🚀 go-pugleaf

daryl@oracorp.com (Daryl McCullough) writes:

>In article <1992Oct21.170822.1775@CSD-NewsHost.Stanford.EDU>,
>casley@Tarski.Stanford.EDU (Ross Casley) writes:

>>>As you note, "all crows are black" and "all non-black objects are
>+=>>non-crows" are logically equivalent.  Now it is reasonable to consider a
>>>black crow as a small piece of evidence for all crows being black; collect
>>>enough such instances and no counterexamples and you can consider "all
>>>crows are black" as being established by observation.
>>>
>>>But by exactly the same reasoning finding a non-black non-crow should be a
>>>small piece of evidence supporting the proposition "all non-black objects
>>>are non-crows," hence it should support "all crows are black."  But this
>>>obviously doesn't work.  So there's something odd about this notion of
>>>evidence.  Either it doesn't respect logical equivalence, or it is not
>>>possible to tell what counts as evidence for a proposition from its
>>>logical form.

>>Karl Popper had a lot to say about this sort of thing. What this
>>paradox shows is that the notion of establishing a law of nature by
>>induction (getting lots and lots of cases in which the law is true) is
>>nonsensical. All that you ever establish is that the law holds in the
>>cases you checked. A better way to test a law is to try everything you
>>think of to prove that the law is *false*. If, in spite of your best
>>efforts, you can never falsify the law, then the law is said to be
>>(provisionally) confirmed.

>>So, while the process of establishing a law by induction seems to
>>allow a green tie to be evidence for "all crows are black", the
>>process of attempting to falsify the law doesn't allow such
>>irrelevancies to count as evidence.

What this shows is the limited power of formal logic as a tool for
induction.  Consider: All crows are black.  An inductive statement
generated from observation of some finite number of black crows and
no white (or non-black) crows.  Now, how do I attempt to verify this?
I might attempt to devise a mathematical theory based on obvious axioms
within which I could deduce All crows are black as a theorem.  Rather
a dicy bit of work, that.  Or, I could go about looking for a non-black
crow as a counter-example.
Note, however, that I am doing something different than when I started.
That is, I am attempting to verify a general statement: All crows are
black.  When I began, looking as bunches of black crows and noting that
I hadn't seen any non-black crows, I was attempting to doscover some
general characterization of crows.  At some point I had an epiphiny
and said Ah Ha!  All crows are black.  After having come up with this
as a hypothesis I reversed myself and, no longer interested in
discovering the genral rule, began to attempt to vberify the rule
I discovered.
This is just the difference Popper makes between the logics of
Discovery and verification.  Popper doesn't have much to say about
discovery--it doesn't fit his model which is based on formal logic.
The point is that there is a double movement here: bottom up and
top down.  I need both, but only in the latter can I appeal to formal
logic.  In the former there are other things which come into play,
which would exclude finding a green tie (e.g.,) as a confirmation
that all crows are black.  Indeed, at that point I don't even have
the statement that all crows are black--I have a question: What is
the essential characteristic of crows?

bv