What is the probability that an arbitrary Mr. X looks exactly like an arbitrary Mr. Y? Clearly the prior probability is virtually zero. This means that for the argument:

Postulate: Mr. X and Mr. Y are identical twins.
Consequence: Mr. X looks exactly like Mr. Y.

the combination "false postulate, true consequence" is virtually impossible.

Consider an oversimplified version of Carnot's 1824 argument:

Carnot's 1824 postulate: Heat is an indestructible substance (caloric) that cannot be converted into work by the heat engine.
Consequence (prototype of the second law of thermodynamics): The reversible heat engine X working between the temperatures T1 and T2 is just as efficient as the reversible heat engine Y working between the same temperatures.

By the years 1840-1850 it was definitively established that Carnot's postulate is false. Should scientists have concluded that the probability that the consequence is true is virtually zero? That is, should they have rejected the combination "false postulate, true consequence" as virtually impossible?

If the consequence of Carnot's 1824 false postulate cannot be true, as the analogy with the twins suggests, then Clausius 1850 argument abandoning Carnot's postulate and deducing the same consequence (prototype of the second law of thermodynamics) from another (true this time) postulate must be invalid:

Clausius' 1850 postulate: In a spontaneous process, heat always flows from hot to cold.
Consequence (prototype of the second law of thermodynamics): The reversible heat engine X working between the temperatures T1 and T2 is just as efficient as the reversible heat engine Y working between the same temperatures.

That is, apart from the true postulate, there must be some auxiliary assumption in Clausius' 1850 paper which is false. In the quotation below, the phrases in capitals - "THE ONLY CHANGE" and "WITHOUT ANY EXPENDITURE OF FORCE OR ANY OTHER CHANGE" - contain the false assumption:

http://www.mdpi.org/lin/clausius/clausius.htm
"Ueber die bewegende Kraft der Wärme", 1850, Rudolf Clausius: "Carnot assumed, as has already been mentioned, that the equivalent of the work done by heat is found in the mere transfer of heat from a hotter to a colder body, while the quantity of heat remains undiminished. The latter part of this assumption--namely, that the quantity of heat remains undiminished--contradicts our former principle, and must therefore be rejected... (...) It is this maximum of work which must be compared with the heat transferred. When this is done it appears that there is in fact ground for asserting, with Carnot, that it depends only on the quantity of the heat transferred and on the temperatures t and tau of the two bodies A and B, but not on the nature of the substance by means of which the work is done. (...) 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."

It is easy to see that the two-substances process considered by Clausius presupposes the action of an OPERATOR; this operator constantly and unavoidably undergoes CHANGES, changes that are absent when heat spontaneously "shows a tendency to equalize temperature differences and therefore to pass from hotter to colder bodies". In other words, the trivial fact that, in a spontaneous process, in the absence of an operator, heat always flows from hot to cold by no means implies that heat will flow from hot to cold in a non-spontaneous operator-driven process as the one considered by Clausius. Clausius' argument is invalid - it is based on the false assumption expressed in the phrases "THE ONLY CHANGE" and "WITHOUT ANY EXPENDITURE OF FORCE OR ANY OTHER CHANGE".

Pentcho Valev