02 Feb 16
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Originally posted by humyI don't think I have said anything to suggest otherwise. It remains the case that every definition I have been able to lay my hands on clearly states that a 'sample space' is the set of all possible outcomes. ie it does not include impossible outcomes.
OBVIOUSLY, he wasn't trying to say you could actually observe impossible events/outcomes occurring in an actual sample space. SURELY you should have figured that out for yourself?
And what do you say of his other comment that I ( + my two brothers which I now asked ) agree with which is:
"Events that are impossible have probability zero. Always."
I say that it is common English usage but is inherently incoherent. We all know that when we say 'the chances of that happening are zero' we usually mean 'it can't happen'. Only people who take a bit of time to think about it would ask 'is it possible but extremely unlikely, or impossible?'. If it is impossible then the word 'chance' doesn't make sense in the sentence any more. If I say 'it happened by chance' then I am implying a random variable. If I say 'it didn't happen because it was impossible' then I am saying it was prevented by a rule. Obeying a rule is not 'chance'.
In mathematics the same is true. To say something has a probability is to say there exists some randomness. In my two headed coin example there is no randomness, so it is incoherent to describe a probability.
02 Feb 16
Originally posted by humyI disagree. There is no such distinction. Violating a natural law is a logical impossibility.
Something can be both 'logically possible', which means there is no logical contradiction in it being true, AND yet NOT 'causally possible', where 'causally possible' means it is possible according to natural law that exists in the actual external world.
Note what is 'logically possible' takes no account of natural law (the laws of physics, chemistry etc. ) because there is no logical contradiction in having the universe with natural law being all different. Thus an earthworm traveling intact to the center of the Earth is causally possible but NOT logically possible since it might be logically possible if all natural laws where different.
So is it your claim that when you ask 'what is the probability of an earth worm burrowing to the centre of the earth you are in fact asking about all possible universes including those in which the laws of physics allow said burrowing? If so, then your earlier claim that it would be impossible is false. If not, then your current claim that it is logically possible is false.
02 Feb 16
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Originally posted by humyAlthough it is an interesting question regarding reality it is irrelevant to the probability discussion.
Yes. I find that comment interesting because I had once thought along very similar lines!
I wondered if perhaps the is some unknown purely deductive reason why the laws of nature couldn't possibly be any different!? If so, I wonder if that reason is so incredibly subtle that it would always be beyond our comprehension?
Probability is about information and randomness. To talk of probability you must set out the rules of what is possible and then probability tells you what frequency they occur at.
In the case of a coin flip, there is no natural law that says all coins must have heads and tails or that coins must be flipped. Those are part of the conditions of the question. You would not say that in a coin flip it is logically possible that the coin comes up 'snakes' because in some other universe coins might have snakes on them.
Similarly in the case of the worm, the question clearly stated 'Earth' which we all know to mean a specific body in our universe subject to the natural laws of this universe. Given that condition in the definition it is logically impossible for the worm to burrow to the centre of the earth.
02 Feb 16
Originally posted by twhiteheadNot in conventional epistemological terminology. You really need to study just a bit of epistemology.
I disagree. There is no such distinction. Violating a natural law is a logical impossibility.
....
For the distinction between logically possible and causally possible, see:
http://www2.drury.edu/cpanza/introreview1-2.html
and
http://www.georgewrisley.com/blog/?tag=causal-possibility
This below doesn't explicitly mention "causally possible" but I think it still helps to implicitly make the distinction:
https://en.wikipedia.org/wiki/Logical_possibility
02 Feb 16
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Originally posted by twhitehead
Although it is an interesting question regarding reality it is irrelevant to the probability discussion.
Probability is about information and randomness. To talk of probability you must set out the rules of what is possible and then probability tells you what frequency they occur at.
In the case of a coin flip, there is no natural law that says all coin ...[text shortened]... in the definition it is logically impossible for the worm to burrow to the centre of the earth.
To talk of probability you must set out the rules of what is possible and then probability tells you what frequency they occur at.
If what you mean by "possible " above is "causally possible" then, If that is true, there wouldn't be such thing as prior probability. And the implication of that is that there wouldn't be such thing as posterior probability either. In other words, ALL probabilities are undefined i.e. there isn't such thing as probability.
If what you mean by "possible " above is "logically possible" then probability doesn't tell you what frequency they actually occur at but rather merely gives you the best rational 'guess' or 'estimate' at what frequency they occur with no absolute guarantee that that estimate is even approximately correct (actually, I would personally insist this is true for all probability anyway; at least pedantically speaking ) Perhaps that is what you really meant? If so, that is correct.
If what you mean by "possible " above is "logically possible" and/or "causally possible", then you need to be more concise at the exactly meaning of that assertion is complex and unclear.
If what you mean by "possible " above is neither "logically possible" or "causally possible", then there isn't such thing as "possible" and there isn't such thing as "probability" either.
02 Feb 16
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Originally posted by twhiteheadI have a brother that is a top professor in philosophy who can explain it pretty well. But I doubt if I can persuade him to do so.
None of those sources are very clear and I have objections to all of them. Do you have any better sources?
I am afraid the best source for information on this is me, as I have clear knowledge on this.
What is that you find 'unclear' about it?
For an apple to magically accelerate upwards thus defy the law of gravity would be causally impossible but not logically possible. 'magic' is causally impossible but not logically possible, unless the said magic thing is defined in some kind of self-contradictory way.
An apple to both accelerate upwards and downwards at the same time (in the same frame of reference) would be logically impossible, because that is a logical contradiction, thus also causally impossible.
All logical impossibilities are causal impossibilities but not all causal impossibilities are logical impossibilities.
02 Feb 16
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Originally posted by humyQuite the opposite in fact. Only in causal possibilities does one deal with information and thus prior probability and posterior probability. If one is dealing in logical possibilities then prior and posterior would make no sense.
If what you mean by "possible " above is "causally possible" then, If that is true, there wouldn't be such thing as prior probability. And the implication of that is that there wouldn't be such thing as posterior probability either. In other words, ALL probabilities are undefined i.e. there isn't such thing as probability.
Prior and posterior involves the introduction of information which changes the world in which you are working which changes the sample space.
If what you mean by "possible " above is "logically possible" then, then probability doesn't tell you what frequency they actually occur at but rather merely gives you the best rational 'guess' or 'estimate' at what frequency they occur with no absolute guarantee that that estimate is even approximately correct.
Perhaps that is what you really meant? If so, that is correct else wrong.
No, that is certainly not what I meant.
By 'possible' I meant 'causally possible in a world as defined (not necessarily the real world). Probability then tells you exactly what frequency they actually occur in such a world as defined.
If I say I have a two headed coin and I flip it, then I am defining a world in which coins have two heads and where flipping them results in exactly even distribution of results (ie random). A third side to the coin might be logically possible but that is totally irrelevant to probability. In that world only two outcomes are causally possible. The sample space only includes head and tails and nothing else.To talk about the probability of a third side is incoherent and not useful.
02 Feb 16
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Originally posted by humyWhy did you throw in 'in the same frame of reference'? Surely that is a 'fact about the world' and thus makes it a causal issue? What if in another world 'up' and 'down' are actually the same direction? What about an apple that is expanding? What if the apple is quantum? Have you just proved that quantum mechanics is logically impossible?
An apple to both accelerate upwards and downwards at the same time (in the same frame of reference) would be logically impossible, because that is a logical contradiction, thus also causally impossible.
02 Feb 16
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Originally posted by twhiteheadWhat! Where did you get all that from?
Quite the opposite in fact. Only in causal possibilities does one deal with information and thus prior probability and posterior probability. If one is dealing in logical possibilities then prior and posterior would make no sense.
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Are you confusing the two kinds of possibility around?
02 Feb 16
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Originally posted by twhitehead
Why did you throw in 'in the same frame of reference'? Surely that is a 'fact about the world' and thus makes it a causal issue? What if in another world 'up' and 'down' are actually the same direction? What about an apple that is expanding? What if the apple is quantum? Have you just proved that quantum mechanics is logically impossible?
Why did you throw in 'in the same frame of reference'?
In one frame of reference the apple may be moving up; In anther, down.
But that wasn't what I wanted to refer to which is why I said "same" frame of reference.
Surely that is a 'fact about the world' and thus makes it a causal issue?
Well, it is a 'fact about the world' and "a causal issue" but only because it is true by definition.
What if in another world 'up' and 'down' are actually the same direction?
I take that as a logical contradiction of the normal way we define 'up' and 'down' thus it is logically impossible.
I suppose you could arbitrary contrive a different definition of up and down which allows that without contradiction. But then we merely wouldn't agree with the same definition thus we would not be talking about exactly the same thing.
02 Feb 16
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Originally posted by humyNo, I am not.
What! where the hell did you get all that from?
Are you confusing the two kinds of possibility around?
Here is the scenario: you have a coin that has three possible symbols on it, 'heads','tails' or 'snakes'. What is the probability of throwing 'heads'? Answer: 1/3. And our sample space has three entries each with equal probability.
That is the prior probability.
Now I tell you that this particular coin does not have a 'snakes' symbol.
The posterior probability of throwing 'heads' is now 1/2. We are in a new world and our sample space has only two entries.
It is incoherent to ask what the probability of throwing a 'bird' is, and it is incoherent to ask what the probability of throwing 'snakes' is in the posterior situation.
It is nonsensical (or at least not useful) to say that the sample space includes all imaginable symbols (logically possible). One can say that all symbols that are not causally possible have probability zero, but that is really just another way of saying 'they are out of the question' or 'they are undefined'. One could equally say the same about all symbols that are logically not possible, so your demarcation of the logically possible seems arbitrary or contrived. The probability of throwing an apple both up and down at the same time could be said to be zero, yet you would have that as undefined.
What is the probability of throwing a 'square circle' symbol?
02 Feb 16
Originally posted by humySo is 'frame of reference' a natural law or a logical law?
In one frame of reference the apple may be moving up; In anther, down.
But that wasn't what I wanted to refer to which is why I said "same" frame of reference.
Well, it is a 'fact about the world' and "a causal issue" but only because it is true by definition.
So if I define a world in which gravity cannot be defied does your apple become logically impossible?