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Teaching logic is urgent



Hugh Haskell wrote:

At 10:46 -0400 6/2/03, Ludwik Kowalski wrote:

But, as I said before, I
would accept experimental evidence, no matter how
much it disagrees with logical thinking.

I would be wary of accepting experimental evidence that disagreed
wildly with logical thinking. All evidence should be looked at
skeptically, even evidence that agrees with the conventional wisdom.
Experiments have been known to be wrong, even after many repetitions.
But more often, experiments are looking at the edges of knowledge and
are often digging deeper into the signal to noise ratio than previous
experiments have. Sometimes the new results are right, but not always.

It is always good policy to bear in mind the even-handed thought of Eddington:

"Observation and theory get on best when they are mixed together,
both helping one another in the pursuit of truth. It is a good rule
not to put overmuch confidence in a theory until it has been
confirmed by observation.
"I hope I shall not shock the experimental physicists too much if I
add that it is also a good rule not to put overmuch confidence in the
observational results that are put forward until they have been
confirmed by theory."

Let me elaborate on this. In a deductive approach, one initially advances a set of
premises (some of them implicit) and then derives conclusions from them. One is
not forced to test the premises as long as the derived results are confirmed by
experiment or otherwise. However this logical liberalism has its dark (and very
dangerous) side. If the premises form an inconsistency (i.e. all cannot be true
simultaneously) the self-same approach becomes so devastating as to prevent any
rational activity in the affected domain. Neither experiments not further logical
analysis matter anymore. The reason is that, in a strict logical sense, an
inconsistency can validly produce any imaginable conclusion. Logicians often give
examples of the sort:

Logic is easy.
Logic is difficult.
Therefore crocodiles can fly.

Some time ago I showed that special relativity is based on inconsistent premises.
Now I am giving another example. In thermodynamics, the entropy is defined for a
succession of equilibrium states but then, in chemical thermodynamics, it is
applied to non-equilibrium states. The two inconsistent premises are combined in
the so called fundamental equation of chemical thermodynamics which, in a famous
textbook, is introduced in the following way:


"We regard equation (1) as an axiom and call it the fundamental equation for a
change of the state of a phase. It is one half of the second law of
thermodynamics. We do not ask where it comes from. Indeed we do not admit the
existence of any more fundamental relations from which it might have been derived.
Nor shall we here enquire into the history of its formulation, though that is a
subject of great interest to the historian of science. It is a starting point; it
must be learnt by heart. It may be allowed to stand as an axiom until any single
one of the host of equations that can be derived from it (with the help of other
axioms of thermodynamics) has been shown experimentally to be false." M. L.
McGlashan, Chemical thermodynamics, Academic Press, London(1979).

In my view, both physics and chemistry students urgently need to hear a course of
logic before they learn specific physical or chemical stuff. Otherwise confusions
in physical sciences will continue forever.

Pentcho