Perhaps the most dangerous situation in a deductive science is one in
which conclusions are derived from a set of inconsistent premises
(all the premises in the set cannot be true simultaneously). One can
VALIDLY derive ANY conclusion from an incosistency. Logicians often
give examples of the sort:

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

The argument is valid so far as no circumstances can be imagined in
which both premises are true and the conclusion false.
If deriving from an inconsistency is taught (not explicitly of
course) the effect is remarkable - the affected people not only stop
applying logic - they don't even see why logic SHOULD be applied. For
instance, there are perhaps 20-30 versions of the second law of
thermodynamics, some traditional others exotic. Try to suggest to a
thermodynamicist that perhaps the EQUIVALENCY of the versions should
somehow be PROVED - I bet the reaction would be hostile.
Let me be more concrete. Consider the versions:

No process is possible in which the sole result is the absorption of
heat from a reservoir and its complete conversion into work.

A system cannot absorb heat from a reservoir, completely convert it
into work and return to its initial state.

The former version is a corollary of the latter but not vice versa.
The difference is extremely important but thermodynamicists have no
receptor for that.

In the above case there is still some hope that sooner or later
the logical subordination will be established. Things look much more
desperate when other versions are considered, e.g.

Every process occuring in nature proceeds in the sense in which the
sum of the entropies of all bodies taking part in the process is
increased. (Planck)

In every open neighborhood of every state s there are states that
cannot be reached adiabatically from s. (Caratheodory)

How many second laws are there? Why is their equivalency never
checked? Why should the confusion be taught? Does anybody care?

Pentcho Valev