> >When you say "absence of evidence can never be evidence of absence", I
> >think the key is what exactly is meant by "absence of evidence". In
> >its purest sense: absence of evidence for or against a proposition,
> >you are completely right.
>
> According to the philosophy of science, you can only get one of three
> results whenever you test a concept: positive evidence that verifies the
> concept, positive evidence that refutes the concept, or negative evidence,
> which is generally defined as a lack of positive evidence; the implication
> being that if you get negative evidence you cannot say whether the concept
> has been verified or refuted. So the "purest" sense of what is meant by
> absence of evidence -- namely that it constitutes negative evidence as
> defined by the philosophy of science -- is the correct way to look at this
> problem. Any other way tends to be subjective.
Neither have I extensively studied the philosophy of science, so bear
with me (I am familiar with the mathematics of logic however).
as I think you suggest it can't be used as evidence --- yes? Anyway,
moving right along...
I think you are effectively agreeing with what I said, just that our
language is slightly different --- I talk about "proposition", you
talk about "concept". I talk about evidence "for" or "against", you
talk about evidence "verifying" or "refuting".
> >Here "absence of evidence" means "a search has failed to produce
> >any pre-Cambrian fossils".
>
> No, that is not what it means; as I outlined it above, it would
> properly mean that "a search of Precambrian sedimentary layers has
> so far failed to produce any positive evidence that either verifies
> or refutes the existence of Cambrian ancestors".
Well, let us stick to the earlier definition of "absence of evidence"
outlined above --- in which case I am arguing that, in principle, a
non-complete search of Precambrian sedimentary layers could furnish
positive evidence that refutes the existence of Cambrian ancestors.
> The only way it could mean how you wish to define it is if every
> Precambrian sedimentary rock layer has been thoroughly and
> exhaustively searched in a systematic manner.
I am arguing that it is not necessary for the search to be exhaustive,
or even close to exhaustive. I presented the marble scenario to
illustrate this, which I will further comment on below.
> Since that has not been done, since that has not even been begun, it
> is rather arrogant to believe that the extremely limited and poor
> results so far obtained can serve as evidence that tends to refute
> the concept in question.
Current results may be "limited and poor" --- I'll take your word on
that for now --- however your "appeal from ignorance" criticism
suggests that you would still reject "absence of evidence" arguments
with much more substantial results. I am arguing in principle. (It
could possibly be that the current search is so small, that although
the lack of ancestors furnishes positive evidence, it is extremely
weak evidence.)
> >As I will expand upon below, in this sense, "absence of evidence"
> >can produce evidence of absence.
>
> But since your sense of what "absence of evidence" means is
> incorrect, your conclusion that it can constitute "evidence of
> absence" is also incorrect.
I gladly accept, that using the definition of "absence of evidence"
we've agreed upon above, absence of evidence does not constitute
evidence of absence. Under this definition, my argument is then that
"absence of Precambrian fossils" can, in principle, be positive
evidence --- thus this is not an example of "appeal from ignorance"
--- which is effectively what I argued.
> There is no such thing as a truly random search in practical terms;
> as such, it is theoretically possible to predict which holes will be
> searched. There is in fact an entire field of probability
> statistics that studies exactly this problem. I understand very
> little about it, but from what I've read the statisticians are
> convinced that any quasi-random search pattern can be predicted if
> you know what the underlying order of the pattern is. Some of these
> theories are being used to create and break new mathematical codes.
This is a bit of a red herring. It is true that there are
difficulties in generating truly random sequences, especially on
computers. But firstly it is possible to generate random sequences
without these problems. Secondly, quasi-random sequences are still
very useful and usable --- relied upon every day --- providing they
are used in a manner which steers clear of their weaknesses.
For the purposes of the marble illustration, it is easiest to assume a
random search. If you prefer, you can assume a random distribution of
any marbles instead, but it is really of no consequence. In the case
of fossils, the important thing is that you don't spend your time
searching in places where fossil distribution processes would be
unlikely to leave specimens.
> My point is that since no search can be truly random, you cannot say
> after searching only 200,000 holes what is really going on. Had you
> instead specified a random distribution of marbles coupled with a
> systematic search, however, then your claim after 200,000 holes
> would be on firmer ground, as I admitted in my last post.
The search could be truly random, and for the purposes of the
illustration it is perfectly reasonable to assume it to be so. If you
want this analogy to be even closer to the "fossil search scenario",
we simply need to assume that the marble distribution process and the
hole searching process be independent (in the statistical sense).
But let me put to you my original point again. Do you accept, that if
the search for marbles was truly random, that "examining 200,000 holes
without finding a marble" would be good evidence of there being at
most, a small number of marbles?
> >Suppose there were in fact 100 marbles. The chance of not finding one
> >after 200,000 searches, can be calculated. It is:
> >
> > 999,900 999,899 999,898 799,901
> >---------.---------.---------. ... .---------
> >1,000,000 999,999 999,998 800,001
> >
> >which is a _very_ small number --- we're talking around 1/100,000,000.
> >
> >In fact, further calculations would show that if no marble were found
> >after 200,000 searches, we could have 99% statistical confidence that
> >there were fewer than 20 marbles.
> >
>
> Those calculations are based on the assumptions that the marbles were
> randomly distributed and that the search was orderly and systematic, which
> is the simplest case.
Well actually, it was based on the assumption that the search was
random --- but your assumption will yield the same probabilities.
> I cannot reproduce the mathematics (I barely understood them when I
> first encountered them) but I know that if you assume a non-random
> distribution coupled with a random search, you get a very different
> result, one in which the chance of finding no marble after 200,000
> searches is much higher.
The only think I can think you might be referring to, is the situation
where effectively, multiple marbles per hole are allowed --- which is
not the scenario I was considering. Given the assumption of "maximum
of one marble per hole", my calculations are perfectly correct.
> >> >It is not however enough evidence to conclude that there are no
> >> >marbles at all. If however you examined 950,000 of the holes and
> >> >still there were no marbles found, it would be strong evidence that
> >> >are no marbles.
> >
> > "at least one marble present" means "one or more than one" marbles
> > present.
>
> It's still too vague a statement to make a simple straight-forward
> testable hypothesis; the null hypothesis would be too complex and
> virtually meaningless, rendering any result that was not an exact
> verification of the hypothesis too ambiguous to interpret.
It isn't a vague statement --- it is very precise. There are two
hypotheses --- one is that there is "one or more than one marble", the
other is that there are "no marbles". A random search of 950,000
holes without success would lead you to reject the former in favour of
the latter.
> >It is _possible_, after searching 999,999 holes without success, that
> >the last hole contained the marble, but _very_ _very_ improbable ---
> >certainly not 50/50! A 999,999 hole search would not give you
> >_absolute_ certainty of no marbles, but it would give you extremely
> >high _statistical_confidence_ of no marbles.
>
> That would only be true at the beginning of your search, and even
> then it would not be strictly true. At the beginning of your search
> (# of holes = n = 1,000,000) the chance that any **specific** hole
> had that one marble
What "one marble"? We don't know _a_priori_ how many marbles there are.
> would be so low as to be negligible (specifically 0.5^1,000,000;
> which my calculator could not solve)
What you have calculated here is the _a_priori_ probability of a
specific hole containing a marble and the other holes being empty.
This has nothing to do with the _a_posteriori_ probability of there
being a marble in the last hole, given that the previous search of
999,999 holes failed to discover a marble --- which is what I was
referring to above.
> but the chance that **any** random, unspecified hole would have the
> marble would be 50/50 (or 0.5^1). As you eliminated holes that had
> no marble (n < 1,000,000) the chance that a **specific** hole would
> have the marble would increase (0.5^800,000; 0.5^600,000;
> 0.5^400,000; 0.5^200,000; and so on), until finally when you had
> eliminated every hole but the last one (n = 1) you would reach the
> maximum probability of 50/50 (or 0.5^1).
I'm afraid this is faulty reasoning. Let me explain the difference
between _a_priori_ and _a_posteriori_ probabilities, just in case you
are not aware of the terms. _a_priori_ probabilities, are those able
to be determined by the very nature and symmetries of the scenario ---
these are the probabilities before any other information like
experimental data, is taken into account. The calculation that the
probability of "rolling a 3 on a six sided die" is 1/6, is an
_a_priori_ calculation --- based on the symmetry of the six sides of
the die. _a_posteriori_ calculations are those based on "evidence
that comes in after", ie calculations which make use of any
experimental data you obtain. Suppose you took your die and after
rolling it 1000 times, found that it rolled a 3, 946 times. You would
have strong evidence for suspecting it was a weighted die. Your
_a_posteriori_ estimate of the probability of "rolling a 3" would be
946/1000 --- considerably different from 1/6.
So back to your calculation. It is true that _a_priori_, the
probability of the last hole containing a marble is 1/2 --- but this
is a probability that doesn't take into account any experimental data.
When you take into account the fact that searching the last 999,999
holes failed to find any marble, the probability dramatically drops to
almost 0.
> >Well this "marbles scenario" is analogous to the "missing fossil
> >scenario", though the latter is obviously not so neat. There are a
> >finite number of potential fossil locations on earth (though we may
> >not know where they all are). Theoretically we could break this up
> >into small regions --- our "holes". Finding a pre-Cambrian fossil in
> >a region is equivalent to finding a marble. Clearly there are lots of
> >complications, and probability calculations are much more difficult
> >than in the marble scenario, but the essential idea is still there.
>
> And when examined correctly the marble example tells us that we should
> expect to find empty holes; i.e., regions that are devoid of fossils. As
> such, our current lack of success based on a so-far limited search cannot
> definitively tell us anything about our overall liklihood of success.
How limited or otherwise the search has been I do not know --- others
seem to disagree with this assessment. But my point is that this
where the argument should centre: how significant is the lack of
Precambrian fossils. You seemed to be arguing that no matter how
extensive a search for Precambrian fossils was, a failure to find any
would not be evidence of lack --- on the grounds that this would
amount to an "appeal from ignorance" fallacy. It is this suggestion
which I am disputing.
> In that second example I established that finding 200,000 empty
> holes would refute the hypothesis that 100,000 marbles were
> distributed randomly throughout the holes, though I could not say
> what was invalid, the number of marbles or that they were
> distributed randomly. In any event, while this would constitute a
> **negative result** (hypothesis refuted) it would not constitute
> **negative evidence** (an absence of positive evidence that verifies
> or refutes the hypothesis) because in fact the result constitutes
> definitive evidence that contradicts the hypothesis and verifies the
> null hypothesis. So rather than being an example of an absence of
> evidence that provides evidence of absence, it is in fact an example
> of the presence of evidence that directly refutes the hypothesis in
> question.
Well, some of the mathematical details need a bit of modification (as
I've indicated above), but essentially your conclusion is in agreement
with the point I've been trying to make --- that in principle, a
search resulting in no marbles found, can furnish positive evidence
for the proposition that the number of marbles is small.
> At our current point in our search for Cambrian ancestors, however,
> the lack of fossils is due more to a lack of holes (i.e., a lack of
> regions) rather than a lack of marbles. A lack of holes would
> constitute a true absence of evidence -- i.e., a lack of positive
> evidence that verifies or refutes the hypothesis; in other words,
> negative evidence -- but we cannot say that this constitutes
> evidence of absence because we are lacking the very data we would
> need to make that determination.
But those who are arguing for the absence of Cambrian ancestors are
not doing so on the grounds that there is a paucity of Precambrian
sediment beds. Rather, their argument is that there are sediment beds
where one would expect Precambrian fossils, were there ancestors, and
the fossils aren't there. You may dispute this argument, but not on
the basis that it is an "argument from ignorance" fallacy.
> That is true only after a "large enough search" has been done (which
> it hasn't) and only if that search turns up positive evidence that
> refutes the claim that Cambrian ancestors exist. So far all we have
> is negative evidence that neither verifies nor refutes any claim;
> attempting to use this negative evidence as an argument for claiming
> that Cambrian ancestors do not exist is classified as an "appeal
> from ignorance" fallacy.
But you see, your dispute should be over "whether the search has been
large enough", not over questions of logical fallacy. The evidence we
have so far is _not_ negative evidence, it is _weak_ positive evidence
(well, assuming you are correct about a paucity of data). The
evidence we have to date is able to say _something_ about the scarcity
of Precambrian fossils in probabilistic terms, even if it is not very
much --- even if what it says is not statistically significance. As
such, it is positive evidence, albeit weak.
Furthermore, Art and others would disagree that the evidence is weak.
In the posting that triggered all this we have the quote
"Professor Chen insisted that the biological explosion exhibited at
Chengjiang is not an illusory artifact of an incomplete fossil
record, but an accurate preservation of the true history of life on
earth."
This is effectively an opinion that the evidence is _strong_. You may
disagree with this opinion, but that is where your disagreement should
lie --- it is not a question of logical fallacy.
Mark.
_/~~~~~~~~\___/~~~~~~\____________________________________________________
____/~~\_____/~~\__/~~\__________________________Mark_Phillips____________
____/~~\_____/~~\________________________________mark@ist.flinders.edu.au_
____/~~\HE___/~~\__/~~\APTAIN_____________________________________________
____/~~\______/~~~~~~\____________________________________________________
__________________________________________________________________________
"They told me I was gullible ... and I believed them!"