Originally posted by humyBut that isn't information about whether or not either option could be the case. So is it the case that you simply have no information whatsoever about whether or not either option could be the case?
Yes and, as I said/implied, this information that I took into account specifically literally was;
" they are 2 mutually exclusive exhaustive theories (there exists true randomness; there doesn't ) and neither one can be broken down to two or more 'simpler' theories."
Do you think any such information could ever be found? If so, how?
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Originally posted by twhitehead
But that isn't information about whether or not either option could be the case. So is it the case that you simply have no information whatsoever about whether or not either option could be the case?
Do you think any such information could ever be found? If so, how?
But that isn't information about whether or not either option could be the case. So is it the case that you simply have no information whatsoever about whether or not either option could be the case?
There is information but not information to favor either one of those two theories over the other. When you say "could" in " could be the case", do you mean what is logically possible? -there cannot ever be any evidence or information that rules out any logical possibility, not be confused with causal possibility ( + there cannot ever be any evidence that changes the value of any prior probability of any possibility )
Do you think any such information could ever be found?
Only if the hypothesis that there exists true randomness is false and then only if it just happens to be physically possible for us to detect/observe/measure the causes of the apparent quantum randomness. Even then, we cannot ever rule out there existing true randomness somewhere in the universe even if it were to increasingly seem an idiotic hypothesis given the evidence.
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Originally posted by humyWhy do you place quantum randomness as the prime candidate?
Only if the hypothesis that there exists true randomness is false and then only if it just happens to be physically possible for us to detect/observe/measure the causes of the apparent quantum randomness.
Even then, we cannot ever rule out there existing true randomness somewhere in the universe even if it were to increasingly seem an idiotic hypothesis given the evidence.
Why would it ever seem even slightly idiotic? Given that it cannot be ruled out, surely the probability remains 0.5?
Suppose we prove conclusively that quantum effects are deterministic in nature.
What will the new probability be?
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Originally posted by twhitehead
Why do you place quantum randomness as the prime candidate?
[b]Even then, we cannot ever rule out there existing true randomness somewhere in the universe even if it were to increasingly seem an idiotic hypothesis given the evidence.
Why would it ever seem even slightly idiotic? Given that it cannot be ruled out, surely the probability rema ...[text shortened]... onclusively that quantum effects are deterministic in nature.
What will the new probability be?[/b]
Why do you place quantum randomness as the prime candidate?
because of the Copenhagen interpretation. I don't know of any other example of a hypothesis like that in science which claims true randomness but not in quantum effects.
Why would it ever seem even slightly idiotic? Given that it cannot be ruled out, surely the probability remains 0.5?
Not being able to rule out something out doesn't mean its probability cannot be less than 0.5.
We cannot ever rule out any logical possibility, no matter what the evidence against it, but we can lower its probability below 0.5.
Example; the hypothesis that evolution is false; there must be a probability much less than 0.5 that it is false of that logical possibility and yet, even if that probability given the evidence is ~0.0000000000001, that is still not zero probability that it is false thus not ruled out. Note the causal possibility, not to be confused with the logical possibility, that evolution is false given the evidence, CAN be ruled out i.e. given exactly 0 probability.
Suppose we prove conclusively that quantum effects are deterministic in nature.
What will the new probability be?
1, some value arbitrarily very close to but not equal to 0 probability to the logical possibility that there exists true randomness for quantum effects.
2, Exactly 0 probability for the causal possibility that there exists true randomness for quantum effects.
3, Actually I admit not sure about the effect that would have on the probability that there exists true randomness somewhere other than in quantum effects; I admit I haven't really researched that aspect of probability properly yet but will get round to it eventually. Earlier in this thread I just intuitively assumed it would lower that probability via extrapolation and might have implied as much but, now I start to think about it more, not so sure such an extrapolation could ever be valid.
Originally posted by humyAnd this is what concerns me about assigning a probability in the first place. All the 0.5 probability really means is 'we haven't got a clue' and as you say here, we can't really use it in any useful calculations.
3, Actually I admit not sure about the effect that would have on the probability that there exists true randomness somewhere other than in quantum effects; I admit I haven't really researched that aspect of probability properly yet but will get round to it eventually. Earlier in this thread I just intuitively assumed it would lower that probability via extrapol ...[text shortened]... but, now I start to think about it more, not so sure such an extrapolation could ever be valid.
Originally posted by twhiteheadI would say what 'we haven't got a clue' about something means to me we haven't even got 0.5 probability because we have NO probability for that something. I gave one example of that with the true prior probability of a coin toss when we don't even know that coins have heads on one side but not the other.
And this is what concerns me about assigning a probability in the first place. All the 0.5 probability really means is 'we haven't got a clue' and as you say here, we can't really use it in any useful calculations.
But lets for a moment forget about that true prior probability and just look at the statistical probability of the outcome of a coin toss; If I say there is a 0.5 probability (statistical probability implied) of tossing heads, would you say that means I have 'not a clue' because that is what '0.5 probability' means?
But I DO have a clue to what the probability is, right? I mean, from observation of the statistics, I KNOW the probability is 0.5, right?
And as for your assertion of "we can't really use it in any useful calculations", well, I give an example of a 'useful' calculation from that 0.5 probability: the calculation of throwing 10 heads in a row is 0.5^10 = 1024.
That contrasts with not having even that 0.5 probability but NO probability (such as in the true prior of the outcome of a coin toss) in which case I would agree we really 'do not have a clue' because we wouldn't be able to calculate ANYTHING with that 'NO probability'!
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Originally posted by humyEven that prior probability can be given : The probability that a coin landing heads up when you do not know what possible symbols are on the coin is zero. In fact, that seems like a more useful result than the 0.5 one. If someone tosses a random coin and asks me if a random picture is on the upper face after the toss, I can safely say 'no'. I can not draw any useful conclusions from the 0.5 result with regards to the existence of randomness in the universe.
I would say what 'we haven't got a clue' about something means to me we haven't even got 0.5 probability because we have NO probability for that something. I gave one example of that with the true prior probability of a coin toss when we don't even know that coins have heads on one side but not the other.
But lets for a moment forget about that true prior probability and just look at the statistical probability of the outcome of a coin toss; If I say there is a 0.5 probability (statistical probability implied) of tossing heads, would you say that means I have 'not a clue' because that is what '0.5 probability' means?
No, there is clearly a difference. So there are cases where probability figures are useful and cases where they are not.
And as for your assertion of "we can't really use it in any useful calculations", well, I give an example of a 'useful' calculation from that 0.5 probability: the calculation of throwing 10 heads in a row is 0.5^10 = 1024.
Clearly a different situation. Lets see you toss the universe 10 times. Now tell us whether or not the existence of randomness in tossed universes is actually random or do all universes actually have randomness?
If there are 10 universes, are you saying the probability that all 10 have randomness is 0.5^10?
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Originally posted by twhitehead
Even that prior probability can be given : The probability that a coin landing heads up when you do not know what possible symbols are on the coin is zero. In fact, that seems like a more useful result than the 0.5 one. If someone tosses a random coin and asks me if a random picture is on the upper face after the toss, I can safely say 'no'. I can not dra ...[text shortened]... If there are 10 universes, are you saying the probability that all 10 have randomness is 0.5^10?
Even that prior probability can be given : The probability that a coin landing heads up when you do not know what possible symbols are on the coin is zero.
NO! Not zero because that means it is not logically possible! Zero probability = impossible. And yet we observe a coin can land on heads which contradicts it being logically impossible. And if, hypothetically, all coins had blue on one side and red on the other (so no heads and tails), and you tossed a coin and tossed a red, that proves that prior probability was never zero although, for true prior probabilities, you don't need to actually observe that to deduce its probability cannot be zero .
So, in this case, we cannot say what the prior probability is for that.
We say that "the probability is undefined" which is just another way of saying there doesn't exist a probability for that.
Note that the slight problem with saying "the probability is undefined" is that it misleadingly makes it sound like there exists a probability that is undefined. There doesn't. If the said 'probability' has no definable numerical value, the said 'probability' is a misnomer because it isn't a probability.
No, there is clearly a difference. So there are cases where probability figures are useful and cases where they are not.
I clearly have misunderstood what you said but I thought you where basically implying a 'useless' probability of 0.5 is 'useless' because it is 0.5; hence why I gave that example to the contrary.
So if a statistical probability of 0.5 CAN be 'useful' why cannot a prior probability of 0.5 be also 'useful? I would think both tell me something meaningful about the world although, admittedly, I would think statistical probabilities are generally more directly 'useful' to me in my everyday life.
If there are 10 universes, are you saying the probability that all 10 have randomness is 0.5^10?
yes.
BUT note, that is only true prior probability that all 10 have randomness is 0.5^10, not statistical probability (which can be thought of as the 'stronger' probability than prior probability because it is backed up by some empirical evidence). Since we have no relevant evidence for that to say one way or the other, we rationally cannot have any idea whatsoever of the statistical probability for that, which is just another way of saying there currently doesn't exist a statistical probability for that.
P.S. I must thank you for inadvertently helping me by encouraging me to explain these things properly in actual words which has the effect of forcing me to clarifying my own thoughts on the matter. My thoughts tend to be too visually-intuitively-orientated and not nearly enough of the hard verbal-orientated.
Originally posted by humyI obviously meant infinitesimally small.
NO! Not zero because that means it is not logically possible! Zero probability = impossible.
And if, hypothetically, all coins had blue on one side and red on the other (so no heads and tails), and you tossed a coin and tossed a red, that proves that prior probability was never zero
Clearly in that instance the prior probability of tossing a head, (if you know that coins are read and blue without heads) is truly zero. So I really don't get what you are saying there.
So, in this case, we cannot say what the prior probability is for that.
We can always say what the prior probability is. Always.
We say that "the probability is undefined" which is just another way of saying there doesn't exist a probability for that.
I disagree. One can always assign a prior probability regardless of the situation. Its just a question of what information you take into account. My argument is that it is simply not useful to do so in many situations.
I clearly have misunderstood what you said but I thought you where basically implying a 'useless' probability of 0.5 is 'useless' because it is 0.5; hence why I gave that example to the contrary.
Yes, you misunderstood. I am referring to the situation not the exact figure.
I would think both tell me something meaningful about the world...
What meaningful thing did you learn from the existence of randomness having a probability of 0.5?
yes.
BUT note, that is only true prior probability that all 10 have randomness is 0.5^10, not statistical probability (which can be thought of as the 'stronger' probability than prior probability because it is backed up by some empirical evidence). Since we have no relevant evidence for that to say one way or the other, we rationally cannot have any idea whatsoever of the statistical probability for that, which is just another way of saying there currently doesn't exist a statistical probability for that.
Is the result useful?
What meaningful thing did you learn from the calculation that with 10 universes the prior probability of all ten having randomness is 0.5^10 ?
If we discovered that randomness, if it exists always exists in all universes (ie it is either pervasive or not) then suddenly the probability that all 10 have randomness suddenly goes from 0.5^10 back to 0.5
Can we get really clever and somehow work backwards to work out the probability that randomness is pervasive?
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Originally posted by twhitehead
I obviously meant infinitesimally small.
[b]And if, hypothetically, all coins had blue on one side and red on the other (so no heads and tails), and you tossed a coin and tossed a red, that proves that prior probability was never zero
Clearly in that instance the prior probability of tossing a head, (if you know that coins are read and blue withou ...[text shortened]... ally clever and somehow work backwards to work out the probability that randomness is pervasive?[/b]
I obviously meant infinitesimally small.
OK
Clearly in that instance the prior probability of tossing a head, (if you know that coins are read and blue without heads) is truly zero.
Right, and if you didn't know what pictures are on either side of coins, it wouldn't be truly zero, and yet you cannot say what that probability is.
We can always say what the prior probability is. Always.
So what is the prior probability of tossing heads if you didn't know what pictures are on either side of coins?
Note; "infinitesimally small" is not an answer; how small is "infinitesimally small"? can you rationally define the specific numerical value of "infinitesimally small"? if not, then its value is undefined which means there is no probability for that.
I disagree. One can always assign a prior probability regardless of the situation. Its just a question of what information you take into account.
Strictly speaking, you should take ALL information we have into account else it isn't a true probability. Thus, at least if we are pedantic, there is no question of 'what' information you take into account, unless you include information we don't actually have but rather is purely 'hypothetical' information we could imagine having.
Admittedly, in practice, we often cannot take into account all the information we have. But that is only because there is often far too much of it for our limited intellect to take into account so we have to over-simplify to give simplistic pseudo probabilities as I often done here (esp with my explanation of the probability of a God) just for the sake of argument.
If there is information x and y both known to you and you only take into account x and ignore info y to assign a probability when taking into account both x and y would make you assign a probability with a different numerical value, that is not the 'true' probability by any reasonable definition of probability although we may just use that pseudo probability anyway for practical reasons or at least just for the sake of making our arguments about probability vastly more manageable just as we have done here.
Now, suppose there is an INFINITE amount of such information to take into account before we can assign a prior probability of something!? Then we cannot ever assign the true prior probability of that something! In fact, it would be mathematical nonsense (and I will mathematically prove that via contradiction in my book). Thus, if there is an INFINITE amount of such information to take into account before we can assign a prior probability (or indeed any other kind of probability), then you cannot assign it with a value in that situation thus it doesn't exist.
Now, how many logically possible combinations of pictures on either side of a coin could there be and how many different possible proportions of each combination in a logically possible universe?
Think about this: All coins could have, for example, red and blue sides, no heads or tails. Or, say, exactly 23.75537% of all coins could have red and blue sides and exactly 4.566% could have heads or tails, and the rest could have heads on both sides. You should see from this exemplification that there is an infinite number of possibilities here. To take into account that infinite number of possibilities before assigning a true prior probability would mean taking into account an INFINITE amount of information, which cannot be done. And, that means there exists no true prior probability of, for example, tossing heads with a flip of a coin.
Sorry for such a long post -so I will stop right here.
Originally posted by humyOf course you can. It is infinitesimally small.
Right, and if you didn't know what pictures are on either side of coins, it wouldn't be truly zero, and yet you cannot say what that probability is.
So what is the prior probability of tossing heads if you didn't know what pictures are on either side of coins?
Note; "infinitesimally small" is not an answer;
Yes, it is an answer, and it is the correct answer.
how small is "infinitesimally small"?
It is infinitesimally small.
can you rationally define the specific numerical value of "infinitesimally small"?
No, but you can't rationally define the specific numerical value of infinity. But to claim that infinity is never the correct answer to a maths problem is clearly wrong.
if not, then its value is undefined which means there is no probability for that.
Not so. Continuous probability that we had a whole thread on not so long ago, is such that the probability of every point is infinitesimal small (not undefined). Its there in every textbook.
Now if this is a case of your own definition of probability that simply doesn't take into account such things, then feel free to give your definition, but under the standard definitions found in text books, it is most definitely valid to have an infinitesimally small probability.
Strictly speaking, you should take ALL information into account else it isn't a true probability.
Incorrect. Probability is tied to what information you take into account. You are free to ignore certain information so long as you state that you are doing so. In fact if this was not allowable then the whole idea of 'prior probability' would be invalid as it is by definition the calculation of probability based on partial information prior to adding more information.
Thus, at least if we are pedantic, there is no question of 'what' information you take into account.
I disagree. Probability is basically a question of 'given this information, what is the likelihood that this will be the case?'. It does not require that all information be present nor that the asker nor answerer use all information they are privy to.
If there is information x and y both known to you and you only take into account x and ignore info y to assign a probability when taking into account both x and y would make you assign a probability with a different numerical value, that is not the 'true' probability by any reasonable definition of probability
I think you are getting confused about what probability is. Suppose it is really the case that true randomness exists in the universe. Suppose the information that this is the case exists somewhere in the universe. You appear to be claiming that your probability of 0.5 is now not the 'true probability' because that information exists and was not taken into account. Obviously for any question that is either true or false, the supposed 'true probability' now becomes the actual value of the question (ie 0 or 1). So after a coin is tossed, we may not know its heads yet, but it is in reality heads, so you are claiming that the 'true probability' that it is heads is now 1 and that the probability that we tell ourselves of 0.5 is just a pseudo probability.
Now I thought for a moment that you might be confusing events that have already taken place vs events that are yet to happen, but that would not fit with some of the items under discussion which do have an already decided truth value, we just don't know what it is.
Now, how many logically possible combinations of pictures on either side of a coin could there be and how many proportions of each in a logically possible universe?
An infinite number.
To take into account that infinite number of possibilities before assigning a true prior probability would mean taking into account an INFINITE amount of information, which cannot be done
Yes, actually, it can be done, and I did it, and I gave the correct answer : the probability was infinitesimally small. Infinity is not out of reach of mathematics.
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can you rationally define the specific numerical value of "infinitesimally small"?
No, but you can't rationally define the specific numerical value of infinity. But to claim that infinity is never the correct answer to a maths problem is clearly wrong.
But this isn't pure mathematics but probability; can probability be assigned infinity? -no. And it also cannot be assigned both "infinitesimally small" and "has no numerical value" as in, say, 0.0000000000001. If it has no definable numerical value (such as 0.0000000000001 ) , it isn't a probability.
if not, then its value is undefined which means there is no probability for that.
Not so. Continuous probability that we had a whole thread on not so long ago, is such that the probability of every point is infinitesimal small (not undefined). Its there in every textbook.
I assume you meant "probability density" form "Continuous probability". We actually DID establish in that thread that a "probability density" is a misnomer because it isn't itself a probability and I then recommended that it should be renamed a "densi" to avoid such confusion. Every textbook agrees that a "probability density" is not itself a probability but rather you can readily derive a probability over some integral of it.
I think you are getting confused about what probability is. Suppose it is really the case that true randomness exists in the universe. Suppose the information that this is the case exists somewhere in the universe. You appear to be claiming that your probability of 0.5 is now not the 'true probability' because that information exists and was not taken into account.
No, because we don't HAVE that information i.e. we don't KNOW true randomness exists in the universe, even if it actually does. How can we 'take it into account' what we don't know?
Obviously for any question that is either true or false, the supposed 'true probability' now becomes the actual value of the question (ie 0 or 1).
No, that is not what i meant by "true probability" at all, true probability takes into account ALL information that is currently KNOWN to us, even if we have insufficient information to tell us with absolute certainty whether something is true or false.
To take into account that infinite number of possibilities before assigning a true prior probability would mean taking into account an INFINITE amount of information, which cannot be done
Yes, actually, it can be done, and I did it, and I gave the correct answer : the probability was infinitesimally small. Infinity is not out of reach of mathematics.
Right, it is not out of reach of pure mathematics; what about out of reach of probability? exactly what numerical value is it? is "infinitesimally small" a specific numerical value such as 0.0000001? Don't all probabilities have to have a definable value between 0 and 1 meaning an actual number as in numerical number between 0 and 1? Do the words "infinitesimally small" state an actual specific number between 0 and 1? if so, is it greater than or smaller than or equal to 0.000000000000000000000001 ? If you cannot say, isn't that because you cannot state its actual numerical value? If so, that means it has none defined.
How can a probability have no definable numerical value but have a numerical value between 0 and 1?
OK, let me put it this way;
Suppose I told you "my claimed probability has the value of x therefore it has a definable value and it is a probability".
Then you ask "what value is x".
I say "I just told you, it is "x" "
Then you ask "yes, but what exact numerical value is x; O.5?, 0.7? or what exactly? How many digit zeros does it have before you reach the first significant figure".
I say "I cannot say how many such zeros but so what? I just given my answer, it is "x". ".
Will you be satisfied with my answer and that I have defined a probability?
Originally posted by humyProbability is a branch of mathematics. Whether or not it is 'pure mathematics' could be debated, but I assure you that infinities exist in probability theory.
But this isn't pure mathematics but probability;
can probability be assigned infinity? -no.
Well that follows trivially from the definition that it must be between zero and one. If you think that proves anything with regards to whether or not it can be infinitesimally small which does lie between zero and one, then you are mistaken.
And it also cannot be assigned both "infinitesimally small" and "has no numerical value" as in, say, 0.0000000000001. If it has no definable numerical value (such as 0.0000000000001 ) , it isn't a probability.
As I stated, it is a probability by any standard textbook definition. Disagree? Post your definition. Here is the first one I could find, but I am sure that any other textbook will have something similar:
https://www.probabilitycourse.com/chapter4/4_1_1_pdf.php
for a continuous random variable P(X=x)=0P(X=x)=0 for all x∈Rx∈R.
I assume you meant "probability density" form "Continuous probability".
No, I did not.
No, because we don't HAVE that information i.e. we don't KNOW true randomness exists in the universe, even if it actually does. How can we 'take it into account' what we don't know?
You said nothing about knowing the information earlier, only about information existing.
Do you know an infinite amount of information? Earlier you said that an infinite amount of information existed and that we must take it into account. This contradicts the new claim that you must know the information for it to matter.
No, that is not what i meant by "true probability" at all, true probability takes into account ALL information that is currently KNOWN to us, even if we have insufficient information to tell us with absolute certainty whether something is true or false.
And I find it unnecessary to arbitrarily be concerned about the knowledge of the speaker. Rather it is simply a matter of tying the information to the probability figure.
What you are saying is that if two ordinary coins are tossed and I know that one landed heads and you don't, then there are two different 'true probabilitys' for two heads dependending on which of us makes the calculation. I find it much simpler to simply say that the two probabilities are based on the information taken into account. When I tell you 'one coin is heads' I would not expect you to say "now the true probability I had is a psudo probability and I now have a new 'true probability'".
Right, it is not out of reach of pure mathematics; what about out of reach of probability?
It is not out of reach of probability as I have demonstrated with the textbook definition above.
exactly what numerical value is it? is "infinitesimally small" a specific numerical value such as 0.0000001? Don't all probabilities have to have a definable value between 0 and 1 meaning an actual number as in numerical number between 0 and 1?
Not necessarily. Infinities are funny that way.
Do the words "infinitesimally small" state an actual specific number between 0 and 1? if so, is it greater than or smaller than or equal to 0.000000000000000000000001 ?
Smaller than.
How can a probability have no definable numerical value but have a numerical value between 0 and 1?
Its a tricky concept, but still a valid one. Note that textbooks tend to just call it zero.
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Originally posted by twhitehead
Probability is a branch of mathematics. Whether or not it is 'pure mathematics' could be debated, but I assure you that infinities exist in probability theory.
[b]can probability be assigned infinity? -no.
Well that follows trivially from the definition that it must be between zero and one. If you think that proves anything with regards to whether ...[text shortened]... /b]
Its a tricky concept, but still a valid one. Note that textbooks tend to just call it zero.[/b]
Do you know an infinite amount of information?
No.
Earlier you said that an infinite amount of information existed
correct. NOT an infinite amount of information known, an infinite amount of information existing as in available to us; that is what I mean. There is an infinite number of logical possibilities I could consider so that's an infinite amount of information available to me. But I don't know all that information because my limited intellect means I cannot consider and remember all that information. At any one moment of time, I can only know or consider a finite amount of it.
and that we must take it into account.
We cannot take into account an infinite amount of information.
What I said was IF we have to take into account and infinite amount of information to assign the said probability with a value, we can't thus no such probability exists.
What you are saying is that if two ordinary coins are tossed and I know that one landed heads and you don't, then there are two different 'true probabilitys' for two heads dependending on which of us makes the calculation.
I don't recall that being what I said exactly but, that is correct, yes. Here we are talking about personal probability. personal probability depends on what a person personally knows so, because your knowledge is different from mine, the personal probability for me (of something) can, without contradiction, be different i.e. have a different numerical value for the personal probability for you (of something) .
I find it much simpler to simply say that the two probabilities are based on the information taken into account.
You are talking about personal probability here, not collective knowledge probability. I was some of the time talking about collective knowledge probability as in taking into account collectively what 'we' know which is why I often used the word 'we'.
However, concerning personal probability:
If I personally know x and y but only take into account y to assign a probability when taking account both would make the probability value different from taking account only either x or y alone, then I haven't assigned a true probability. So, even with personal probability, you must take into account all knowledge to assign a true probability; but the difference is just that that "all knowledge" is not all knowledge of we but just you.
How can a probability have no definable numerical value but have a numerical value between 0 and 1?
Its a tricky concept, but still a valid one.
I disagree. It is a 'tricky concept' because it is wrong; and I intend to prove it and publish that in my book.
Note that textbooks tend to just call it zero.
And one of the main points of my research (far from the most important point which is to mathematically solve the problem of induction) is to mathematically prove all those textbooks wrong and publish that proof for all to see and scrutinize.
incidental; just a matter of interest, I have already worked out the conventional method to solve the German tank problem is also wrong!
https://en.wikipedia.org/wiki/German_tank_problem
I also intend to mathematically prove all those textbooks (and web links ) are wrong about the tank problem and publish that proof for all to see and scrutinize. I also intend to show the correct equation for calculating it and prove it valid. The correct equation gives approximately similar but not exactly the same probabilities.
And in case you wondering WHY the conventional method is wrong: short answer; -all the mathematical inferences in the above link are correct BUT implicit premise FALSE; output is NOT a probability;
rubbish in - rubbish out.
( Too much risk of plagiarism before publication so cannot elaborate too much on that. All will be explained post publication )
Originally posted by humyGiven that you clearly accept that probability may vary based on perspective and that perspective is really about what information a person has, it seems unreasonable to not simply refer to a given probability based on what information was used to generate it rather than instead tying it to and individual or group and then calling it 'true probability'. I just don't think the qualifier 'true' makes any sense in this instance.
You are talking about personal probability here, not collective knowledge probability. I was some of the time talking about collective knowledge probability as in taking into account collectively what 'we' know which is why I often used the word 'we'.
I disagree. It is a 'tricky concept' because it is wrong; and I intend to prove it and publish that in my book.
Well then you will fail. The issue is a definitional one and not something you can disprove logically.
I also find your rejection of infinities because you can't understand them to be highly suspect.