Proof of Immortality III

[caveman1917]

Dividing by ∞ implies you're in the extended real number system. The reals are a subset of the extended reals, so any real number can be divided by ∞, despite what Caveman thinks.

Better yet:

for all r in R^+: r / ∞ > 0

True or false?

There is no such "implies" without being explicit as to what set you're talking about.

 

[jsfisher]

Yes, really. If P = 0 for all n then P is not a probability function, calling it a "probability" would be incorrect. Or differently, there is no such thing as a "fair die with countably infinitely many sides".

I think we are talking past each other while actually agreeing. Were there such a die (or some equivalent random number generator), one might "calculate" the probability of a specific roll by taking the limit of an N-sided fair die as N approaches infinity.

Sure enough that would yield 0 for the probability, if you can call it that. This is the situation Jabba is in with his ~H realities.

Unfortunately, that isn't a proper probability; it is into a realm where probability cannot be defined. This is really the situation Jabba is in.

 

[caveman1917]

Yeah, supposedly, you only need one type of interval: open, closed, or half-open, and all the other sets follow from the properties of a σ-algebra, but I'm not sure I could figure out how to get them all.

I just considered that an open interval is a countable union of closed intervals, and a closed interval is a countable intersection of open intervals, so you can get from one to the other using the properties of a sigma-algebra.

 

[caveman1917]

I think we are talking past each other while actually agreeing. Were there such a die (or some equivalent random number generator), one might "calculate" the probability of a specific roll by taking the limit of an N-sided fair die as N approaches infinity.

The limit of sequence of probability functions is not necessarily a probability function. But yes, we are probably all talking past each other while actually agreeing.

 

[jt512]

Then the problem is the double use of the "/" symbol for both /_R and /_R* (ie division as defined over R or over R*). Either way, something has got to give here, as "for any r ∈R r / ∞ = 0" can not be correct as stated

- I could after all just define another extension of R in which that doesn't hold.

In this case:
for all r in R: r /_R inf is undefined
for all r in R: r /_R* inf = 0

The authors that are stating that are defining the extended number system, and they make the statement pretty much verbatim.

Claim: for all r in R_0: r / 0 = ∞

What would your response be?

My answer would be that, to the best of my knowledge, division by 0 is not defined for either the reals or the extended reals.

Better yet:

for all r in R: r / ∞ > 0

True or false?

There is no such "implies" without being explicit as to what set you're talking about.

OK. Good point. What I should have written is that if someone writes the equation r / ∞ = 0, it implies that they are using the (a particular) extended real number system. They must be because ∞ is not an element of the real number system. Thus, I don't think Jabba violated and mathematical rule by claiming that a number divided by ∞ was 0. Rather, his error was to use ∞ to represent a large (but possibly unknown) finite number.

 

[caveman1917]

The authors that are stating that are defining the extended number system, and they make the statement pretty much verbatim.

True, but they are making the statement explicitly in context of defining the (affinely) extended real numbers. However there are a whole bunch of extensions of the real numbers, not all of which evaluate "r / ∞" to 0. So when just presented with "r / ∞ = 0" without further information we can't really know what extension the person is working with. Or if the person is even working in some extension rather than just having made an error.

My answer would be that, to the best of my knowledge, division by 0 is not defined for either the reals or the extended reals.

True. It is, however, defined for the projectively extended reals (yet another extension of the real numbers, basically the usual extended reals but where +∞ = -∞).

OK. Good point. What I should have written is that if someone writes the equation r / ∞ = 0, it implies that they are using the (a particular) extended real number system. They must be because ∞ is not an element of the real number system.

Personally I'd go with saying that it's an error unless the person makes explicit what set they are working with.

Thus, I don't think Jabba violated and mathematical rule by claiming that a number divided by ∞ was 0. Rather, his error was to use ∞ to represent a large (but possibly unknown) finite number.

There's no hard mathematical rule against using ∞ as a symbol representing a large (but possible unknown) finite number either. It's against convention, surely, but in the end symbols are just symbols. But then again, it's also against convention to state that a real number divided by infinity is zero without making explicit what extension you're working with.

To be honest though, I don't think Jabba is aware of any of this and was just making both errors.

 

[Jabba]

That's not quite the fallacy. Let's say you have a hypothesis K that the possible outcomes of a die roll are random and equally likely, and therefore that the probability that the outcome will be "three" is 1/6. You then roll the die and the outcome is indeed a three. Then, the following is still correct: P("three"|K) = 1/6. The outcome of the experiment does not change the probability of the outcome under the hypothesis. If you don't believe this, roll the die a million times and calculate the empirical relative frequency of the outcome "three."

Jabba's fallacy is that, under his "scientific" hypothesis, he is unwittingly conditioning on the observed outcome as well as the hypothesis, and he is not taking this into account when he states the probability. He observes "Jabba exists" and states that, under the hypothesis R that "Jabba" was a random outcome, P("Jabba"|R) is very small. This is indeed true. But Jabba exists. Even if Jabba is the outcome of a random process, it was the random outcome that actually occurred. Furthermore, Jabba could only make the observation "Jabba exists" if Jabba exists. Therefore, the event he is observing is not an event in a sample space that contains the events "Jabba exists" and "Jabba does not exist," but rather, it is an event in the conditional sample space in which "Jabba exists" is the only element. Therefore, he is actually calculating P("Jabba"|R, "Jabba"), the probability that Jabba exists given that a random process occurred and he was the outcome. This probability is 1, and, since he is conditioning on his own existence, it is this probability he must use in Bayes' formula.

This fact that he is conditioning on his own existence is fatal to his argument. Since P("Jabba"|R, "Jabba") = 1, the posterior probability of his immortality hypothesis cannot be greater that its prior probability (because P("Jabba"|~R) ≤ 1). So his argument, which is intended to increase the posterior probability of immortality relative to its prior, can only lower it.

jt,
- Isn't that what P(E|H) usually does -- i.e., take an event that has, in fact already happened, and see how it affects existing hypotheses, based upon the likelihood of it happening given that hypothesis?

 

[jt512]

Jabba's fallacy is that, under his "scientific" hypothesis, he is unwittingly conditioning on the observed outcome as well as the hypothesis, and he is not taking this into account when he states the probability. He observes "Jabba exists" and states that, under the hypothesis R that "Jabba" was a random outcome, P("Jabba"|R) is very small. This is indeed true. But Jabba exists. Even if Jabba is the outcome of a random process, it was the random outcome that actually occurred. Furthermore, Jabba could only make the observation "Jabba exists" if Jabba exists. Therefore, the event he is observing is not an event in a sample space that contains the events "Jabba exists" and "Jabba does not exist," but rather, it is an event in the conditional sample space in which "Jabba exists" is the only element. Therefore, he is actually calculating P("Jabba"|R, "Jabba"), the probability that Jabba exists given that a random process occurred and he was the outcome. This probability is 1, and, since he is conditioning on his own existence, it is this probability he must use in Bayes' formula.

This fact that he is conditioning on his own existence is fatal to his argument. Since P("Jabba"|R, "Jabba") = 1, the posterior probability of his immortality hypothesis cannot be greater that its prior probability (because P("Jabba"|~R) ≤ 1). So his argument, which is intended to increase the posterior probability of immortality relative to its prior, can only lower it.

jt,
- Isn't that what P(E|H) usually does -- i.e., take an event that has, in fact already happened, and see how it affects existing hypotheses, based upon the likelihood of it happening given that hypothesis?

To understand the fallacy, you have to read the whole two paragraphs.

 

[Jabba]

That's not quite the fallacy. Let's say you have a hypothesis K that the possible outcomes of a die roll are random and equally likely, and therefore that the probability that the outcome will be "three" is 1/6. You then roll the die and the outcome is indeed a three. Then, the following is still correct: P("three"|K) = 1/6. The outcome of the experiment does not change the probability of the outcome under the hypothesis. If you don't believe this, roll the die a million times and calculate the empirical relative frequency of the outcome "three."

Jabba's fallacy is that, under his "scientific" hypothesis, he is unwittingly conditioning on the observed outcome as well as the hypothesis, and he is not taking this into account when he states the probability. He observes "Jabba exists" and states that, under the hypothesis R that "Jabba" was a random outcome, P("Jabba"|R) is very small. This is indeed true. But Jabba exists. Even if Jabba is the outcome of a random process, it was the random outcome that actually occurred. Furthermore, Jabba could only make the observation "Jabba exists" if Jabba exists. Therefore, the event he is observing is not an event in a sample space that contains the events "Jabba exists" and "Jabba does not exist," but rather, it is an event in the conditional sample space in which "Jabba exists" is the only element. Therefore, he is actually calculating P("Jabba"|R, "Jabba"), the probability that Jabba exists given that a random process occurred and he was the outcome. This probability is 1, and, since he is conditioning on his own existence, it is this probability he must use in Bayes' formula.

This fact that he is conditioning on his own existence is fatal to his argument. Since P("Jabba"|R, "Jabba") = 1, the posterior probability of his immortality hypothesis cannot be greater that its prior probability (because P("Jabba"|~R) ≤ 1). So his argument, which is intended to increase the posterior probability of immortality relative to its prior, can only lower it.

jt,
- Isn't that what P(E|H) usually does -- i.e., take an event that has, in fact already happened, and see how it affects existing hypotheses, based upon the likelihood of it happening given that hypothesis?

To understand the fallacy, you have to read the whole two paragraphs.

jt,
- I did read the whole two paragraphs, but I was only dealing with that particular section because I had already accepted your point in the next section (to the extent that I needed to do some more thinking about it).
- Wouldn't you agree with what I said about the first section was correct?

 

[Loss Leader]

jt,
- I did read the whole two paragraphs, but I was only dealing with that particular section because I had already accepted your point in the next section (to the extent that I needed to do some more thinking about it).
- Wouldn't you agree with what I said about the first section was correct?

Jabba -

- I didn't read your entire post above because I was only dealing with the first depenednt clause.
- Wouldn't you agree I was correct with what I said about your refusal to consider an infinite number of alternate scenarios?

 

[jt512]

jt,
- I did read the whole two paragraphs, but I was only dealing with that particular section because I had already accepted your point in the next section (to the extent that I needed to do some more thinking about it).
- Wouldn't you agree with what I said about the first section was correct?

jt,
- Isn't that what P(E|H) usually does -- i.e., take an event that has, in fact already happened, and see how it affects existing hypotheses, based upon the likelihood of it happening given that hypothesis?

The way Bayesian inference works, is that you formulate a hypothesis, or a set of competing hypotheses. Then you perform an experiment in which you collect a random sample of data. The sample is random in the sense that the outcome of the experiment belongs to a larger set of possible outcomes, and which outcome will be observed cannot be determined in advance. Then the relative compatibility of the data with each hypothesis is computed, and combined with the prior probabilities of the hypotheses to compute the posterior probabilities.

 

[JoeMorgue]

Jabba there is a criticism of your soul/physical mind opinion that has been brought up multiple times across multiple threads that you have refused to address.

How does brain damage work within your theory?

If physical neurological processing of the brain does not produce all of our "consciousness" and there is some mystical "soul" that has to hook up with our brain in order to complete our "selves" why does damage to the brain alter our mental processing?

So by your argument there was some predetermined "Phineas Gage" soul out there that was waiting for the physical manifestation of "Phineas Gage" to come along.

So on September 13, 1848 when a railway construction explosion drove a tampering rod through Phineas Gage's skull, heavily damaging his frontal lobe how did his "soul" get damaged? Phineas Gage's behavior, his "self" changed after the incident but if our "self" is not physical why would physical damage change it?

 

[The Sparrow]

Jabba there is a criticism of your soul/physical mind opinion that has been brought up multiple times across multiple threads that you have refused to address.

How does brain damage work within your theory?

If physical neurological processing of the brain does not produce all of our "consciousness" and there is some mystical "soul" that has to hook up with our brain in order to complete our "selves" why does damage to the brain alter our mental processing?

So by your argument there was some predetermined "Phineas Gage" soul out there that was waiting for the physical manifestation of "Phineas Gage" to come along.

So on September 13, 1848 when a railway construction explosion drove a tampering rod through Phineas Gage's skull, heavily damaging his frontal lobe how did his "soul" get damaged? Phineas Gage's behavior, his "self" changed after the incident but if our "self" is not physical why would physical damage change it?

That's an easy one. It is dealt with the (completely un-evidenced) brain is a radio analogy. The soul is intact and undamaged, its the brain which acts as a portal for the soul to interact with the world that is actually damaged (supposedly). Good luck debating that one, its pretty much unflasifiable

 

[Garrette]

That's an easy one. It is dealt with the (completely un-evidenced) brain is a radio analogy. The soul is intact and undamaged, its the brain which acts as a portal for the soul to interact with the world that is actually damaged (supposedly). Good luck debating that one, its pretty much unflasifiable

Not falsifiable, perhaps, but certainly capable of having its ridiculousness pointed out.

If the image of the soul is damaged because the receiver is damaged, then one would have to know what constitutes a perfect receiver. Given that those arguing for a soul cannot do such a thing, then one must assume that all receivers are in some fashion damaged. Which means we do not know what the actual soul is. They may, in fact, all be dark souls, hissing their eternal wishes for our damnation.

 

[Jabba]

The way Bayesian inference works, is that you formulate a hypothesis, or a set of competing hypotheses. Then you perform an experiment in which you collect a random sample of data. The sample is random in the sense that the outcome of the experiment belongs to a larger set of possible outcomes, and which outcome will be observed cannot be determined in advance. Then the relative compatibility of the data with each hypothesis is computed, and combined with the prior probabilities of the hypotheses to compute the posterior probabilities.

jt,
- Can't we do the same thing with something that just occurs, that we didn't plan an experiment for?

 

[Jabba]

That's an easy one. It is dealt with the (completely un-evidenced) brain is a radio analogy. The soul is intact and undamaged, its the brain which acts as a portal for the soul to interact with the world that is actually damaged (supposedly). Good luck debating that one, its pretty much unflasifiable

Sparrow,
- I hadn't actually considered that issue before (that I can remember) -- but, that's how I would have answered...
- Thanks.

 

[Loss Leader]

So by your argument there was some predetermined "Phineas Gage" soul out there that was waiting for the physical manifestation of "Phineas Gage" to come along.

Congratulations, JoeBentley!

Despite years and years of this nonsense, you are the first poster to cite Phineas Gage in any of Jabba's immortality threads.

[IMGw=600]http://www.internationalskeptics.com/forums/picture.php?albumid=681&pictureid=10892[/IMGw]


(Grantor not acting in his capacity as a mod.)

 

[Garrette]

Not that any more is needed, but if anyone wanted more proof that Jabba has absolutely no interest in discussing honestly and never has, his last post says he has never considered the issue of personality-changes-caused-by-damage-to-the-brain. He says this despite it having been brought up repeatedly over the years. The only time he responds is when someone offers him a pre-written out (and despite that person mentioning that it isn't really an out). And he ignores the following post that shows especially why the out doesn't work.

There is a lot of interesting discussion in this thread, but Jabba has contributed none of it.

 

[The Sparrow]

Sparrow,
- I hadn't actually considered that issue before (that I can remember) -- but, that's how I would have answered...
- Thanks.

So, you've never even considered it, but magically you would have settled on the un-falsifiable out I just quoted.
Great. Have you ANY proof for this 'out' you have latched onto? ANY?

 

[JoeMorgue]

Record Players don't actually play records. Record players are actually a type of radio. The reason a record will skip if you scratch is because it damages the receiver.

There's a running joke amongst electricians and computer techs that electricity is a myth and that all electronics run on magic blue smoke. The proof? Well if you break an piece of electronics enough that the magic blue smoke comes out, it don't work.

That's more scientific then what Jabba is arguing.