<Language> Proving Negatives

[H. Mark Hubey]

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I see this phrase often. I don't understand what it means.
I have this feeling that it has to do with a point of
view in Philosophy of Science. PoF has gone thru many
stages. The first, and earliest stage is attributed
usually to Bacon and may be termed Baconian. It is the
usual high school rant about, hypothesis/theory, experiment, etc.

The experiment was supposed to verify the theory. That
does not work out according to laws of logic.

So someone attempted to change "verification" to
"confirmation". The experiment was supposed to "confirm"
the theory. That does not work out either. That was done
clearly by Hempel in the so-called RAven Paradox. It goes
like this; the statement "Ravens are black" can be written
as R => B (where => stands for "material implication" of
logic). According to confirmationism, every time we see
a raven that is black, this added further confirmation to the
statement R => B. But the contrapositive of this statement
~B => ~R (where the tilde indicates negation) which is equivalent
to the original statement says "If it is not black, it is not
a raven". But then this says that everytime we see an object
that is not black, such as a red corvette, or a yellow banana,
we are also "confirming" the statement "ravens are black"!

So "confirmationism" is as bad as "verificationism".

The only thing left, as vigorously propounded by Popper
is "falsificationism" which means essentially that a
scientific statement can only be falsified. So the acid
test for a statement being a scientific statement (not necessarily
true) is that it be at least falsifiable in principle.

So a statement like "elephants are pink" is a scientific
statement in the sense that if we can find a non-pink
elephant we can falsify the statement. Obviously, "elephants
are not pink" is also falsifiable since to falsify it we need
only to find a pink elephant.

How does a "negative" not get proven?

Maybe some people mean a statement like this; "the sun
will always rise in the east". That can be falsified only
if we can wait an eternity. But this is the problem of
induction, which is what all the sciences (aside from
math) have to face, and that includes physics and all the
engineering that follows from it. So that problem is not
about negatives but about induction. Induction itself
causes no problems for math since it is a type of
mathematical proof. Induction causes problems for sciences
other than math.

--
Best Regards,
Mark
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hubeyh at montclair.edu =-=-=-= http://www.csam.montclair.edu/~hubey
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