53564

神经网络昆斯林的新闻组分类2006

> does not support a disbelief. 

The hypotheses don't have to be falsifiable, and indeed in my `model',
the theism isn't falsifiable.

> [...]

> I used the phrase "SHOULD obverse". Given any specific 'x' theism 
> does not make the prediction "P(x | Ht) > 0". That's why I used the 
> word "should" - theism makes no predictions about any specific event.
> I can only say "I believe" that God did such and such after such
> and such happens, or "I believe God will" do such and such. But
> for any given 'x' I can never, a priori, say P(x | Ht) > 0. I can
> not even say this for the set of all 'x' or some 'x'. This is what 
> don't like about your use of probability. We also have no way of
> assigning these probabilities - I hold science to positivistic
> criteria - if someone cannot tell me how to measure, even in principle,
> P(x | H), then probability is not applicable to hypothesis H. Such
> is the case when H = Ht (theistic) and Ha (atheistic). For example,
> P(x | Ha) = P(x & Ha)/P(Ha). What is P(Ha)?!? How do I measure it? 

You don't have to. We don't need, in the above analogy, to know *any*
prior probabilities to deduce that the updating multiplier for the
fair-coin hypothesis is less than unity, and that the corresponding
multiplier for the two-headed coin hypothesis is greater than unity.
You don't need to know the initial values of the running estimates
either. It's clear that after a large number of observations, P(fair-coin)
approaches zero and P(two-headed-coin) approaches unity.

All you need to know is whether P(x | Ha) is larger than P(x | Ht) for
observed x, and this follows from the assumptions that there are certain
events rendered *possible* (not necessary) under Ht which are not possible
under Ha, and all else is equal.

> Baysian statistics relies upon a series of observations. But
> what if the hypothesis isn't amenable to observation? And even for
> statements that are amenable to observation, some observations are
> not relevant -- a sequence of observations must be chosen with care.
> I'm curious to know what types of observations x[1],x[2],... you have 
> in mind concerning theism and atheism.

Any observations you like; it really doesn't matter, nor affect the
reasoning, provided that there are some possible observations which
would count as "appearances of god/s". Examples of this might be
a demonstration of the efficacy of prayer, or of the veracity of
revelation.

>> But any statement about P(x | H) for general x still counts as a 
>> prediction of H. If the theism in question, Ht, says that prayer may 
>> be answered, or that miracles may happen (see my interpretation, quoted 
>> again above, of what `God exists' means), then this is a prediction, 
>> P(x | Ht) > 0 for such x. It's what distinguishes it from the atheist 
>> hypothesis Ha, which predicts that this stuff does not happen, P(x | Ha)
>> = 0 for such x.

> Theism does not make the claim that "P(x | Ht) > 0 for such x".
> Or I should say that my "theism" doesn't. Maybe I was too quick to
> say we had a common language. You said that by the existence of God 
> you "mean the notion that the deity described by the Bible and by 
> Christians *does* interact with the universe as claimed by those agents".
> I agreed with this. However, I must be careful here. I BELIEVE
> this - I'm not making any claims. Maybe I should have changed *does*
> to *can* - there is an important shift of emphasis. But any way,
> since I "only" have a belief, I cannot conclude "P(x | Ht) > 0 for 
> such x".

OK, we'll downgrade "*does* interact" to "*may* interact", which would
actually be better since "does interact" implies a falsifiability which
we both agree is misplaced.

> I don't think my theism makes "predictions". Maybe I'm not
> understanding what you mean by "prediction" - could you explain what
> you mean by this word?

I'll explain, but bear in mind that this isn't central; all I require of
a theism is that it *not* make the prediction "Appearances of god/s will
never happen", as does atheism. (Before somebody points out that quantum
mechanics doesn't make this prediction either, the difference is that
QM and atheism do not form a partition.)

Predictions include such statements as "Prayer is efficacious" (implying
"If you do the stats, you will find that Prayer is efficacious"), or "Prayer
is *not* efficacious", or "Verily I say unto you, This generation shall not
pass, till all these things be fulfilled." I don't think we have any problems
of misunderstanding here.

>> Persistent observation of this stuff not happening, *consistent* with
>> Ht though it may be, is *more* consistent with Ha, as explained in the
>> Bayesian stats post. 
>>
>> Even if Ht ("God exists") is unfalsifiable, that's
>> no problem for my argument, other than that you have to let the number 
>> of observations go to infinity to falsify it asymptotically. 

> BTW, I do not consider an argument that requires an infinite number of 
> observations as valid - or rather that part of the argument is not valid. 
> We, as existing humans, can never make an infinite number of measurments 
> and any conclusion that reilies on this I don't accept as valid.

That's fine; I don't claim that theism is false, merely that the [finite
number of] observations available to me so far suggest that it is, and
that as I continue to observe, the suggestion looks better and better.

> [Renormalization stuff deleted]

>> In the Bayesian stats post, I assumed that theism was indeed unfalsifiable
>> in a finite number of observations. Here's the relevant quote:
>> 
>> $ The important assumption is that there are *some* observations which 
>> $ are compatible with the theist hypothesis and not with the atheist 
>> $ hypothesis, and thus would falsify atheism; these are what I called 
>> $`appearances of god/s', but this need not be taken too literally. Any 
>> $ observation which requires for its explanation that one or more gods 
>> $ exist will count. All other observations are assumed to be compatible 
>> $ with both hypotheses. This leaves theism as unfalsifiable, and atheism 
>> $ as falsifiable in a single observation only by such `appearances of 
>> $ god/s'.

> Here is my problem with this. For something to be falsifiable it
> must make the prediction that 'x' should not be seen. If 'x' is 
> seen then the hypothesis has been falsified. Now, atheism is a word 
> in oposition to something - theism. A theism aserts a  belief and an 
> atheism aserts a disbelief. So there are certain atheisms that are 
> certainly falsifiable - just as there are certain theisms that are 
> falsifable (e.g. if my theism asserts the world is only 6,000 years 
> old and that God does not decieve then this has been falsified). However, 
> the atheism that is in oposition to an unfalsifiable theism is also 
> unfalsifiable. I could be wrong on this statment - [...contd]

I think you are; an "appearance of god/s" is sufficient to falsify
atheism, whereas in general the corresponding theism is unfalsifiable.

> I'll think more about it. Until then, here is a general question.
> Suppse X were unfalsifiable. Is not(X) also unfalsifiable? 

No: by way of a counterexample, let X = "the coin is fair", or more
accurately (so that not(X) makes sense) "the two sides of the coin are
different". This is unfalsifiable by tossing the coin; even a string of
heads is consistent with a fair coin, and you have to go to an infinite
number of tosses to falsify X in the limit. Its converse is falsifiable,
and is falsified when at least one head and at least one tail have appeared.

>>> This is partly what's wrong with you Baysian argument - which 
>>> requires observations x[1] ... x[n] to be made. There are simply 
>>> no such observations that have a truth value in relation to the 
>>> statement "God exists". Now, by use of your symmetry argument, I 
>>> can understand why someone would say "Since the statement 
>>> 'God does not exist'
>>   ~~~~~~~~~~~~~~~~~~
>>> makes no predictions I will choose not to believe it." But none
>>> the less this would be founded on a type of faith - or if you don't
>>> like the word faith insert "belief for which there is no falsifiable
>>> evidence" instead. 

>> I'll assume you meant `God exists' up there at the highlight. But by our
>> agreed definition of "exists", the statement makes predictions as I said
>> above, although it isn't falsifiable in a finite number of observations.

> Actually, I mean 'God does not exist' makes no predictions.

Oops. Sorry. Mea culpa.

> The truth of this statment actually depends upon which god you are
> refering to. But I can think of some conceptions of God for which 
> it is true. But once again I'm open to the posibility that I could
> be wrong. So give me some examples of predictions of the statment
> "God does not exist". Here is one that I can think of. If true, then 
> there would be no healing or miricles. But this can in principle never 
> be determined one way or the other. There are cases in which people 
> seem to recover and are healed without the help of a doctor and for no  
> known reason. These situations do in fact happen. They are consistent
> with a theistic hypothesis, but IN NO WAY support such a hypothesis.

We agree here.

> They are not inconsistent with an atheistic hypothesis. I can't
> think of one "prediction" from 'God does not exist' that isn't of
> this type. But I might be missing something. 

"The Rapture will not happen on October 28 1992." Said Rapture would have
falsified atheism to my satisfaction had it happened, although its failure
to happen does not, of course, falsify any theisms other than those which
specifically predicted it.

"No phenomenon which requires the existence of one or more gods for its
explanation will ever be observed." That about sums the whole thing up.

> bob singleton
> [e-mail]

Cheers

Simon
-- 
Simon Clippingdale                [e-mail]
Department of Computer Science    Tel [phone]
University of Warwick             FAX [phone]
Coventry CV4 7AL, U.K.