🚀 go-pugleaf

Can a false premise produce, validly, a true conclusion? Generally,
yes:

If it rains, then the soil is wet.

The argument is valid, the premise "it rains" can be false and yet the
conclusion "the soil is wet" can be true (the gardener has watered the
lawn). However there is a type of valid arguments for which a false
premise necessarily entails a false conclusion. The so-called Carnot
theorem is an argument of this type:

If heat is conserved (cannot be converted into work in the heat
engine), then all reversible heat engines working between the same two
temperatures T1 and T2 (T2 > T1) have the same efficiency.

The premise "heat is conserved (cannot be converted into work in the
heat engine)" is false. However by 1850 Clausius and Kelvin had built
their scientific careers on the false conclusion "all reversible heat
engines working between the same two temperatures T1 and T2 (T2 > T1)
have the same efficiency" and decided to save it. In 1850 Clausius
deduced the false conclusion from a true premise but the argument was
invalid:

If heat always flows spontaneously from hot to cold, then all
reversible heat engines working between the same two temperatures T1
and T2 (T2 > T1) have the same efficiency:

http://web.lemoyne.edu/~giunta/Clausius.html
"Ueber die bewegende Kraft der Warme" 1850 Clausius: "If we now
suppose that there are two substances of which the one can produce
more work than the other by the transfer of a given amount of heat,
or, what comes to the same thing, needs to transfer less heat from A
to B to produce a given quantity of work, we may use these two
substances alternately by producing work with one of them in the above
process. At the end of the operations both bodies are in their
original condition; further, the work produced will have exactly
counterbalanced the work done, and therefore, by our former principle,
the quantity of heat can have neither increased nor diminished. The
only change will occur in the distribution of the heat, since more
heat will be transferred from B to A than from A to B, and so on the
whole heat will be transferred from B to A. By repeating these two
processes alternately it would be possible, without any expenditure of
force or any other change, to transfer as much heat as we please from
a cold to a hot body, and this is not in accord with the other
relations of heat, since it always shows a tendency to equalize
temperature differences and therefore to pass from hotter to colder
bodies."

Pentcho Valev