Nope. YOU have stated that YOU don't know what a grue is. Then you did some magical math to asign a probability to it. That's what I am objecting to. If you were uncertain, that'd be different--but YOU said YOU don't know.
I'm saying nothing about knowledge as such. I am saying that your self-reported knowledge OF THIS SITUATION is nil. We can state with certainty that you do not know what a grue is, because you said so. It's a given. Anything that comes after that, therefore, that isn't "How do I find out what a grue is?", is a statement not based on evidence.
The propositions H1, there is a grue in my house, and H2 there isn't have equal probabilities to me
because of my total ignorance about them. The logic is simple: I have no reason to believe that P(H1) > P(H0) and no reason to believe that P(H0) > P(H1), but P(H1) + P(H0) = 1; therefore, P(H1) = P(H0) = 0.5. This is the
principle of indifference. As the article explains:
The principle of indifference (also called principle of insufficient reason) is a rule for assigning epistemic probabilities. Suppose that there are n > 1 mutually exclusive and collectively exhaustive possibilities. The principle of indifference states that if the n possibilities are indistinguishable except for their names, then each possibility should be assigned a probability equal to 1/n. In Bayesian probability, this is the simplest non-informative prior....
The "Principle of insufficient reason" was renamed the "Principle of Indifference" by the economist John Maynard Keynes (1921), who was careful to note that it applies only when there is no knowledge indicating unequal probabilities.
A principle of how to assign probabilities to two mutually exclusive and collectively exhaustive possibilities that are indistinguishable except for their names, you know, like "grue" and "no grue," that applies when there is
no knowledge indicating unequal probabilities.
Actually, it's rather hillarious that you accuse me of not acknowledging shades of confidence in conclusions, given my area of expertise. Paleontology is basically a case-study in how to determine how confident one can be in one's conclusions.
On the contrary, it is rather sad that if that is your job that you don't understand how to apply Bayesian statistics.
However, it also demands a very strict acknowledgement of the limits of one's knowledge, and that's where I find you committing an error. If you have no data, you can't say anything--that's the principle I was taught, and the principle every scientist ostensibly if not actually accepts.
On the contrary, most scientists, when doing a Bayesian hypothesis test, would give equal prior probability to the two competing hypotheses, to avoid biasing the test in one direction or the other.
If you can't define the term, how can you asign probability? How can you possibly know that the probability is 50%?
As I've said more than once in the thread, it is a mistake to think that there is a "the probability" to know. Bayesian probabilities are numbers used to quantify our degree of uncertainty about things. In the grue problem, my degree of uncertainty is equal for both propositions precisely because I know nothing about either of them. Equal uncertainty about two propositions whose uncertainties have to add to 1 implies that my degree of uncertainty in each should be represented by the number 0.5.
Why not 25%? Why not 99%?
Because 25% would imply that I think the other proposition is 3 times as likely, but I don't; and 99% would imply that I think the proposition is 99 times as likely as the other, but I don't.
Saying "Well, there are two posibilities" doesn't work.
It does if you have no reason to believe that one possibility is more probable than the other.
My dad used to say that all statistics were 50/50--either it happened or it didn't. You're using the same logic here, except that when my dad did it he was at least joking.
No, just because the numbers are the same, the logic is not.
ETA: I'm always willing to be proven wrong. Please provide the data you used to asign the probabilities--the data regarding grues, not the number of possible outcomes. If you can't do that, you can't asign probability, not rationally. And the only rational conclusion is "I don't know"--which you've already stated.
No, you are not willing to be proven wrong; you're not even willing to consider that you might be wrong. But your steadfastness is easy to understand. After all, you are a better scientist than Feynman, and apparently a better mathematician than Laplace.