Then you should choose a mathematical model that's up to the task. An independent random variable with the sample space of {Real, Unreal] isn't it. — Dawnstorm
Not if you treat O as an independent random variable. If you do that the math forces you to consider those cases, lest the math be rendered useless. — Dawnstorm
You <i>can</i> ignore those cases of coure. Let me show you:
RRR - 12.5 %
RUU - 12.5 %
RUR - 12.5 %
RRU - 12.5 %
URR - 12.5 %
UUR - 12.5 %
URU - 12.5 %
UUU - 12.5 %
Turns into:
RRR - 12.5 %
RUU - 12.5 %
RUR - 12.5 %
RRU - 12.5 %
URR - 12.5 %
UUR - 12.5 %
URU - 12.5 %
UUU - 12.5 %
And your probability that O is real remains 50 %, because 12.5 % are 50 % of 25 %. — Dawnstorm
You're talking experimental probability and it's a fallback measure when theoretical probability can't be calculated.
In our case, theoretical probability can be calculated. — TheMadFool
And I've already informed you that the probability for observation O being real can be broken down into three choices, mutually exclusive and jointly exhaustive: — TheMadFool
Yes, and I have countered that by stating that doesn't work, and an alternative. — Philosophim
In other words, I've provided you choices that represent every possible value P(real) can assume. So, "that doesn't work" is essentially nonsense. — TheMadFool
Ok, you're ignoring the discussion of theoretical probability, the cave with the bat scenario, and everything else I've put forward and simply keep repeating the same thing without addressing them. You have made your choice. Enjoy the discussion with others, there is nothing more to say at this point — Philosophim
What is the main issue here? Whether the observation O is real/not real, right? What model do you propose other than that which has to do with the probability of O being real/not? As far as I can tell, P(real) lies at the heart of the issue where P(A) means the probability of A. :chin: — TheMadFool
You haven't quite made clear what "observation O is real/not real" means. — Dawnstorm
There are three observations: O(x, y, z). Variable O can have two values:
"sees unicorn"/"does not see unicorn".
We know the values of the variable. The input comes straight from our experience. So O is not a random variable. No probability. It's either "sees" or "doesn't see", and we get the values by asking. — Dawnstorm
No matter who sees the unicorn, they all flip a coin, and if the coin comes up heads they say the unicorn is there, and if the coin comes up tails they say it's not there. But they'll only accept that the unicorn is there by full consensus, so they keep flipping coins until it's all heads or tails. In that case the likelihood that the unicorn exists or doesn't exist, as per consensus, would be equal, but only because there are exactly 2 ways the game can end. With a different likelihood the probability changes according to how many constellations end the game, and how many of those constellations are dis/favourable. — Dawnstorm
For instance, if the probability that the observation O is real, say, 90% then the probability of O being real if all 3, X, Y, and Z observe O is 90% * 90% * 90* = 72.9% and the probability that O is not real = 27.1%. — TheMadFool
First, if I observe x, that is presumptive evidence that x happened. There is no a priori reason to suppose that x did not happen. — Dfpolis
Second, the purpose of repeatability in science is not to confirm or dispute what you observed, but to see if you have correctly identified the factors causing x. Perhaps x was caused by some extraneous factor you have not identified. If I can set up my experiment using all the factors you identified, and observe x, that is good evidence that you have correctly identified the relevant factors. — Dfpolis
Third, there is no rational basis for assigning numbers to things we cannot count or measure. Among these innumerables is the "probability" subjectively assigned to beliefs, and the "utility" of acts and decisions. Bayesian probability is simply transvestite prejudice -- prejudice in mathematical garb. Putting lipstick on it does not make it rational. — Dfpolis
You have hit the nail in the head. This is a serious problem.
Have you read "The Black Swan"? It's a notorious no-BS book regarding this exact subject. — dussias
We're not on the same page on this. The very idea of repeatability is to either confirm or disconfirm an observation. — TheMadFool
There's no need to bring up the issue of causality because at the end of the day it's about an observation - whether it can be observed by different people in different settings. — TheMadFool
What concerns us is whether a given observation is real or not. Either it's real or it's not. If one person makes an observation then the odds of that being real are 50:50. — TheMadFool
And its interpretation. Perhaps you observed x because your electronics failed, not because of what you believed was the experimental arrangement. Perhaps your sample was contaminated or unrepresentative. I can think of many possible scenarios, none of which call your experience or veracity into question, only the adequacy of its description — Dfpolis
Every observation of the same supposed type is a different token. None is exactly the same. You report, "I did x, and observed y." Someone else does x, but does not observe y. Does that mean that you lied? Or that y was a miracle? Or does it mean that factors not included in x lead to the observation of y? All are possible, but statistically, the last is most common. — Dfpolis
On what basis are you calculating the probabilities? — Dfpolis
All what you said boils down to the issue of whether a single individual's observation is real or not. — TheMadFool
I have no clue whether it's likely to be real or unlikely to be real — TheMadFool
If I assign a value greater than 50% to the probability that means I think it's likely but this contradicts my assertion that I'm uncertain — TheMadFool
The only probability value that fits my epistemic state - uncertainty (not knowing whether likely/unlikely) - is 50%. — TheMadFool
Not by my definition of "real." If your meter read 17, for whatever reason, you really observed 17. — Dfpolis
Of course you do. Unless you have a sensory, neural or cognitive disorder, all the clues point to the fact that what you observed what was really there. As I said earlier, your use of "real" is non-standard. — Dfpolis
Your subjective certainty is more likely to reflect your childhood experience than your observation. If you are only 50% sure that what you saw is real, that says your self-confidence has been harmed -- not that there is any question involving reality. — Dfpolis
So the odds of a coin landing on edge is 50%. — Dfpolis
1. Not everyone has picked up on it, but the "real" and "not real" thing is a bad framing right away. As Mww correctly pointed out, we know the observation is real, the question is just whether it points to some new phenomenon or just, say, noise in a cable or something. — Mijin
2. The idea that if we have two options then those two options must have 50% probability is a logical fallacy. I can't seem to find the name of the fallacy right now, but it is a known, named fallacy. Probability does not work like that.
3. Multiplying the "50% chance of being real" is also wrong. The whole point of repeating the experiment is to raise our confidence level that it wasn't just experimental error. To the extent these numbers make any sense at all, the 50% needs to be updated after each positive result.
I beg to differ. When you observe something, say a reading on weighing scale that reads 12 kg, what's the checklist you have to go through before you come to the conclusion that what there is a mass that's 12 kg? — TheMadFool
That raises a lot more questions than answers, friend. — TheMadFool
It's being updated - probabilities are being multiplied. What other mathematical operation would you say is the correct method of updating to the final probability? — TheMadFool
What wouldn't be on the checklist is the words "real" or "not real". — Mijin
The question for me is whether you're interested in understanding this, or if the whole thread is just for you to proselytize. Numerous examples have been given as to why the number of alternatives has nothing to do with their probability. Ergo there is no reason to assign a probability of 50%. — Mijin
It's not as simple as one operation; the actual calculation of a P value depends on the specifics of how much data is being collected, what the noise range is for that data and so on. But yes, as we gather more data our confidence in a proposition goes up.
Multiplying this number, as you've done, comes up with obviously absurd results. Imagine I am trying to figure out if you ate my cookie. If there are cookie crumbs on your shirt, I'm 80% confident you did it. If your fingerprints are on the cookie jar, 50%. But if I see both things, then by your logic, it's somehow less likely than either individual piece.
(and note, even if you quibble with the actual numbers, the point is, as long as they are less than 100% this will always be the case; multiplying them will decrease our confidence, by your logic. — Mijin
Also consider a scenario where you observe a gold ingot on a table. Before you start measuring its weight, you must first determine whether the ingot is actually real or not, right? You couldn't measure the weight if it weren't real. — TheMadFool
What you say implies that the probability has to be something other than 50%. Two possibilities - either less than 50% or more than 50% - make your choice and explain why. — TheMadFool
If three people are involved, the probability that each one's observation being real is 50%. The probability that all three of them are observing something real is calculated thus: 50% * 50% * 50% — TheMadFool
No; there is clearly something being weighed here, the observation is "real".
However, the proposition that I have N kilograms of gold needs further investigation to confirm.
Is the difference clear now? — Mijin
The probability will depend on the specifics of what's being measured and how. It's something calculated, not something known apriori from the number of alternatives. — Mijin
No it's not calculated like that. Can you respond to the argument I just made, refuting this (with the cookie example) — Mijin
If there are cookie crumbs on your shirt, I'm 80% confident you did it. If your fingerprints are on the cookie jar, 50%. But if I see both things, then by your logic, it's somehow less likely than either individual piece. — Mijin
Does that single measurement suffice in, say, writing a paper that's to be submitted in a peer-reviewed journal? I don't think so. — TheMadFool
I'm mainly interested in the distinction between real and hallucination - this has priority over whatever may follow, right? — TheMadFool
How confident are we that a certain observation is real or not? By the way, do you mean that you would assign a value other than 50% to the probability that a single observation is real? What are your reasons for that? — TheMadFool
So the odds of a coin landing on edge is 50%. — Dfpolis
There is no third option between being real and not being real. — TheMadFool
2. If all 3, X, Y, and Z observe O then the probability of O being real (call this R) = 50% * 50% * 50% = 12.5% — TheMadFool
1. If all 3, X, Y, and Z observe O then the probability of O not being real (call this NR) = 50% * 50 * 50% = 12.5% — TheMadFool
That is a totally different question than asking if the meter reading was real. The question of reality is ontological, that of what suffices for publication is methodological. — Dfpolis
No, it does not have priority. The presumption is that unless you have a medical history of hallucinations, what you see is really there. Priority goes to relevant questions, not to vague and unsupported possibilities. In the first quotation above, you posed the standard of publication in a peer reviewed journal. No such journal has ever asked me to submit medical records showing I have no history of hallucination or mental illness. — Dfpolis
We are morally certain that our careful observations are correct. Moral certitude means that we can rely on a proposition in good conscience. It does not mean that our belief in it is infallible.
I assign no numerical values to what cannot be counted or measured, because, strictly speaking, it is meaningless to do so. Of course, people do assign probability numbers to their beliefs. One might interpret such probabilities in terms of the odds of a fair bet, but such numbers are not a measure of the probability of a proposition being true, because there is no such probability. If the proposition is meaningful, by which I mean that it asserts some determinable fact, then it is either true or false relative to a determined context. — Dfpolis
It depends on what you mean by "being real." Still, the existence of a third option is irrelevant to what I said.
Your claim is that "X is either y or not y" justifies assigning equal probabilities to y and not y. Since a flipped coin will either land balanced on its edge or not, then (by your logic) there is a 50% chance that it will end on edge. I do not see how you can escape this conclusion. — Dfpolis
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