John_Thacker
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John_Thacker has not written any posts yet.
John_Thacker has not written any posts yet.
Or, I suppose, I would compare it to the other noted statistical paradox, whereby a famous hospital has a better survival rate for both mild and severe cases of a disease than a less-noted hospital, but a worse overall survival rate because it sees more of the worst cases. Merely because people don't understand how to do averages has little to do with them requiring an agent.
Probability theory still applies.
Ah, but which probability theory? Bayesian or frequentist? Or the ideas of Fisher?
How do you feel about the likelihood principle? The Behrens-Fisher problem, particularly when the variances are unknown and not assumed to be equal? The test of a sharp (or point) null hypothesis?
It does no good to assume that one's statistics and probability theory are not built on axioms themselves. I have rarely met a probabilist or statistician whose answer about whether he or she believes in the likelihood principle or in the logically contradicted significance tests (or in various solutions of the Behrens-Fisher problem) does not depend on some sort of axiom or idea of what simply "seems right." Of course, there are plenty of scientists who use mutually contradictory statistical tests, depending on what they're doing.
Are you also an empiricist in mathematics, akin to Quine and Putnam?
Now, if at least one child is a boy, it must be either the oldest child who is a boy, or the youngest child who is a boy. So how can the answer in the first case be different from the answer in the latter two?
Because they obviously aren't exclusive cases. I simply don't see mathematically why it's a paradox, so I don't see what this has to do with thinking that "probabilities are a property of things."
The "paradox" is that people want to compare it to a different problem, the problem where the cards are ordered. In that case, if you ask "Is your first card an ace,"... (read more)
have you ever actually seen an infinite set?
Wait, are you an finitist or an intuitionist when it comes to the philosophy of mathematics? I don't think I've ever met one before in person?
Clearly you have to deal with infinite sets in order to apply Bayesian probability theory. So do you deal with mathematics as some sort of dualism where infinite sets are allowed so long as you aren't referring to the real world, or do you use them as a sort of accounting fiction but always assume that you're really dealing with limits of finite things but it makes the math and concepts easier?
Do you believe in the Axiom of... (read more)
To add to the comment about gambling-- professional gamblers are well aware of the term Dutch book, if not necessarily with arbitrage (though arbitrage is becoming more commonly used).
Sorry, posted too soon. I'm a little confused because you said that you rejected coherentist views of truth, but most mathematical empiricists these days use the idea of coherence to justify mathematics. (Mathematics is necessary for these scientific theories; these theories must be taken as a whole; therefore there is reason to accept mathematics, to grossly simplify.)
A calculated probability of 0.0000001 should diminish the emotional strength of any anticipation, positive or negative, by a factor of ten million.
And there goes Walter Mitty and Calvin, then. If it is justifiable to enjoy art or sport, why is it not justifiable to enjoy gambling for its own sake?
if the results are significant at the 0.05 confidence level. Now this is not just a ritualized tradition. This is not a point of arbitrary etiquette like using the correct fork for salad.
The use of the 0.05 confidence level is itself a point of arbitrary etiquette. The idea that results close to identical, yet one barely meeting the arbitrary... (read more)
I consider myself a 'Bayesian wannabe' and my favorite author thereon is E. T. Jaynes.
Ah, well then I agree with you. However, I'm interested in how you reconcile your philosophical belief as a subjectivist when it comes to probability with the remainder of this post. Of course, as a mathematician, arguments based on the idea of rejecting arbitrary axioms are inherently less impressive than to some other scientists. After all, most of us believe in the Axiom of Choice for some reason like that the proofs needing it are too beautiful and must be true; this is despite the Banach-Tarski paradox and knowing that it is logically independent of... (read more)
Sorry, ambiguous wording. 0.05 is too weak, and should be replaced with, say, 0.005. It would be a better scientific investment to do fewer studies with twice as many subjects and have nearly all the reported results be replicable. Unfortunately, this change has to be standardized within a field, because otherwise you're deliberately handicapping yourself in an arms race.
Ah, yes, I see. I understand and lean instinctively towards agreeing. Certainly I agree about the standardization problem. I think it's rather difficult to determine what is the best number, though. 0.005 is as equally pulled out of a hat as Fisher's 0.05.
From your "A Technical Explanation of Technical Explanation":
Similarly,... (read more)