Proof of Immortality III

[Loss Leader]

. Also, reincarnation is only one of the possibilities under ~H, and a couple of the possibilities may not require anything immaterial: e.g., time is not absolute and "something else" (multiverse for instance).

That's true. And many of those have nothing to do with either immortality or reincarnation. We could live in a clockwork universe where you're existance is certain. We could live in a slightly smaller universe where there are fewer arrangements of atoms. We could live in a universe where only five people have souls and the rest are p-zombies.

How do you separate your preferred hypothesis from the infinite others included in -H?

 

[JayUtah]

You keep insisting that ~H is a single thing as far as I can see.

I don't interpret it that way. That is, I think Jabba understands that ~H can be any of several things, such as perhaps reincarnation or the Bilblical afterlife or what have you. He may consider any of these alternatives a reasonable alternative to one finite life. The problem is that he can't mathematicslly do that in his formulation and have it remain valid. ~H is a disjunction, meaning a set of alternatives separated by "or." You can't apply the effects of new data on the union of a disjunction because such a union can't generally exist as a non-empty set. Instead of considering the space as H,~H you have to consider it H₁, H₂, H₃, ...,H_n and describe P(E|~H_i) for each, among other things.

 

[Filippo Lippi]

Looks like a successful fringe reset.

 

[Mojo]

Dave,
- I don't understand why that's a problem.

~H includes all the hypotheses other than the 'current scientific model' under which you are not immortal, for example (but not limited to) designed or deterministic universes in which you do not have an immortal soul.

 

[Slowvehicle]

Gopher wood, of course.

...a chip(munk) off the old block...

 

[abaddon]

I don't interpret it that way. That is, I think Jabba understands that ~H can be any of several things, such as perhaps reincarnation or the Bilblical afterlife or what have you. He may consider any of these alternatives a reasonable alternative to one finite life. The problem is that he can't mathematicslly do that in his formulation and have it remain valid. ~H is a disjunction, meaning a set of alternatives separated by "or." You can't apply the effects of new data on the union of a disjunction because such a union can't generally exist as a non-empty set. Instead of considering the space as H,~H you have to consider it H₁, H₂, H₃, ...,H_n and describe P(E|~H_i) for each, among other things.

Therein lies the problem. It is not clear what any definitions of anything might be in Jabba's arguments. Thus one must rely upon interpretation and opens the door to the accusation the one's interpretation is wrong at any point, and thus invites fringe resets aplenty. jt512 had a carve at me for even attempting such an interpretation. This is not a bug in Jabba's method, it is a feature. If one's interlocuters are forced to "interpret" meaning instead of having it plainly stated, one is free to accuse any particular interpretation as being wrong at a whim. Apparently, this is part and parcel of "effective debate".

I did not smash the plate, I am simply attempting to clean up the shards.

 

[Slowvehicle]

Dave,
- I don't understand why that's a problem.

My Dear Mr. Savage:

I find it incomprehensible that you are pretending that this has not been explained to you, over and over. Go back and read the DOG/~DOG arguments...

I remain, somewhat distantly, yours.

 

[Mojo]

Mojo,
- That often happens when new theories are proposed -- a problem in the theory is pointed out to the author who sees if they can come up with a reasonable reset. You don't think that my resets are reasonable, but I do.

Your resets fail to address the problems. Rather than addressing the criticisms, or altering your argument to allow for them, you just restate your argument as if the criticisms hadn't been made.

"Actually effective written debate"? You gotta be kidding.

 

[JayUtah]

Go back and read the DOG/~DOG arguments...

If you recall, he never really addressed those either. When asked, he made an argument for CAT and a separate argument for ~DOG, but never faced head-on the fact that his argument required CAT and ~DOG to be identical.

A conscientious claimant would, at that point, say something like "Whoops, I see the error now, thanks." Instead, Jabba assiduously avoids any questions that put the false dilemma in harsh light. It's one thing to pretend not to understand the error. It's another thing to act surreptitiously so as to try to draw attention away from the error.

 

[JayUtah]

Your resets fail to address the problems. Rather than addressing the criticisms, or altering your argument to allow for them, you just restate your argument as if the criticisms hadn't been made.

Which, of course, would handily distinguish a "reset" from a "refinement." Jabba desperately wants his actions to be interpreted as the latter, but they are quite clearly the former. Yes, in investigations we refine hypotheses all the time as new data becomes available. Investigators are taught not to knee-jerkedly reach either for the de minimus solution or a de novo solution.

However here there is no de minimus refinement possible. An argument so flawed at its core by fatal fallacy as Jabba's cannot be rehabilitated by changing the wiper blades and polishing the chrome and rolling back the odometer. I've seen this before in fringe argumentation. Not all the time, but in a significant number of cases the claimant ignores the irrecoverable defects of his argument and concedes a few ephemeral errors in apparent hope of softening his critics and purporting to rehabilitate the claim.

 

[Mojo]

An argument so flawed at its core by fatal fallacy as Jabba's cannot be rehabilitated by changing the wiper blades and polishing the chrome and rolling back the odometer.

How many fatal flaws does Jabba's argument have? I suspect that any one of Texas sharpshooter, prosecutor's, and false dilemma would be enough on its own to sink it, and it has all three. I also suspect that there are others that I gave missed. Any suggestions from expert fallacy spotters?

 

[jt512]

I don't interpret it that way. That is, I think Jabba understands that ~H can be any of several things, such as perhaps reincarnation or the Bilblical afterlife or what have you. He may consider any of these alternatives a reasonable alternative to one finite life. The problem is that he can't mathematicslly do that in his formulation and have it remain valid. ~H is a disjunction, meaning a set of alternatives separated by "or." You can't apply the effects of new data on the union of a disjunction because such a union can't generally exist as a non-empty set. Instead of considering the space as H,~H you have to consider it H₁, H₂, H₃, ...,H_n and describe P(E|~H_i) for each, among other things.

If a hypothesis K is a collection (discrete, countable, or infinite) of hypotheses, in statistics, we say that K is a composite hypothesis. Bayes tests involving composite hypotheses are common. Probably the most common is the test of a null hypothesis, H₀, that the mean of a distribution θ=0, vs an alternative hypothesis, H₁, that θ≠0. Since, under H₁, θ can be any real number except 0, H₁ is a composite hypothesis comprising an infinite set of simple hypotheses under each of which θ equals a different non-zero number.

If E is the data, then we calculate the single number P(E|H₁), called the marginal likelihood of H₁, as:

P(E|H₁) = ∫_θ P(E|θ, H₁) p(θ|H₁) dθ ,​

where p(θ|H₁) is the prior probability density of θ under H₁.

Similarly, if H₁ comprises a finite or countable set of hypotheses H_1i, i=1,2,... , we calculate P(E|H₁) as

P(E|H₁) = Σ_i P(E|H_1i) p(H_1i) .​

Thus, if Jabba's ~H is a composite hypothesis, he can represent its likelihood by the single number P(E|~H) if he can formulate P(E|~H) as a weighted average of simple hypotheses whose weights are their conditional prior probabilities given ~H.

 

[Humots]

If a hypothesis K is a collection (discrete, countable, or infinite) of hypotheses, in statistics, we say that K is a composite hypothesis. Bayes tests involving composite hypotheses are common. Probably the most common is the test of a null hypothesis, H₀, that the mean of a distribution θ=0, vs an alternative hypothesis, H₁, that θ≠0. Since, under H₁, θ can be any real number except 0, H₁ is a composite hypothesis comprising an infinite set of simple hypotheses under each of which θ equals a different non-zero number.

If E is the data, then we calculate the single number P(E|H₁), called the marginal likelihood of H₁, as:

P(E|H₁) = ∫_θ P(E|θ, H₁) p(θ|H₁) dθ ,​

where p(θ|H₁) is the prior probability density of θ under H₁.

Similarly, if H₁ comprises a finite or countable set of hypotheses H_1i, i=1,2,... , we calculate P(E|H₁) as

P(E|H₁) = Σ_i P(E|θ,

P(E|H₁) = Σ_i P(E|θ, H_1i) p(θ|H_1i) .​

) p(θ|H_1i) .​

Thus, if Jabba's ~H is a composite hypothesis, he can represent its likelihood by the single number P(E|~H) if he can formulate P(E|~H) as a weighted average of simple hypotheses whose weights are their conditional prior probabilities given ~H.

Could you please clarify the definition of H_1i? I don't understand the double "1i" subscript.

Does P(E|θ, H_1i) = P(E|θ, H₁, H_i)?

 

[JayUtah]

...he can represent its likelihood by the single number P(E|~H) if he can formulate P(E|~H) as a weighted average of simple hypotheses whose weights are their conditional prior probabilities given ~H.

That's the concept I was alluding to. Jabba's formulation for P(~H) is simply 1-P(H). I don't dispute the weighted average principle. I'm asserting that if you know nothing about any of the hypotheses in ~H then any number you derive for its likelihood doesn't actually relate to any hypothesis. Does that make sense?

 

[Humots]

Could you please clarify the definition of H_1i? I don't understand the double "1i" subscript.

Does P(E|θ, H_1i) = P(E|θ, H₁, H_i)?

Never mind. Now I see.

H₁ comprises a finite or countable set of hypotheses H1i, i=1,2,...

 

[jt512]

Could you please clarify the definition of H_1i? I don't understand the double "1i" subscript.

Does P(E|θ, H_1i) = P(E|θ, H₁, H_i)?

My second equation in that post was wrong. It shouldn't have have had any θs in it. I've fixed the mistake.

 

[JayUtah]

My second equation in that post was wrong. It shouldn't have have had any θs in it. I've fixed the mistake.

Oh, thanks, I was puzzling over that syntax forever. But yeah, a continuous versus discrete weighted average formulation shouldn't be too difficult a concept. The point in both cases being that you can't derive that weighting -- continuous or discrete -- by a simple compliment such as 1-p. Jabba is doing precisely that. He wants to assume P(H) is some microscopic number such that he can assume by the unity theorem, and some fancy footwork, that P(~H) is huge. A lot of us have tried to explain how it doesn't work that way.

 

[jt512]

That's the concept I was alluding to. Jabba's formulation for P(~H) is simply 1-P(H). I don't dispute the weighted average principle. I'm asserting that if you know nothing about any of the hypotheses in ~H then any number you derive for its likelihood doesn't actually relate to any hypothesis. Does that make sense?

Whatever P(H) is, P(~H) must be 1 – P(H). So, it is possible, in principle, to assign a prior probability to a composite hypothesis ~H without elaborating the simple hypotheses comprising it.

The difficulty comes in computing P(E|~H). This requires positing a probability distribution p for the simple hypotheses comprising ~H, and explicitly computing the weighted average of their likelihoods using their probabilities under p as weights. Without elaborating the elements of the set ~H, and explicitly assigning each a probability, any value you asserted for P(E|~H) would be meaningless.

 

[JayUtah]

Whatever P(H) is, P(~H) must be 1 – P(H). So, it is possible, in principle, to assign a prior probability to a composite hypothesis ~H without elaborating the simple hypotheses comprising it.

Agreed. The question in my mind is not its computability so much as its meaning. I am comfortable with the notion that P(~H) is 1-P(H), but I am not comfortable with Jabba's use of this fact, which is more often than not to consider ~H some singular outcome. If you undertake the pain of reading his other threads, you see him equating ~H with some H_i in classic false-dilemma fashion. This is what we're referring to when we talk about CAT and ~DOG. He painted himself into a corner on that example and abandoned the thread in which it arose.

The difficulty comes in computing P(E|~H). [,,,] Without elaborating the elements of the set ~H, and explicitly assigning each a probability, any value you asserted for P(E|~H) would be meaningless.

Also agreed, and what I expressed a page or so back. In either the discrete or continuous case, P(E|~H) requires insight into the nature of the composition ~H.

 

[Loss Leader]

How many fatal flaws does Jabba's argument have? I suspect that any one of Texas sharpshooter, prosecutor's, and false dilemma would be enough on its own to sink it, and it has all three. I also suspect that there are others that I gave missed. Any suggestions from expert fallacy spotters?

We can't let by the fact that he has defined the "self" incorrectly in all of his formulations. He considers it a constant and unchanging thing, rather than a process.

In doing so, he commits the fallacy of Appealing to Popularity. He reasons that most people experience consciousness as continuous and distinct, therefore it is.