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.
>
>But that is not the sense meant when
>talking about a pre-Cambrian fossil search.
>
On the contrary, the Precambrian fossil search is a perfect example of this
kind of confusion.
>
>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". 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. 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.
>
>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.
>
>> >Suppose you have a million holes in the ground, and you want to see
>> >if at least one of them contains a marble. You examine 200,000
>> >holes at random and find no marble. This is good evidence that, if
>> >there are any marbles at all, their number is quite small.
>>
>> Assuming that the marbles were themselves distributed randomly, which you
>> did not specify. Otherwise there could be 500,000 of them, but placed in
>> specific arrangements meant to defeat a random search. As such, your
lack
>> of evidence at this point really tells you nothing about how many there
are.
>
>No assumptions need be made about the distribution of the marbles.
>The fact that the search is _random_, means that there is _no_
>distribution strategy which can defeat it. It would be impossible to
>arrange the marbles in such a way as to defeat the search because
>there is no way of predicting, ahead of time, which holes will be
>searched.
>
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.
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.
>
>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. 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. Those results also indicate that no statistical
confidence can be applied to any specific number of marbles.
>
>> >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.
>>
>> Not really. Your hypothesis is that there is at least one marble
present,
>> but nothing is said about the probability of there being more than one.
>
>"at least one marble present" is mathematical speak for "one marble,
>or two marbles, or three marbles, or four marbles, ..." --- in other
>words, it is an expression often used when one wants to talk about the
>probability of there being "one or more than one" marbles present. I
>hope this clarifies things --- a technical point in any case.
>
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.
>
>> That makes the null hypothesis that there are no marbles. As such,
>> to verify or refute either hypothesis you would have to examine every
single
>> hole; even 950,000 holes would be insufficient to verify or refute either
>> hypothesis. Even 999,999 holes would be insufficient because the last
hole
>> still has a 50/50 chance of containing a marble.
>
>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 would
be so low as to be negligable (specifically 0.5^1,000,000; which my
calculator could not solve), 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). So again, even after you have searched all but one hole you
still can make no definitive statement about whether a marble is present in
any of the holes.
>
>> Despite appearances, however, this is not a case where a lack of
>> evidence verifies one hypothesis and refutes another, because in
>> this kind of study the lack of marbles is not a lack of evidence;
>> you would expect to find some holes empty in any event.
>
>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.
>
>My point is that just as "finding many empty holes" is admissible
>evidence as to the number of marbles, so too is "finding many fossil
>beds with no pre-Cambrian fossils" evidence as to the number of
>pre-Cambrian fossils.
>
My second marble example, in which 100,000 marbles are randomly distributed
throughout the holes, and in which no marbles are found after a search of
200,000 holes, is closer to the reality of our search for Precambrian
fossils than your at-least-one-marble example or my single-marble example.
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.
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.
>
>> >I don't believe the "lack of pre-Cambrain fossils argument" correctly
>> >matches the "appeal from ignorance" logical falacy. If no one had
>> >bothered to look for fossilized Cambrian ancestors, and then somebody
>> >claimed that because there were no such specimins they hadn't evolved,
>> >_then_ this would be an appeal from ignorance falacy. But the fact
>> >that people have been looking without success, is admissible evidence.
>>
>> The fallacy doesn't depend upon whether you look for the evidence or not;
it
>> only depends upon whether you use a lack of evidence to try to prove or
>> disprove a concept. The fallacy doesn't say, claiming a concept is false
>> because no one has tried to prove it true; it says, claiming a concept is
>> false because it hasn't been proven true. The implication is that people
>> could have been trying to prove it true but had not yet succeeded.
>
>You are correct in suggesting that _trying_to_prove,_without_success_
>does not invalidate a claim --- *providing* the very process of
>_trying_to_prove_ does not in itself yield evidence in favour of the
>counter claim.
>
True, but it would have to yield positive evidence that verifies the
counter-claim, not negative evidence that neither verifies or refutes any
claim. That's why the appeal from ignorance is a fallacy.
>
>I am saying that, a large enough search for pre-Cambrian fossils which
>results in none being found, can be taken as positive evidence in
>favour of the proposition that no pre-Cambrian fossils exist. And
>thus, this kind of argument cannot be classified as an "appeal from
>ignorance" falacy.
>
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.
PS -- A few quick technical notes: it's "Precambrian", not "pre-Cambrian";
Precambrian fossils have been found, but the point of this discussion
concerns fossils that should be older still; and it's "fallacy", not
"falacy".
Kevin L. O'Brien