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> > In 1824 Sadi Carnot deduced the prototype of the second law of
> > thermodynamics:
>
> > All reversible heat engines working between two fixed temperatures
> > have the same efficiency.
>
> > from two premises:
>
> > 1. Perpetuum mobile of the first kind is impossible.
>
> > 2. Heat is conserved (cannot be converted into work by the heat
> > engine).
>
> > Then the second premise was officially declared false but the
> > conclusion, the prototype of the second law of thermodynamics,
> > remained gloriously true. More precisely, the glory was introduced by
> > Clausius who, in 1850, managed to convince the world that the false
> > premise should be forgotten and replaced by a true one:
>
> > 2'. Heat flows spontaneously from hot to cold.
>
> > Theoreticians and philosophers of science have never seen any problem
> > in the fact that, originally, a false premise was ESSENTIAL in the
> > deduction of a true conclusion. At least they should have considered
> > the following hypothesis:
>
> > The conclusion, the prototype of the second law of thermodynamics, is
> > false as well; Clausius' 1850 ad hoc deduction was invalid.
>
> Carnot's conclusion was a law, and the prior probability of any law is
> zero. That is, if the efficiency of the heat engine A (working
> reversibly between the temperatures T1 and T2) is a, and if the
> efficiency of the heat engine B is b, the probability one should
> assign to a=b BEFORE THERE IS ANY EVIDENCE is zero. Since Carnot's
> first premise ALONE is obviously no evidence, one is forced to accept
> that in 1824 the false second premise was crucial for establishing a
> law whose prior probability was zero. If one refuses to accept such an
> absurdity, one should move to the only reasonable alternative: THE LAW
> IS FALSE as well. Violations of the second law of thermodynamics are
> discussed in this (not very well written) paper of mine:
>
> http://www.wbabin.net/valev/valev2.htm
> BIASED THERMAL MOTION AND THE SECOND LAW OF THERMODYNAMICS

It would be reasonable to define a class of conditionals (if P then Q)
such that the prior probability of the conclusion (Q) is zero:

If P then Q: If heat is conserved, then all reversible heat engines
working between two fixed temperatures have the same efficiency.

So far, by definition, the truth-table of ANY conditional was:

P...................Q.....................if P then Q
true................true.................true
true................false................false
false...............true.................TRUE
false...............false................true

For the class of conditionals just defined, the correct truth-table
is:

P...................Q.....................if P then Q
true................true.................true
true................false................false
false...............true.................FALSE
false...............false................true

Note that the correct truth-table, although formally identical to that
of the biconditional, does not convert the conditional whose
conclusion has zero prior probability into biconditional.

Pentcho Valev
pvalev@yahoo.com