On 3/13/2012 6:02 PM, Ive wrote:
> Am 13.03.2012 19:52, schrieb Kevin Wampler:
>> This is just off of the top of my head, so it may not coincide with the
>> "accepted" answer to your question, if such a thing even exists. It's
>> also not necessarily very well thought out yet.
>>
> As it is fun, a good exercise and I do have an ill cat sleeping on my
> lap (and therefor cannot stand up and go to bed) out of my head and
> based on my understanding from Kant to Popper a few remarks - with a
> high possibility of wrong citations ;)

Excellent, as I haven't read any Popper this should be fun!  FWIW I 
don't necessarily agree 100% with all the arguments I'm making, but it's 
fun to see how well the viewpoint holds up, and I do rather like many 
aspects of it.

> David Hume's point was: laws are general, and therefore apply to an
> infinity of cases, so no finite number of observations increase their
> likelihood by any amount.


I don't follow this line of reasoning, so if it's important could you 
elaborate?  As I'm currently interpreting it it seems mathematically 
incorrect.  To pick a really simple example, a Gaussian probability 
distribution pertains to an "infinity of cases" in that it's defined 
over the continuum, but it's perfectly estimate a "most likely" 
distribution from a finite number of "observations".  This concern seems 
particularly relevant since I'm interpreting theories as defining 
probability distributions.


> But Emanuel Kant: In science, only observation and experiment may decide
> upon the acceptance or rejection of scientific statements, including
> laws and theories.

Hmmmm, not entirely sure I agree with this as stated, although knowing 
Kant his point was probably more subtle than what can be accurately 
conveyed in a sentence.  Basically, however, I think there's reason to 
prefer some theories over others on the merits of the theory itself.  If 
course in the end evidence must be king, but I think it's reasonable 
(actually mathematically unavoidable in the statistical interpretation 
I'm giving) that evidence sometimes has to find an uphill battle.  More 
on this when I talk about what I meant by "aesthetic criteria" later.


> AFAIK Kant did not *solve* this logical problem but Popper did *avoid*
> it by stating: a scientific theory is tentative only (that is, all laws
> are only conjectures, not true generalizations).

Sounds reasonable.


>> In addition, instead of talking about the merits of a theory by itself,
>> I'll switch to the view that, strictly speaking, evidence can only be
>> used to differentiate between different competing theories.
>
> I do not think that a competing theory is necessary but we often have an
> *established* theory versus a *risky* new one:

I limited my discussion to deciding between competing theories because 
it seemed "safer" as my spider-sense warned of potential technical 
difficulties of judging a theory by itself without at least implicit 
reference to competing possibilities.  You may be right though, but I 
wasn't sure how well I could mathematically justify my argument if I 
didn't limit it a bit.  Nevertheless, you can get pretty far with just 
the "competing theories" way of looking at things by defining an 
(infinite) class of "permissible theories".  In this case you can judge 
the theories in the class against each other in a rigorous way.

Also, you put quite a bit of weight on the phrase "risky", but I'm not 
entirely sure how you precisely define the risk of a theory.  I assume 
you mean that a theory is risky if it's (potentially) easy to prove 
wrong?  If so this pretty well fits within the statistical view.  In the 
statistical view a good theory should be "as specific as possible 
without becoming unlikely based on the evidence".  Does this match what 
you're saying?


>> So what of your question then? Fossil evidence can support a theory like
>> evolution in the case where evolution predicts a high likelihood of some
>> events (like your fish example) which competing theories don't ascribe
>> any particularly high probability to. For instance your basic
>> intelligent design argument would probably give finding such a fish the
>> same probability as finding countless other sorts of things which
>> weren't observed.
>
> Comparing "Intelligent Design" to "Evolution" is like comparing apples
> and eggs as the basic requirements for a scientific theory are not
> fulfilled by ID.

I certainly get you point here, but I think it's a strength of a 
philosophy of science if you can permit things like ID as theories of a 
sort and let them fail on their own terms, rather than just defining 
them as inadmissible.  I'd tend to view ID as theories which are 
exceptionally unlikely because they're vastly too general.  That is, ID 
can predict many many things (almost anything really) as possible, and 
as such necessarily give very low probabilities to things which have 
actually been observed, as well as a huge probability mass to things 
which have never been observed, making the theory itself exceptionally 
unlikely.

This is, of course, assuming you take the "honest ID" approach and 
actually try to consider what the predictions of such a theory might be. 
  If your view of ID is more of people taking the "this is true and I 
don't care what the predictions are" line of thought then yeah, that's 
not a theory.

> To state Popper again: "The point of the criterion of falsifiability is
> not to solve a problem of meaningfulness, or significance, nor truth,
> nor acceptability. It is the problem of demarcation between science and
> non-science."

It's a perfectly reasonable view, I'm just not yet convinced that it's 
an entirely necessary one.  If there's a good mathematical explanation 
why unfalsifiable theories are bad, so much the better.  No need to 
exclude them outright in that case.


>> As an aside, the fact that you mention a case where the evidence was
>> found *after* the theory was formulated is interesting. Strictly
>> speaking you'd think it wouldn't matter when the evidence was found,
>> just what that evidence was. Nevertheless, such examples are extremely
>> useful because they help assure us that we haven't "cheated" and created
>> a theory which is little more than rephrasing known evidence in a
>> different way, as it's impossible to bake predictions into a theory if
>> you don't know what these predictions should be. So I see this as more a
>> vital psychological tool rather than something directly related to the
>> theories themselves.
>>
> If you replace "psychological" with "philosophical" I might agree,
> partial... my sentence above (about Freud, Adler, Marx and Einstein)
> goes in this direction.

What is the critical aspect that makes "philosophical" more palatable 
than "psychological"?  Here's why I chose the term I did.  Imagine a 
"science algorithm" which you run on a computer, give some evidence, and 
which tried to construct a good theory to fit the evidence (such things 
have been made for very restricted settings).  In this case the 
mathematical analog of why you want new predictions is as 
cross-validation to prevent overfitting.  But since such an algorithm 
can be examined to be relatively "bias free" you can also counteract 
overfitting by defining good priors over your theories, in which case I 
couldn't come up with a totally solid argument why the cross-validation 
would be necessary (although it's still probably the simplest way to 
make sure nothing is going wrong).  Since humans aren't as 
well-understood or controlled as such an algorithm, the cross-validation 
serves a vital role for us, but it's sort of an aspect of the fact that 
we have a psychology which doesn't match that of such an algorithm.  I'm 
kind of abusing the term "psychology" here I suppose.


> Well, I for one would be interested in your "aesthetic criteria".

Ok, here goes.  I made the comment on aesthetic criteria for a rather 
mathematical reason.  That is, the viewpoint I've been arguing is a 
pretty Bayesian way of looking at science, and under such an 
interpretation if you want to determine the likelihood of a theory then 
you need not only evidence, but also a notion of the prior probability 
of a theory before any evidence is taken into account.

I used the term "aesthetic criteria" as a way to hint at the need for 
some way to judge this prior probability of a theory.  The most obvious 
specific choice for me falls in line exactly with Occam's razor -- all 
other things being equal we should prefer simple theories over complex 
ones.  This is why I mentioned information theory as possibly being a 
useful tool to formalize this notion, since it seems to be dealing in 
the same mathematical space, but I'm not sure if there's actually a 
solid mathematical argument to be made here or not.

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