Occam’s razor, you should read further before making accusations about who misunderstands what. Again, start with the section of that Wikipedia article you linked that talks about Solomonoff induction, Turing machines, and minimum message length. See also Shannon entropy, Kolmogorov complexity.

Note that the word “aliens” hides the complexity of the hypothesis behind a short English word, just like it would if you said UFOs were “magic.” Most of the complexity for these short words lives in the mind of the speaker and listener; the word is just a pointer to those meanings.

51

This topic was automatically closed after 5 days. New replies are no longer allowed.