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Possibility and lack of knowledge of the facts
 Posted: 31 May 2007 03:27 PM [ Ignore ]
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I’m interested to know how philosophers distinguish between a genuine possibility and one due to lack of knowledge of the facts?

So let’s say there are two boxes in front of me. Box A has ten pounds in it and box B is empty but I don’t know that.

I’m invited to pick one and I pick box B.

As far as I’m concerned it is possible that ten pounds is in box B

But the truth is it is not because in fact there is nothing in box B

Stephen

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 Posted: 31 May 2007 03:50 PM [ Ignore ]   [ # 1 ]
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This remains a real controversy and subject for discussion in the area of probability theory, however IMO it is still pretty inchoate. You can check for example the Wikipedia entry on Bayesianism HERE for a short discussion of the issue. See particularly the section marked “Varieties”.

There is a general discussion between “objectivists” about probability, and “subjectivists”. The “objectivists” believe that probability distributions are real things, and that epistemic probability (what you call probability “due to lack of knowledge of the facts”) isn’t real probability at all, or at least not the “objective” kind.

It might be argued that the probabilities involved in quantum mechanics, for instance, are “objective” probabilities. It appears that we have all the relevant facts, there are no “hidden variables”, but all we get are probability distributions. Perhaps at the most basic level that’s all that there are. If so, those would be “objective probabilities”.

Epistemic probabilities, or “subjective” probabilities are as you note, dependent on the observer, and on the actual frequency of particular regularities in the real world. E.g., the frequency of a fair coin coming up heads is 50%.

Where it gets complex is that one might say that the “actual frequency of particular regularities in the real world” (e.g., the frequency of “heads”) is an objective feature of the world, hence not a variety of subjective probability at all. One might then go on to say that subjective probability is just how things seem to me, where I might get wrong the frequency of heads, and think it was only 30%.

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 Posted: 31 May 2007 05:12 PM [ Ignore ]   [ # 2 ]
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I wonder if part of the issue hinges on the difference between “possibility” and “probability?” What you talk about, Doug, is the way we determine the probability or liklihood of something, and whether there is any subjectivity to this or not. But the word “possibility” seems to be a little different. I’m not sure if, Stephan, you meant to say there was a possibility that the 10 pounds was in both boxes because there was a 50% probability of it being in either box before you made your choice (which, of course changed to a 0% or 100% probability after you discovered where it was). In this sense, there is what I think Doug would call an epistemological possibility, which can be quite precisely defined as a probability and is determined by the state of the observer’s knowledge. Or did you mean, more generally, that objectively the 10 pounds either was or wasn’t in the box regardless of what you knew, and there was no possiblity of it being in the box that was empty? In which case, the objective or real probability was already 0% or 100% and the only “possibility” was subjective, not objective. Of course, in something like the coin toss, the actual state of the thing is not fixed in advance, so the epistemilogical and objective probabilities are the same (unless you are a determinist, I guess). But in your example, the objective state is determined in advance and only from the observer’s point of view is there any possibility of the empty box containing the 10 pounds. As usual, in the everyday world the difference between objective and subjective “possibility” is usually unknown to the observer, so we regularly see things as possible which are truly possible (and which may have an objective probability, whether we know it or not) or as possible when they are actually impossible because the state or outcome is fixed only we don’t know it. From the observer’s point of view, I guess there isn’t much real difference.

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 Posted: 01 June 2007 02:11 PM [ Ignore ]   [ # 3 ]
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mckenzievmd - 31 May 2007 05:12 PM

Ithere is what I think Doug would call an epistemological possibility, which can be quite precisely defined as a probability and is determined by the state of the observer’s knowledge. Or did you mean, more generally, that objectively the 10 pounds either was or wasn’t in the box regardless of what you knew, and there was no possiblity of it being in the box that was empty?

I think my question is answered by your calling it an epistemological possibility.

I’ll ponder on the rest of the thoughts and information from you and Doug.

Thank you

Stephen

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 Posted: 23 June 2007 12:12 PM [ Ignore ]   [ # 4 ]
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Assuming both boxes are in exactly identical states at the time of putting the money in and that neither is preferred, it is equally possible for the putter-inner to put the money into either of the two boxes.  In saying that it is equally possible that the money is in either box, the philosopher is using a short hand way of stating the probabilities that the guy who put the money in put it in either box was 0.5.  The guy who put the money in has assymetric information.  Take him out of the loop and the philosopher is true to the rigour of his discipline in saying that the probability of it being in either one of the two boxes is 0.5, since the probability is normalised.  You will of course agree, that the probability that is in one of the two boxes is 1.  It is simply a statement that if you have limited information, and therefore the solution as far as you can discern has two equally likely possibilities, you should make that clear to whoever you are explaining your findings to (i.e. The guy who is jumping up and down in frustration screaming “for fuck’s sake just open the goddamn boxes and have a look, damn you!”).

[ Edited: 23 June 2007 12:20 PM by narwhol ]
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 Posted: 23 June 2007 12:16 PM [ Ignore ]   [ # 5 ]
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removed

[ Edited: 23 June 2007 12:18 PM by narwhol ]
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 Posted: 25 June 2007 11:50 AM [ Ignore ]   [ # 6 ]
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Questions like this are really about knowledge, not reality - epistemology, not ontology.  The question puts the people discussing it in the position of knowing more than the person in the question.  So, you end up confusing questions of what actually is the case with what someone can actually know actually is the case.

In the example given the difference is contained in the “as far as I’m concerned”.  “As far as you are concerned” is epistemology - what you know, or what you can know (is, in principle, knowable, by you).  “The truth is” is ontology - what actually is the case, what actually exists, what is really real (or truly true).

I don’t know why you would bring probability into it, because the question is not about probability.  (Probability cannot even apply to a case without similar previous cases - otherwise what do you base the probability on?  A coin toss has the combined history of billions of tossed coins - what history does this case have?)

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 Posted: 25 June 2007 01:07 PM [ Ignore ]   [ # 7 ]
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The probabilities thing was just a way of explaining what the philosopher means in saying that the money is “possibly” in box a or box C

In saying that it is equally possible that the money is in either box, the philosopher is using a short hand way of stating the probabilities that the guy who put the money in put it in either box was 0.5.

It’s true that in the way the conundrum was posed, we know that the money is in one of the boxes and that there is no genuine possibility of it being in the other one (given the fact that it’s not).  However, liguistically speaking (which is simultaneuously both the way in which most of us tend to speak and a redundant adverb) the philosopher is quite correct in saying that it is equally possible that it is in either box.

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 Posted: 22 August 2007 02:08 PM [ Ignore ]   [ # 8 ]
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Hi Brennan,

I’m using this post, as much as anything, to try and show Doug what I’m getting at but would welcome your thoughts also.

mckenzievmd - 31 May 2007 05:12 PM

Or did you mean, more generally, that objectively the 10 pounds either was or wasn’t in the box regardless of what you knew, and there was no possiblity of it being in the box that was empty? In which case, the objective or real probability was already 0% or 100% and the only “possibility” was subjective, not objective.

Yes this is what I meant and this is how it appears to me.

But compare this to my discussion about what I’m going to have for breakfast tomorrow, on the “what will be” thread.

This is the issue I’ve been confused about for months.

If the fact of the matter is I’m going to have scrambled eggs for breakfast tomorrow and nothing else, then the real probability of my having bran flakes is and always was o and the only “possibility” is subjective, not objective.

This seems to be the same as my boxes example because there is a fact of the matter, it is just I don’t know what it is.

In the case of the future the example is a little more complicated because nobody knows what the fact of the matter is but in principal, it appears to be the same?

Stephen

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 Posted: 22 August 2007 02:29 PM [ Ignore ]   [ # 9 ]
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Well, with regard to the future I think it’s a slightly different issue. In the boxes example, there is a reality (one box full, one empty) and there is a subjective knowledge about reality (either certainty or uncertainty). In the case of the future, knowledge is always absent (though reasonable projections can be made based on past history). But is there a reality that is fixed, as with the boxes? I don’t know. Traditional understanding of the future is either that it is largely undetermined, or that it is absolutely predetermined. Personally, I bleieve it is undetemrined but sontrained within boundaries by what is more or less likely. If you hate eggs and have never had them for breakfast, the chances of doing so tomorrow are pretty low, though I suppose never 0. But I do’t think the event has happened so I don ‘t think there yet is an objective reality (a “fact of the matter”) to talk about yet. And even if narwhol proves me completely wrong in my understanding of time on this one, subvjectively that is how it is, and likely will, seem to us regardless, so that is how it for all practical purposes is.

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 Posted: 23 August 2007 05:54 AM [ Ignore ]   [ # 10 ]
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mckenzievmd - 22 August 2007 02:29 PM

Well, with regard to the future I think it’s a slightly different issue.

As far as I understand, the theory scientists use and the one Doug is telling me about is that it isn’t.

In the boxes example, there is a reality (one box full, one empty) and there is a subjective knowledge about reality (either certainty or uncertainty).

Yes but again the theory is there are many other possible worlds, where the reality is different.

In the case of the future, knowledge is always absent (though reasonable projections can be made based on past history). But is there a reality that is fixed, as with the boxes? I don’t know. Traditional understanding of the future is either that it is largely undetermined, or that it is absolutely predetermined. Personally, I bleieve it is undetemrined but sontrained within boundaries by what is more or less likely.

I think this may be true but also may be a red herring, it makes no difference if the future is determined or indetermined, it makes no difference what we can know or not know about the future because we are not dealing with epistemology. The only question is, is there a fact of the matter about what the future is, in the same way as there is a fact of the matter about which box the £10 is in? I, like you, am tempted to answer no and then things make more sense to me. What will be simply doesn’t exist but I’m exploring the idea that the answer is yes.

If you hate eggs and have never had them for breakfast, the chances of doing so tomorrow are pretty low, though I suppose never 0.

So is this just purely chance because we don’t know or real genuine chance? Or is chance because we don’t know, what real genuine chance is? What if it is the fact of the matter that I won’t eat eggs tomorrow, what chance is there of my eating eggs tomorrow?

It looks like the answer is zero chance, which in my language I would say means it is not possible (this could be my mistake I think?)

But if I write it is not possible, then apparently I’m contradicting myself because I will eat eggs tomorrow in another possible world. I’m really tempted to ditch all the other possible worlds because everything seems to work much better that way.

But I do’t think the event has happened so I don ‘t think there yet is an objective reality (a “fact of the matter”) to talk about yet.

Yes, so this is your solution, I may commit to this idea too eventually but I can see the arguments against, the idea is that another time is just like another place(I think) so if another place is objectively there when we are not there, then so is another time. Mind you, I’m not sure another place is objectively there either yet! You can tell I’ve got along way to go ‘til I make my mind up on any of this.

And even if narwhol proves me completely wrong in my understanding of time on this one, subvjectively that is how it is, and likely will, seem to us regardless, so that is how it for all practical purposes is.

Perhaps, perhaps not, it’s certainly how I view it, in my daily life, too.

Stephen

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 Posted: 23 August 2007 08:00 AM [ Ignore ]   [ # 11 ]
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I should probably add that while it is possible that there is one particular future to which our present will lead, if the many-worlds interpretation of quantum mechanics is true, then the universe branches into the future, and every quantum-mechanically possible future will in fact be instantiated. In that case we are also certain as to what the future will bring. It will bring all (physical) possibilities, each in its own branching universe.

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 Posted: 12 October 2007 02:29 PM [ Ignore ]   [ # 12 ]
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I brought this up on the wrong thread yesterday, so to use the right thread.

The only type of possibility I can imagine is of the epistemic variety.

So the different possibilities arise simply because we don’t know which is actually true.

I’m not convinced I’m right but it seems the best thing is to take the stance that I am and see what knocks me over.

I don’t believe it is always possible to know something, so I would say in cases where it is impossible, that would create a class of epistemic possibilities which were genuine, as opposed to a situation where the answer is knowable or known by others but we ourselves don’t happen to know.

Any thoughts? Can anyone give an example of a genuine possibility beyond the type I believe in?

Doug has tried to help with other possible worlds but they just seem like fantasy to me, although I accept they may not be.

Do we really need other possible worlds to make sense of this world?

Why can’t what happens be the one and only thing that could possibly happen?

Stephen

[ Edited: 12 October 2007 02:31 PM by StephenLawrence ]
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 Posted: 22 November 2007 07:18 AM [ Ignore ]   [ # 13 ]
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StephenLawrence - 12 October 2007 02:29 PM

The only type of possibility I can imagine is of the epistemic variety.

Possibly that could change?  :grin:

So the different possibilities arise simply because we don’t know which is actually true.

I think you develop that perception because of semantic imprecision.  Plus there’s more than one model that’s been brought up, increasing the chance that the terms will drift in meaning.

Originally, possible worlds excluded worlds that contained contradictions.  A multiverse apparently allows for some contradictions (you can eat eggs and not eat eggs at the same time and in the same sense), so it kind of changes the game.

I don’t believe it is always possible to know something, so I would say in cases where it is impossible, that would create a class of epistemic possibilities which were genuine, as opposed to a situation where the answer is knowable or known by others but we ourselves don’t happen to know.

In the most radical version of the many-worlds theory you could know it all except for contradictory states of affairs that could not be instantiated regardless of the number of worlds (square circles?).

Any thoughts? Can anyone give an example of a genuine possibility beyond the type I believe in?

It looks to me as though you refer to the actual as the possible.  It’s possible to find a few quid in a box regardless of whether the actual box contains money.  I think using the your terms with great care should allow that to make sense to you.

Doug has tried to help with other possible worlds but they just seem like fantasy to me, although I accept they may not be.

This sentence of yours may serve to illustrate.
You regard many-worlds theory as possible whether or not it is actual (may not be fantasy).

Do we really need other possible worlds to make sense of this world?

I don’t know if we need it, but it doesn’t seem to hurt.  :grin:

Why can’t what happens be the one and only thing that could possibly happen?

Stephen

It expresses your idea more clearly to say “Why can’t what happens be the one and only thing that could actually happen?”

Philosophically, if there were truly only one set of things that could actually happen, then everything would be logically necessary (could not be otherwise in any possible world—in this case there would not be any such thing as another possible world).

Stephen, this issue is very tough to discuss without a rigorous effort to keep the vocabulary unequivocal.  Even when everybody puts an effort into it confusion will often result.

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