🚀 go-pugleaf

In article <1992Nov2.093014.26439@black.ox.ac.uk> microsoc@black.ox.ac.uk (Microsoc) writes:

   In article <MARTINC.92Nov1181255@grover.cs.unc.edu> martinc@grover.cs.unc.edu (Charles R. Martin) writes:
   >In article <1992Oct30.235244.463@black.ox.ac.uk> microsoc@black.ox.ac.uk (Microsoc) writes:
   >
   >   As we seem to be on about Popper can anyone answer me this;
   >   How can you falsify (even in principle) a probabilistic theory, eg QM..?
   >
   >At the risk of sounding facetious, the answer is
   >"Probabilistically".  That is, the theory predicts a certain
   >probability distribution; if experiment shows a different
   >distribution, it's a falsification.  Looked at the other way, an
   >experiment that establishes a particular distribution eliminates the
   >whole class of theories that predict another distribution. 

   Ah yes, BUT... it really depends on what you mean by probability
   here. A common definition (not _necessarily_ a good one, though) is
   the limit of relative frequency as the number of observations -->
   infinity. Any finite number of observations _could_ just be a fluke:
   we have no a priori way of counting them as a definitive
   falsification. And the definitive is import- ant here. If we have to
   look at an infinite series to disprove someting , or if we only say
   that our experiments "lend support" to our proababilistic theory,
   then we are right back to the position that Popper put his theory
   forawrd in order to escape from... The point is that probabilistic
   theories aren't subject to the sort of "once and for all" disproofs
   that Popper needs.

   Sorry if I've misunderstood you, though - perhaos you would clarify
   your position...?

I think instead that you've misunderstood Popper's "falsification" in
this context.  I can't reach my copy of Logik der Forschung easily right
now, so I can't quote you chapter and verse,  but I believe that the
demand for absolute falsification is itself an oversimplification of his
position; even if it isn't, that doesn't invalidate the LdF "style" of
reasoning as applied to probabilistic argument.

Consider as an example the hypothesis "this coin is a `fair coin' --
that is, in the limit, heads will occurs equally probably with tails."
Now, no finite experiment can either confirm or deny this hypothesis,
and as such the hypothesis is untestable.  However, this untestability
-- unfalsifiability -- comes about because the question is ill-formed.
It makes an "infinite assertion".

Restating that hypothesis as "this coin is a fair coin -- that is, over
a large number of trials, the number of heads will be very close to the
number of tails", then we have a testable assertion.  (We still have to
determine the meaning of "a large number of trials" and "very close to",
but these can be determined easily by applying mathematical probability
theory.)

Of course, the experiment that might falsify the hypothesis is to flip
the coin for an appropriate number of trials, and record the results.
If the comparison of heads and tails is not "very close to" 50-50, then
that increases our certainty that the coin is not a fair one..  We
cannot state with certainty that it isn't -- heads every time for 10^6
trials has probability > 0 -- but our suspicion will be very strong.

But this is precisely what Popper's falsifiability criterionis meant to
show.  The central point is that no experiment can with certainty show
that a hypothesis is "right", for the reason that we can't know if there
is some other hypothesis that better explains the observed events than
any we've thought of.

As an example of this, Newtonian mechanics is a very good explanation of
certain events in a non-relativistic frame.  However, by Popper's
notions, Newton couldn't claim his theory was "right", only that it had
not yet been falsified; eventually it *was* falsified under certain
conditions, which led to relativistic and quantum mechanics.  But both
of *these* theories must also not be falsified by those experiments
Newton's mechanics already passed.

This example demonstrates that the falsifiability criterion is *never*
one of absolute certainty; as such, probabilities fit perfectly well
with the Popper approach.
--
		Charles R. Martin/(Charlie)/martinc@cs.unc.edu
     Dept. of Computer Science/CB #3175 UNC-CH/Chapel Hill, NC 27599-3175
	    3611 University Dr #13M/Durham, NC 27707/(919) 419 1754
     "Oh God, please help me be civil in tongue, pure in thought, and able
      to resist the temptation to laugh uncontrollably.  Amen." -- Rob T