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keiths

Posts: 2041
Joined: Jan. 2006

 Quote (Reciprocating Bill @ Oct. 18 2009,08:17) Knowing that any draw of a red marble (cracked or not) increases the probability that our cracked-blue hypothesis is correct to an equal degree, and having time to kill, we proceed to draw only red marbles... With every removal our excitement grows, as with each (per the logic above) it is becoming more likely that all blue marbles are cracked.

Another wild night at Reciprocating Bill's place.

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And the set of natural numbers is also the set that starts at 0 and goes to the largest number.  -- Joe G

Please stop putting words into my mouth that don't belong there and thoughts into my mind that don't belong there. -- KF

Raevmo

Posts: 235
Joined: Oct. 2006

Consulting "Probability Theory: The Logic of Science", by E.T. Jaynes, I found that the black raven/yellow banana situation is apparently a famous paradox, known as Hempel's paradox. But instead of bananas and ravens the original uses crows and shoes:

"Now the hypothesis that all crows are black is logically equivalent to the statement that all non-black things are non-crows, and this is supported by the observation of a white shoe."

Jaynes doesn't buy it and refers to a paper by Good (1967), entitled "The white shoe is a red herring". Good gives the following counterexample: In world 1 there are 1 million birds, of which 100 are crows, all black. In world two there are 2 million birds, of which 200,000 are black crows and 1,800,000 are white crows. We observe one bird, which proves to be a black crow. Which world are we in?

Well, the odds ratio is (200,000/2,000,000)/(100/1,000,000)=1000, hence we're 1000 times as likely to be in world 2 (where not all crows are black) rather than in world 1 (where are crows are black).

Jaynes argues that the general premise "A case of an hypothesis supports the hypothesis" is false.

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After much reflection I finally realized that the best way to describe the cause of the universe is: the great I AM.

--GilDodgen

Raevmo

Posts: 235
Joined: Oct. 2006

Is this sig-worthy or what?

Denyse:
 Quote I am no mathematician and don’t use well-defined terms, as I don’t know any.

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After much reflection I finally realized that the best way to describe the cause of the universe is: the great I AM.

--GilDodgen

Occam's Aftershave

Posts: 1786
Joined: Feb. 2006

O'Dreary on pi and her understanding of the term 'irrational numbers':

 Quote - about pi – look, I was taught in school that it just goes on and on irrationally, like a drunk after the bar closes. At a certain point, one would just cut the karaoke mike, right?We staff are sweeping up and the thing is still going on and on, still making no sense.

(picks jaw up from floor)

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"Science is what got us to the humble place weâ€™re at, and what hard-won progress we might realize comes from science, with ID completely flaccid, religious apologetics bitching from the sidelines." - Eigenstate at UD

keiths

Posts: 2041
Joined: Jan. 2006

 Quote (Raevmo @ Oct. 18 2009,11:31) Consulting "Probability Theory: The Logic of Science", by E.T. Jaynes, I found that the black raven/yellow banana situation is apparently a famous paradox, known as Hempel's paradox.

Yep:
 Quote I agree that Coppedge is a tard, but on this particular issue (the famous raven paradox of Carl Hempel) his position is defensible.

 Quote Jaynes doesn't buy it and refers to a paper by Good (1967), entitled "The white shoe is a red herring". Good gives the following counterexample: In world 1 there are 1 million birds, of which 100 are crows, all black. In world two there are 2 million birds, of which 200,000 are black crows and 1,800,000 are white crows. We observe one bird, which proves to be a black crow. Which world are we in?Well, the odds ratio is (200,000/2,000,000)/(100/1,000,000)=1000, hence we're 1000 times as likely to be in world 2 (where not all crows are black) rather than in world 1 (where are crows are black).

Good's argument itself strikes me as a red herring.  The question is not "which world am I in?". The question is "in my world, are all crows black?"

With each new black crow we see, our confidence in the hypothesis "all crows are black" increases.  This is true whether we are in world 1 or world 2. The hypothesis ultimately turns out to be wrong in world 2, but that is not the issue. We don't know whether we are in world 1, world 2, world 3, world 4,520,772, or any of an infinitude of other possible worlds.  We're trying to figure that out, and our confidence in our hypothesis must depend only on what we have already observed.

 Quote Jaynes argues that the general premise "A case of an hypothesis supports the hypothesis" is false.

That strikes me as absurd.  Does Jaynes really think that observing one hard diamond after another doesn't strengthen the hypothesis that all diamonds are hard?

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And the set of natural numbers is also the set that starts at 0 and goes to the largest number.  -- Joe G

Please stop putting words into my mouth that don't belong there and thoughts into my mind that don't belong there. -- KF

keiths

Posts: 2041
Joined: Jan. 2006

Denyse:
 Quote - about pi – look, I was taught in school that it just goes on and on irrationally, like a drunk after the bar closes. At a certain point, one would just cut the karaoke mike, right?We staff are sweeping up and the thing is still going on and on, still making no sense.

Denyse, are you trying to make a case for or against an Intelligent Designer?

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And the set of natural numbers is also the set that starts at 0 and goes to the largest number.  -- Joe G

Please stop putting words into my mouth that don't belong there and thoughts into my mind that don't belong there. -- KF

Texas Teach

Posts: 1480
Joined: April 2007

Quote (keiths @ Oct. 18 2009,13:30)

 Quote (Reciprocating Bill @ Oct. 18 2009,08:17) Knowing that any draw of a red marble (cracked or not) increases the probability that our cracked-blue hypothesis is correct to an equal degree, and having time to kill, we proceed to draw only red marbles... With every removal our excitement grows, as with each (per the logic above) it is becoming more likely that all blue marbles are cracked.

Another wild night at Reciprocating Bill's place.

Quote (keiths @ Oct. 18 2009,14:01)

 Quote Jaynes argues that the general premise "A case of an hypothesis supports the hypothesis" is false.

That strikes me as absurd.  Does Jaynes really think that observing one hard diamond after another doesn't strengthen the hypothesis that all diamonds are hard?

Must resist joke...

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"Creationists think everything Genesis says is true. I don't even think Phil Collins is a good drummer." --J. Carr

"I suspect that the English grammar books where you live are outdated" --G. Gaulin

dvunkannon

Posts: 1377
Joined: June 2008

Quote (Reg @ Oct. 18 2009,13:57)
Oh my, O'Leary's mathematics thread. What a mess...

Denyse O'Leary, on 17th October, not a creationist:

 Quote Even though I am not a creationist by any reasonable definition, I sometimes get pegged as the local gap tooth creationist moron. ...

Denyse O'Leary, later the same day, all of creation is the work of God:

 Quote Peter, well, the Cambrian explosion was doubtless the work of God, in my view, but I would say that of all creation. ...

But not a creationist by any reasonable definition. Right.

But she's very clear on something:

 Quote Guys, I am no mathematician and don’t use well-defined terms, as I don’t know any.

You got that right, sister.

BTW, it appears that she was interviewed because she happens to live in a building with an unlucky address, 14 Latimer Ave. Not for being a gap toothed moron.

The background story is that Aurora, a town north of Toronto, will allow people (mostly of East Asian descent) who object to '4' (sounds like the word for death in some Asian languages) in their addresses to change those addresses if there is sufficient gap in the house numbering to keep it sequential.

I was hoping to catch a glimpse of her amazing dialect of English being misspoken in real time, but alas her efforts seem to have fallen on the cutting room floor.

Is there video of Dense-speak on the web?

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I’m referring to evolution, not changes in allele frequencies. - Cornelius Hunter
I’m not an evolutionist, I’m a change in allele frequentist! - Nakashima

dvunkannon

Posts: 1377
Joined: June 2008

Quote (keiths @ Oct. 18 2009,14:30)
 Quote (Reciprocating Bill @ Oct. 18 2009,08:17) Knowing that any draw of a red marble (cracked or not) increases the probability that our cracked-blue hypothesis is correct to an equal degree, and having time to kill, we proceed to draw only red marbles... With every removal our excitement grows, as with each (per the logic above) it is becoming more likely that all blue marbles are cracked.

Another wild night at Reciprocating Bill's place.

It's the Cheetohs laced with Frolic Acid and MSG...

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I’m referring to evolution, not changes in allele frequencies. - Cornelius Hunter
I’m not an evolutionist, I’m a change in allele frequentist! - Nakashima

keiths

Posts: 2041
Joined: Jan. 2006

 Quote (dvunkannon @ Oct. 18 2009,12:39) I was hoping to catch a glimpse of her amazing dialect of English being misspoken in real time, but alas her efforts seem to have fallen on the cutting room floor.Is there video of Dense-speak on the web?

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And the set of natural numbers is also the set that starts at 0 and goes to the largest number.  -- Joe G

Please stop putting words into my mouth that don't belong there and thoughts into my mind that don't belong there. -- KF

Reg

Posts: 112
Joined: Dec. 2008

 Quote (dvunkannon @ Oct. 18 2009,14:39) I was hoping to catch a glimpse of her amazing dialect of English being misspoken in real time, but alas her efforts seem to have fallen on the cutting room floor.Is there video of Dense-speak on the web?

Oh, yes.

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"Even though I am not a creationist by any reasonable definition ... the Cambrian explosion was doubtless the work of God in my view but I would say that of all creation." - Denyse O'Leary, Oct 17, 2009.

Bob O'H

Posts: 2184
Joined: Oct. 2005

Quote (Lou FCD @ Oct. 17 2009,21:11)
Quote (Richardthughes @ Oct. 17 2009,22:07)
Quote (keiths @ Oct. 17 2009,20:22)

 Quote (khan @ Oct. 17 2009,16:42) "Why is a raven like a writing desk?"

a) Lewis Carroll: Because it can produce a few notes, tho they are very flat; and it is nevar put with the wrong end in front!

b) Sam Loyd: Poe wrote on both.

Because neither are a yellow banana, apparently.

I think I love you.

:D

Well give him a PotW then.  Please.

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It is fun to dip into the various threads to watch cluelessness at work in the hands of the confident exponent. - Soapy Sam (so say we all)

Posts: 3094
Joined: May 2006

Quote (Bob O'H @ Oct. 18 2009,15:07)
Quote (Lou FCD @ Oct. 17 2009,21:11)
Quote (Richardthughes @ Oct. 17 2009,22:07)

Quote (keiths @ Oct. 17 2009,20:22)

 Quote (khan @ Oct. 17 2009,16:42) "Why is a raven like a writing desk?"

a) Lewis Carroll: Because it can produce a few notes, tho they are very flat; and it is nevar put with the wrong end in front!

b) Sam Loyd: Poe wrote on both.

Because neither are a yellow banana, apparently.

I think I love you.

:D

Well give him a PotW then.  Please.

Is that a banana in his pocket or is he just glad to see him?

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AtBC Award for Thoroughness in the Face of Creationism

Posts: 3094
Joined: May 2006

Thanks to keiths, raevmo, R.B. et al for the raven discussion. I'd read Hempel and Suppe, Kuhn, etc. on Philosophy in the Natural Sciences, back when "post-processualism" (PoMo) was all the rage in the social sciences and I was getting a better handle on the hypothetico-deductive view

But I really didn't know/recall the raven paradox. Wikipedia acturally had a  good page on it and the Bayesian touch was useful in looking at this twist on the problem of induction.

Using Google, I can see there's a lot else that I've missed, though, so it's off to Amazon for me. Damn you all for making me feel inadequately informed, thus forcing me to learn.

Bastards.

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AtBC Award for Thoroughness in the Face of Creationism

Reciprocating Bill

Posts: 4265
Joined: Oct. 2006

I'm much more accustomed to Fisherian hypothesis testing, relative to which this stuff is a bit alien. But it's interesting stuff.

At the pant-seat level (I told you excitement builds), the Raven paradox calls to mind my murder trial. I pled "not guilty," of course, but then the prosecution selected a woman randomly in Indianapolis and showed that she had an ironclad alibi. They concluded, rightly, that the likelihood that I committed the murder had increased thereby. They repeated this with a priest in Boston, a bureaucrat in Hong Kong, a senile nursing home resident of indeterminate gender in Toronto (still working as a journalist, they claimed) and a dozen others. I was convicted on the basis of this evidence of my guilt.

Thanks you guys.

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Myth: Something that never was true, and always will be.

"The truth will set you free. But not until it is finished with you."
- David Foster Wallace

"Hereâ€™s a clue. Snarky banalities are not a substitute for saying something intelligent. Write that down."
- Barry Arrington

Posts: 62
Joined: Dec. 2008

 Quote Does Jaynes really think that observing one hard diamond after another doesn't strengthen the hypothesis that all diamonds are hard?

I haven't really posted here in a while, but I cannot resist the opportunity to defend Jaynes' honor. The idea is that whether or not a particular instance of a generalization confirms the generalization depends on background knowledge. Good's two worlds example illustrates this, but here's a simpler example.

A chemist friend of mind is out in the field investigating whether all diamonds are hard. He agrees to inform me about the result of his investigations using the following code: if he discovers a diamond that is not hard, he will send me a hard diamond in the mail. I get a hard diamond from him in the mail, and (appropriately) take that as strong evidence against the generalization 'all diamonds are hard'. An instance of the generalization disconfirms the generalization.

The example might seem silly, but the point being made isn't. The degree of confirmation of a particular hypothesis by some evidence is always relative to a set of auxiliary hypotheses about the world. In Hempel's raven paradox, a black raven is more confirmatory than a yellow banana only given a number of auxiliary hypotheses, including the assumption that the sampling procedure is random and the base rate of ravens in the population of interest is smaller than the base rate of non-black objects. You can always find auxiliary hypotheses relative to which a yellow banana would actually be more confirmatory. You could even find auxiliaries relative to which a black raven would be disconfirmatory.

Maya

Posts: 702
Joined: Dec. 2007

 Quote (deadman_932 @ Oct. 18 2009,16:01) Damn you all for making me feel inadequately informed, thus forcing me to learn. Bastards.

Yeah, I never have that problem when reading UD.

OgreMkV

Posts: 3654
Joined: Oct. 2009

So if your chemist friend does not find a soft diamond, then you get nothing in the mail.  As long as you get nothing in the mail, you assume all diamonds are hard.

Now, I'm a not a logician, but it sounds like (in both these cases) that you're trying to find evidence of the positive case, when the only way to verify the positive case is to test every possible case.

I may be off the mark here, but that's why we don't prove positives in science, we can't test every conceivable situation.  However, if we test many of them, then we can begin to say confidently case is positive.

On the other hand, a negative case may totally negate the entire situation OR the negative case might be a unique case that is explainable by a slight modification (e.g. the albino raven, it has the gene for being black, but the gene is turned off).

So, is the 'paradox' a valid view of the world or metaphysical wanking?

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Ignored by those who can't provide evidence for their claims.

http://skepticink.com/smilodo....retreat

Reciprocating Bill

Posts: 4265
Joined: Oct. 2006

 Quote (dvunkannon @ Oct. 18 2009,15:42) It's the Cheetohs laced with Frolic Acid and MSG...

Back in the day we just called it "acid." Back in the day.

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Myth: Something that never was true, and always will be.

"The truth will set you free. But not until it is finished with you."
- David Foster Wallace

"Hereâ€™s a clue. Snarky banalities are not a substitute for saying something intelligent. Write that down."
- Barry Arrington

didymos

Posts: 1828
Joined: Mar. 2008

Quote (didymos @ Oct. 17 2009,22:24)
Quote (sparc @ Oct. 17 2009,21:41)

Quote (olegt @ Oct. 17 2009,08:10)
niwrad summarizes the discussion on the 2nd law of thermodynamics:

 Quote It seem to me an important questions is: Maxvell’s demon does violate or does not violate SLoT? Just here not all commenters agree. In my opinion Maxvell’s demon can be considered in two main senses: (1) a machine, an artificial system (one-way filter); (2) a thermodynamic metaphor of intelligence.(1) Maxvell’s demon as a machine. But there are many kinds of machines, and then we have again to distinguish.(A) Maxvell’s demon as a mechanical-thermo machine. In this case I agree with Monastyrski #71 when says “the decrease in entropy caused by the intelligent demon is more than compensated for by an increase in the demon’s own entropy”. SLoT is not violated.(B) Maxvell’s demon as a computer. If the Maxvell’s demon is a computer for which the Landauer’s principle is involved, according to givemeabreak #75, there is no increase of entropy because computation per se does not consume energy. SLoT is violated.(2) Maxvell’s demon as intelligence. But what is intelligence in the first place? This is one of the above fundamental and difficult questions. Without knowing what intelligence is how can we to speak about Maxvell’s demon, which is one of its symbols? Intelligence can be considered in two main senses: (A) physical intelligence; (B) pure intelligence or metaphysical intelligence.(A) If intelligence is a physical agent then energy is involved. SLoT is not violated.(B) If intelligence is a metaphysical entity then no energy is involved. SLoT is violated.
(...)

Could it be that niwraD comes from eastern Europe? Googling "Maxvell" and "dilema" resulted rather in Russian than in Italian sites.

eddited to correct tags.

Well, we may be getting some more data in the near future:

osteonectin pokes a tard:
 Quote niwrad @76:Are Italian keyboards different from American? Otherwise I would suggest that you try at least to spell Maxwell’s name correct while discrediting physics.

Well, new data has arrived.

 Quote osteonectin #82The idea of discrediting physics is very far from me and I don’t understand what caused such false impression to you. I have an high consideration of physics and think it (and any hard science when is not biased by prejudices) as friend of ID. Moreover I have an high consideration of many physicists and, specifically, for Maxwell my admiration cannot be higher (not only for his important contributions to thermodynamics).I challenge any one to find something in this post (and other posts of mine) that is offensive to physics. The fact itself that I decided to post here about thermodynamics and ID (considering the former allied of the latter) is a proof of that. Besides the fact itself that I consider Maxwell’s demon (which some consider an unimportant imaginary trick only) very seriously and say it can suggest interesting scientific and philosophical remarks is another proof of that.Sorry for my fault in spelling Maxwell’s name. Obviously it doesn’t depend by the keyboard (I always use US keyboards and don’t like IT ones because the former are more apt for scientific work in general while the latter for writing Italian prose only).

The Niwrad == Sermonti hypothesis may or may not have been strengthened by this depending on your philosophical leanings and the fact that no bananas were spotted in the thread.

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I wouldn't be bothered reading about the selfish gene because it has never been identified. -- Denyse O'Leary, professional moron
Again "how much". I don't think that's a good way to be quantitative.-- gpuccio

didymos

Posts: 1828
Joined: Mar. 2008

Clivebaby busts out the ever-effective "Nuh-uh" defense:
 Quote Seversky,“If someone has a radical new theory then, if they want us to believe it, they’d better have some evidence to back it up. We are under no obligation to believe something just on someone’s say-so. If that’s narrow and oppressive orthodoxy then so be it.”Hahaha. What evidence do you have to back this up? I am under no obligation on just your say-so. That is narrow, to be sure.

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I wouldn't be bothered reading about the selfish gene because it has never been identified. -- Denyse O'Leary, professional moron
Again "how much". I don't think that's a good way to be quantitative.-- gpuccio

Lou FCD

Posts: 5402
Joined: Jan. 2006

 Quote (didymos @ Oct. 18 2009,20:29) ...the fact that no bananas were spotted in the thread.

I contest this point. Near as I can tell, they're all bananas over there.

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Lou FCD is still in school, so we should only count him as a baby biologist. -carlsonjok -deprecated
I think I might love you. Don't tell Deadman -Wolfhound

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Richardthughes

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Quote (keiths @ Oct. 18 2009,13:26)
 Quote (Raevmo @ Oct. 17 2009,16:32) Of course, if N is large - and it is very large - observing a yellow banana has almost no effect at all on our posterior

Speak for yourself.  Richardthughes feels a tingling in his posterior when he sees a yellow banana, particularly if it is large.

YAY! Corn covered bananas!

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"Richardthughes, you magnificent bastard, I stand in awe of you..." : Arden Chatfield
"You magnificent bastard! " : Louis
"ATBC poster child", "I have to agree with Rich.." : DaveTard
"...it was Richardthughes making me lie in bed.." : Kristine

Richardthughes

Posts: 10762
Joined: Jan. 2006

POEPLES WHO ARE HOMOS AND LIBRULS AND ARE FIRST AGAINST THE WALL COME TEH DESIGN REVOLUTIONS:

1) TARDEN CHATTERBOX
2) HORSE BOTHERER
3) PLEBMAN
4) *New entry* KIEFS.
5) P.DIDDYMOUSE

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"Richardthughes, you magnificent bastard, I stand in awe of you..." : Arden Chatfield
"You magnificent bastard! " : Louis
"ATBC poster child", "I have to agree with Rich.." : DaveTard
"...it was Richardthughes making me lie in bed.." : Kristine

Ptaylor

Posts: 1033
Joined: Aug. 2006

DATCG:

 Quote Now, I’m not sure exactly how Mr. MacNeill will respond, but I suspect he’ll side with the very humble opinion(!) of Mr. Nakashima.Besides, I miss Allen.

Careful what you wish for, DATCG, as you might just get it, and it might include something like this:

 Quote Allen_MacNeill One of the truly fascinating aspects of following most of the discussions on this website is the general lack of understanding of even the most basic concepts of modern evolutionary theory and its history, much less a nuanced understanding of its fine points. For example, I find it quite telling that virtually none of the discussions I have read here have mentioned (much less discussed) Sergei Chetverikov, Ivan Pavlov, R. A. Fisher, J. B. S. Haldane, Sewall Wright, E. B. Ford, Theodosious Dobzhansky, G. Evelyn Hutchinson, George Gaylord Simpson, G. Ledyard Stebbins, Ernst Mayr, William D. Hamilton, Robert L. Trivers, George R. Price, Robert MacArthur, Edward O. Wilson, Lynn Margulis, Robert H. Whitaker, Carl Woese, Konrad Lorenz, Niko Tinbergen, Karl von Frisch, Erenhaus Eibl-Eibesfeld, or the Hardy-Weinberg Equilibrium Law, much less Otto Schindewolf, Richard Goldschmidt, or C. H. Waddington. Anyone familiar with the general outlines of evolutionary biology would instantly recognize most or all of these names, and would associate them with various important aspects of evolutionary biology as it has evolved over the past century. Not recognizing them or discussing their contributions to modern evolutionary biology is equivalent to not recognizing or discussing the contributions of Rutherford, Bohr, Schroedinger, Heisenberg, Michaelson & Morley, Einstein, Feinman, Gell-Mann, Weinberg, or Guth to modern physics.In other words, with the very rare exception of discussion threads like this one, most of what passes for “discussion” of evolutionary biology on this website is the pummeling of pitiful and ridiculous straw dogs and disputations over the fine points of Christian fundamentalist dogma, sometimes disguised (badly) as “science”.But such an assessment on my part might be somewhat uncharitable. Go ahead, prove me wrong: start a rational and nuanced discussion of the relevance of Fisher’s Fundamental Theorem of Natural Selection to current ideas of microevolution, or the relevance of Goldschmidt’s “hopeful monster” hypothesis to modern theories of evo-devo. This website might actually become interesting for a change, not as the intellectual equivalent of rubbernecking at a motor vehicle accident, but as a forum for intelligent discussion.

Ouch!

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We no longer say: â€śAnother day; another bad day for Darwinism.â€ť We now say: â€śAnother day since the time Darwinism was disproved.â€ť
-PaV, Uncommon Descent, 19 June 2016

DiEb

Posts: 271
Joined: May 2008

Has anyone listened to this? At 3' 22'', W. Dembski says about his paper  "Conservation of Information in Search: Measuring the Cost of Success":

 Quote We have some powerful results that follow up on this paper. This is a paper called "The Search for the Search", which is coming out... It should be out now, but there is some delay in the journal's publishing [???]. That will really nail things down.
(my own transcript)

I didn't have the stomach to listen to the whole thing, but I'm quite interested in this new paper.

BTW, Dembski says about the first paper:
 Quote It shows that Darwinian processes require information.

Um, not information as we know it, Jim.

keiths

Posts: 2041
Joined: Jan. 2006

 Quote (Reciprocating Bill @ Oct. 18 2009,15:16) At the pant-seat level (I told you excitement builds), the Raven paradox calls to mind my murder trial. I pled "not guilty," of course, but then the prosecution selected a woman randomly in Indianapolis and showed that she had an ironclad alibi. They concluded, rightly, that the likelihood that I committed the murder had increased thereby. They repeated this with a priest in Boston, a bureaucrat in Hong Kong, a senile nursing home resident of indeterminate gender in Toronto (still working as a journalist, they claimed) and a dozen others. I was convicted on the basis of this evidence of my guilt.

The reason you're uncomfortable in the seat of your pants, besides the fact that Richardthughes is groping you, is that the jury hasn't quantified the situation correctly.  You have been convicted unjustly.

If there are N people in the world, all of whom are potential suspects, then the prosecution would have to establish the innocence of N-1 people (that is, everyone else but you) with virtual certainty in order to convict you beyond a reasonable doubt.

Suppose for the sake of argument that there are 1 billion people in the world, and that the prosecution has established the absolute innocence of 999,999,998 of them. You and an impoverished Bangladeshi rice farmer are the only remaining suspects.  Even then the jury cannot convict you beyond a reasonable doubt, unless they have some strong reason to finger you over the farmer.

In reality, there is likely to be some such additional information. If the murder took place in Ohio, for example, the likelihood that it was committed by the impoverished Bangladeshi rice farmer is greatly diminished.  In that case the jury might decide to convict you.

But for the jury to convict you on the basis of the demonstrated innocence of only a dozen or so people would show that they haven't understood Hempel's paradox at all.

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And the set of natural numbers is also the set that starts at 0 and goes to the largest number.  -- Joe G

Please stop putting words into my mouth that don't belong there and thoughts into my mind that don't belong there. -- KF

Erasmus, FCD

Posts: 6349
Joined: June 2007

keiths aren't those the sorts of auxiliary hypotheses that MissingShadeOfBlue mentioned?

I'm not sure what that means to the "paradox" but i think part of the "paradox" is in the notion of a hypothesis as a singular sort of entity that stands alone to be falsified or supported.

all hypotheses are networks of statements supported by auxiliary statements

are there any other similar examples you can conceive where the true number or proportion of objects N in that universe is irrelevant?

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You're obviously illiterate as hell. Peach, bro.-FtK

Finding something hard to believe based on the evidence, is science.-JoeG

the odds of getting some loathsome taint are low-- Gordon E Mullings Manjack Heights Montserrat

I work on molecular systems with pathway charts and such.-Giggles

keiths

Posts: 2041
Joined: Jan. 2006

The last time you commented here you were working on your dissertation.  How did that go?

On the raven paradox, I agree that background assumptions are necessary.  But background assumptions are necessary in almost any situation, whether it involves induction or not. If we regard sightings of black ravens as supporting the hypothesis that all ravens are black, then we must assume that black ravens don't appear non-black, and vice-versa.  That seems pretty uncontroversial to me, and I don't think that any of the other necessary background assumptions are very controversial either.

 Quote In Hempel's raven paradox, a black raven is more confirmatory than a yellow banana only given a number of auxiliary hypotheses, including the assumption that the sampling procedure is random and the base rate of ravens in the population of interest is smaller than the base rate of non-black objects.

We haven't been debating which one is more confirmatory.  We've been debating whether a yellow banana is confirmatory at all.  Intuition says no, but logic (in my opinion) says yes.

Also, the assumption of unbiased random sampling is not necessary.  From an earlier comment of mine:
 Quote I should add that even if you do have information about the object, further observations can still be relevant.  If you know that a particular object is in the produce section of your local grocery store, but you haven't observed it yet, you will sensibly conclude that it is far more likely to be a banana than a raven, but there is still a finite probability that it is a raven, and a smaller but still finite probability that it is a non-black raven. Observing that it is, in fact, a banana therefore strengthens the hypothesis that all ravens are black, though by a very small amount.

If you spend your time hanging out in the produce section of grocery stores, as Richardthughes does, then you are likely to encounter bananas at a disproportionate rate over ravens. Nevertheless, despite this bias, encountering a yellow banana still supports the hypothesis that all ravens are black.

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And the set of natural numbers is also the set that starts at 0 and goes to the largest number.  -- Joe G

Please stop putting words into my mouth that don't belong there and thoughts into my mind that don't belong there. -- KF

keiths

Posts: 2041
Joined: Jan. 2006

 Quote (Erasmus @ FCD,Oct. 18 2009,20:56) are there any other similar examples you can conceive where the true number or proportion of objects N in that universe is irrelevant?

Perhaps it will help if I state my position as generally as possible:

Any potentially falsifying observation that turns out not to falsify the hypothesis has strengthened it, because there is now one less opportunity for it to be falsified.

As far as I can tell, the only necessary background assumptions are these:

1. Valid falsifying observations are possible in principle (though they won't be possible in practice if the hypothesis turns out to be true).
2. Nothing (including our own behavior) is systematically preventing such valid falsifying observations from taking place.

If those two conditions hold, then my statement holds. The number and distribution of objects in the universe is irrelevant to the truth of that statement.

It is important to stress that a hypothesis can be strengthened by non-falsifying observations even if it ultimately turns out to be untrue.  For example, suppose that all ravens on earth are black, but that there are millions of red ravens on the planet Beldax.  It's just that we don't know that these ravens -- or the planet Beldax itself -- exist.

The hypothesis "all ravens are black" is false in this case, but since we are stuck on earth, where we never make a falsifying observation, the hypothesis continues to be strengthened.

Ultimate truth is not at issue.  The question is this: Is it rational for us to increase our confidence in a hypothesis based on a particular non-falsifying observation?

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And the set of natural numbers is also the set that starts at 0 and goes to the largest number.  -- Joe G

Please stop putting words into my mouth that don't belong there and thoughts into my mind that don't belong there. -- KF

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