On 3/13/2012 2:07 PM, Warp wrote:
> John VanSickle<evi### [at] kosherhotmailcom>  wrote:
>> The answer to your dilemma is that invalid arguments prove *nothing*.
>
>    I appreciate your input, but it's not what I was asking. I don't have
> a dilemma. I'm looking for a definition.

I would venture to say that relevance is the key criterion to consider 
when deciding whether given observation is evidence for or against a 
given proposition.  In fact, many of the logical fallacies that we are 
warned about (ad hominem, ad populum, etc.) in courses on formal logic 
are called Fallacies of Relevance.

For an observation to be valid or proper evidence for a given 
proposition (or against it), there must be a *necessary* relationship 
between the observation and the proposition.  If there is no such 
relationship, then we can conclude that the observation is not valid 
evidence for or against the proposition being considered; and really, to 
say that a given observation is not valid evidence is to say that it's 
not evidence at all.

Now for observation A and conclusion B, there are four possible 
relationships between them, each of which can be stated in two different 
ways which assert the same thing:

"If A, then B," or, "If ~B, then ~A." (A & ~B = false)
"If A, then ~B," or, "If B, then ~A." (A & B = false)
"If ~A, then B," or, "If ~B, then A." (~A & ~B = false)
"If ~A, then ~B," or, "If B, then A." (~A & B = false)

If we cannot affirm any of these four possible relationships, then A and 
B are irrelevant to each other, and A is not evidence for or against B. 
  But if we can show that at least one of these four conditions is true, 
then A is valid evidence on the question of B.

This probably sounds a bit tautological, but that's the best I can do at 
the moment.

Regards,
John

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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 ;)

> Anyway, It seems that something related to your question is the
> oft-mentioned quip that evidence can only disprove a
> theory, but never prove it.

Popper did say something like: "The purpose of evidence from repeated 
observations is not to confirm already-established theories, but to 
attempt to falsify them and thereby test them."
This is *a bit* different and better to understand when when we look at 
the scientific method and consider the following points:
a) It is easy to obtain confirmations of a theory if we look for them ;)
b) Confirmations should really only count if they are the result of 
*risky* predictions.
c) Every *good* scientific theory is a prohibition: it forbids certain 
things from happening. The more it forbids, the better it is.
d) A non-falsifiable theory is not scientific.
e) -> Every genuine test of a theory is an attempt to falsify it.


> In what sense can it be said that we have
> "evidence for" anything then? Obviously there must be some meaning to
> the phrase, since otherwise a theory which says "anything is possible"
> would be regarded as an ideal theory, since it's obviously never been
> falsified.

see c) above.

> The most obvious answer I can see is to consider the question from a
> statistical perspective rather than a perspective of pure deductive
> logic. In this viewpoint the predictions yielded by a theory would be
> interpreted as a probability distribution over (a subset of) observable
> events. The goal of a good theory should then be to make predictions
> which match the actual observed probabilities (and possibly satisfy some
> aesthetic criteria).

I have no idea what "aesthetic criteria" could have meaning here but 
anyway...
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.
But Emanuel Kant: In science, only observation and experiment may decide 
upon the acceptance or rejection of scientific statements, including 
laws and theories.
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).


> 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:
Geocentric -> Copernican
Where the risky new one does not necessarily falsify the old one, it may 
only limit the scale where it is valid:
Newton -> Einstein


> In this view
> there are, colloquially speaking, *two* ways in which evidence might
> support theory A over theory B. Firstly, as in the logical case, you
> could observe something which theory B predicts is very unlikely or
> impossible, but which theory A give higher probability to. Secondly, you
> might find that theory B predicts more events than are actually
> observed, whereas theory A gives low probability to unobserved events.

In case of competing theories Occam's razor comes in quite handy.


> 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.
This is the basic misunderstanding when creationists call evolution 
*just* a theory. Yes, it is just a theory but this is its strength.
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."
And to leave this sad field of ID and make it maybe even a bit more 
provocative ;)
"The apparent strength of Freudian and Adlerian psychology, and Marx's 
theory of history, that they can explain anything is actually a weakness 
in contrast with Einstein's theory that took risks."
I'm not sure if this has actually been said by Popper but it very well 
might have.


> Of course strictly speaking we don't exactly have evidence "for"
> evolution (or whatever theory you like), just for evolution in favor of
> our ideas for currently competing theories. If some future theory makes
> even more precise and accurate predictions than evolution, then it's
> probable that this theory would also give a high probability to your
> fish example and thus the fossil wouldn't give evidence to evolution in
> favor of this hypothetical new theory.
>
This is exactly how the scientific method works.


> 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.
Also note the interesting fact that contemporary "multi-verse", 
"gravity-quantum-loop" and "string"-theory also fall through the sieve 
when we look at them with Popper's theory about scientific theories in mind.
And dark matter and dark energy are at least very borderline. But, to 
me, this makes science currently quite thrilling ;)


> Does this make sense?
I think so even if that does not mean that I fully agree ;)

> I ask genuinely since I haven't really though much
> about it. I also suspect that you could draw some more rigorous ideas
> about the "aesthetic criteria" a theory should preferably satisfy by
> looking at information theory, but I don't care to give it a go at the
> moment.
Well, I for one would be interested in your "aesthetic criteria".


-Ive

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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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On 3/13/2012 4:15 AM, John VanSickle wrote:
> However, faulty arguments do give their conclusions a bad reputation.
> Somewhere a preacher is citing Piltdown Man as proof that evolution is
> false, and somewhere an atheist is claiming that the Shroud of Turin
> disproves all Biblical claims.
Well, it certainly, by itself, fails to prove anything. However, when 
added to the fact that nothing older than a certain point was written on 
the subject, that nearly all elements of the story are repeated in older 
theologies, that dates any places only superficially, or do not at all, 
add up, etc., the preponderance of evidence suggests a very low 
probability of "most" of it being true, and a high probability of many 
parts being completely wrong. The flaw is not that they are used to 
support one or the other proposition, its that one is a single point 
refutation of a vast collection of data, all of which point one 
direction, while the other is likely actually being presented as an 
exemplar of the sort of flawed evidence that underlies the whole premise 
being defending with it. Its unlikely anyone is actually presenting it 
at **the** single case of such error, instead of an example, and if they 
where, one would be entirely justified in claiming it was neither a 
valid argument, by itself.

Erroneous conclusions are, in this regard, a result of cherry picking 
data, while ignoring the larger picture. It is possible for many 
explanations to exist, some may even be useful, but very few are 
*plausible*, when taking in context of the whole. Skepticism is about 
getting as close to the right one as possible, given as much of the data 
as possible, and with the only presupposition being that the data itself 
may be incomplete, and could change.

This would be the "valid and proper". Where as, taking the first 
explanation, would be "invalid", if evidence suggested it could be 
false, and its certainly not "proper" if reached via that method, or 
through the exclusion of contrary data. Its possible to be a skeptic and 
misinformed. Its not possible to be a skeptic and refuse to be informed 
at all.

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On 3/13/2012 6:02 PM, Ive wrote:
> 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 would say that the flaw in this assumption is that there is an 
infinite number of cases. Often there is in fact a finite number of 
possible outcomes, once you apply existing laws. While one could argue 
that some sort of variation may lie "outside" those laws... unless you 
want to deny all observation, at some point the statistical odds *must* 
narrow. You get a similar dichotomy of principles when talking about how 
people think, with some arguing that there is, somehow, an infinite 
number of possibilities, and other people pointing out that the flaws in 
the human senses, mind, etc., all pretty much mean that no one is 
***anything close*** to as unique, or unpredictable, as they presume 
themselves to be. In reality the former is likely illusion, because a) 
there is no plausible mechanism, which doesn't badly misunderstand a lot 
of things to get there, for people not being state machines, of a sort, 
and b) its only possible in control conditions, with known variables, to 
predict results, over a short span, because even in a state machine, if 
you don't know the starting state, the more complex the machine, the 
less your odds are of predicting its behavior over a longer span.

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On 3/13/2012 8:15 PM, Kevin Wampler wrote:
> 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.
However, its not being called "inadmissible", but rather, "contrary to 
existing evidence, which already falsifies what few predictions it 
bothers to make." Its their side claiming that its being rejected out of 
hand, without proper review. But, its been reviewed. By itself it 
doesn't predict anything useful, and its "sub-predictions", which have 
been claimed that they could show it to be possible, all contradict 
existing facts, even to the point where when they are not trying to find 
some new "irreducibly complex" thing to harp on, they are claiming that 
the last one they tried wasn't shown to be reducible already.

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On 3/13/2012 11:52, Kevin Wampler wrote:
> Anyway, It seems that...

That's exactly what I was going to say. Thanks! ;-)

-- 
Darren New, San Diego CA, USA (PST)
   People tell me I am the counter-example.

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Am 14.03.2012 04:15, schrieb Kevin Wampler:

>> 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?

With pleasure. I already knew that condensing Hume into one sentence 
would fail but as I do definitely include him in my personal list of the 
10 most influential philosophers of all time I thought it would be a 
good idea to start with him.

Often Hume is mentioned as an empiricist (I just skimmed through the 
wikipedia article to look up his year of birth - 1711) while I would see 
his important characterization as the first *modern* skeptic and also 
one of the most radical skeptics ever. In his work "A Treatise of Human 
Nature" (quite easy to read BTW, especially given the time it was 
written, but maybe I should mention one should be in a good mood, I know 
people who do find Hume's view of the world extremely depressing) he 
demolishes all believe-systems, i.e. everything from fairy-tales to 
religion, and as he had a good run, he did not stop there and did 
deconstruct deductive and empirical methods in natural sciences as well.

The only things that do remain for Hume are algebra, geometry and a 
distant echo of humanism.

As an (absolutely incomplete) introduction what a friend of mine did 
call "Hume versus Holmes" (Doyle's Sherlock he did mean ;)):
Given a series of observations that a lady walks her dog by the market 
at 8am on Monday, it seems valid to infer that next Monday she will do 
the same, or that, in general, the lady walks her dog by the market 
every Monday.
That next Monday the lady walks by the market merely adds to the series 
of observations, it does not prove she will walk by the market every Monday.
First it is not certain, regardless of the number of observations, that 
the lady always walks by the market at 8am on Monday.
Second Hume argued that we cannot claim it is "more probable", since 
this still requires the assumption that the past predicts the future. 
Third, the observations themselves do not establish the validity of 
inductive reasoning, except inductively.

Hume was a strong influence to Kant who said something along the line: 
it was Hume who did awake me from my dogmatic slumber. Kant always did 
see it as a problem that he was not able to formulate his theories about 
science without clashing with Hume. While Kant thinks that e.g. the 
concept of space and time is given to us "a priori" for Hume space and 
time are just the *result* of two successive observations.
So Albert Einstein himself did mention David Hume as a source of 
inspiration when formulating the "Special Theory of Relativity".



>> 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,

And you are completely right, my fault, I did forget to write down what 
I was thinking and the result is actually the opposite of what it should 
be: the logical problem of induction that did lead to Poppers 
"solution". It goes like this:
a) Hume's statement from above: laws are general, ... or better Hume's 
reasoning about induction in general.
b) Sometimes science proposes general laws at the drop of a hat, after 
even single observations.
c) Empiricism: In science, only observation and experiment may decide 
upon the acceptance or rejection of scientific statements, including
laws and theories.

But Emanuel Kant did *reject* point c in favor of a and b.
And for good reason especially from todays view: After all, astrology 
(or Adler's psychology) can produce tons of confirmation - as long as we 
limit the view to pure empiricism without Popper's "call for predictions".

Note that both Hume and Kant are always talking about natural sciences 
but not mathematics.


> 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?

Exactly. I like the phrase "risky" for that in the same way as I 
actually do like and accept your phrase "aesthetic criteria".


-Ive

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Am 14.03.2012 05:27, schrieb Patrick Elliott:
> On 3/13/2012 6:02 PM, Ive wrote:
>> 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 would say that the flaw in this assumption is that there is an
> infinite number of cases. Often there is in fact a finite number of
> possible outcomes, once you apply existing laws. While one could argue
> that some sort of variation may lie "outside" those laws... unless you
> want to deny all observation, at some point the statistical odds *must*
> narrow. You get a similar dichotomy of principles when talking about how
> people think, with some arguing that there is, somehow, an infinite
> number of possibilities, and other people pointing out that the flaws in
> the human senses, mind, etc., all pretty much mean that no one is
> ***anything close*** to as unique, or unpredictable, as they presume
> themselves to be. In reality the former is likely illusion, because a)
> there is no plausible mechanism, which doesn't badly misunderstand a lot
> of things to get there, for people not being state machines, of a sort,
> and b) its only possible in control conditions, with known variables, to
> predict results, over a short span, because even in a state machine, if
> you don't know the starting state, the more complex the machine, the
> less your odds are of predicting its behavior over a longer span.

See my latest response to Kevin where I've written a bit more about Hume.

-Ive

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Thanks for the interesting comments!

> Often Hume is mentioned as an empiricist (I just skimmed through the
> wikipedia article to look up his year of birth - 1711) while I would see
> his important characterization as the first *modern* skeptic and also
> one of the most radical skeptics ever. In his work "A Treatise of Human
> Nature"

I think I read this a long while ago.  At the time I remember being 
pretty underwhelmed by it, but perhaps I was just young and didn't fully 
appreciate it, so I'll put it on the queue for a reread.


> As an (absolutely incomplete) introduction what a friend of mine did
> call "Hume versus Holmes" (Doyle's Sherlock he did mean ;)):
> Given a series of observations that a lady walks her dog by the market
> at 8am on Monday, it seems valid to infer that next Monday she will do
> the same, or that, in general, the lady walks her dog by the market
> every Monday.
> That next Monday the lady walks by the market merely adds to the series
> of observations, it does not prove she will walk by the market every
> Monday.
> First it is not certain, regardless of the number of observations, that
> the lady always walks by the market at 8am on Monday.
> Second Hume argued that we cannot claim it is "more probable", since
> this still requires the assumption that the past predicts the future.
> Third, the observations themselves do not establish the validity of
> inductive reasoning, except inductively.

Not yet having reread Hume's texts on the matter myself, I have a few 
more questions/comments.  I think it's pretty obvious that you can't 
inductively deduce absolute truths, but only contingent theories. 
However, he also seems to reject inductively supporting inductive 
reasoning as "probably correct" as a case of circular reasoning.  Is 
there some reason he's ok with deductive reasoning (which surely cannot 
be supported in any less of a circular manner) but sees a problem with 
inductive reasoning?

Furthermore, I'm not entirely sure what Hume sees as the distinction 
between inductive and deductive reasoning.  The generalization of 
probable theories from finite examples is pretty well explained in a 
rigorous way by the theory of probability, and it's not like there's a 
different type of reasoning used here than in other parts of math like 
algebra, geometry, etc.  Maybe you could put forth a sort of "no free 
lunch" style argument to arrive at the same conclusion Hume does, but I 
don't get the impression that's the line of reasoning he's using.

Still, interesting stuff, I'll take a deeper look sometime since I get 
the impression that I should really reread the Hume myself if I'm going 
to ask detailed questions about it.

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