THE FALSE START OF DEDUCTIVE SCIENCE

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.

Pentcho Valev

On Jun 19, 10:32 am, Pentcho Valev wrote:
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.

Why Clausius' 1850 ad hoc deduction is invalid: Clausius' claims given
below in capitals: "THE ONLY CHANGE" and "WITHOUT ANY EXPENDITURE OF
FORCE OR ANY OTHER CHANGE" - are false:

http://web.lemoyne.edu/~giunta/Clausius.html
"Ueber die bewegende Kraft der Warme" 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."

In fact, the process considered by Clausius and essential for his
deduction presupposes the constant 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".

Pentcho Valev

On Jun 19, 9:32 am, Pentcho Valev wrote:
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.

The false second premise used by Carnot could have been:

(1) MISLEADING. Then the conclusion, the prototype of the second law
of thermodynamics, is FALSE.

(2) REDUNDANT. Carnot would have realized that and would not have used
it.

(3) INDISPENSABLE for the deduction of the TRUE conclusion.

How can a FALSE premise be INDISPENSABLE? (1) seems to be the only
reasonable solution.

Pentcho Valev

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.

Why Clausius' 1850 ad hoc deduction is invalid: Clausius' claims given
below in capitals: "THE ONLY CHANGE" and "WITHOUT ANY EXPENDITURE OF
FORCE OR ANY OTHER CHANGE" - are false:

http://web.lemoyne.edu/~giunta/Clausius.html
"Ueber die bewegende Kraft der Warme" 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."

In fact, the process considered by Clausius and essential for his
deduction presupposes the constant 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".

Encouraged by his 1850 successful introduction of a new logic of
science (when a precious conclusion follows from a false premise, you
are allowed to abandon the premise and rededuce the precious
conclusion from another premise, true this time), later Clausius
gloriously introduced the concept of entropy. Yet consider:

http://www.me.umn.edu/education/cour...331-Mod-28.pdf

more precisely "The Clausius Theorem" and the assumption entitled
"Equivalent reversible and irreversible processes" according to which
any "Irreversible Process" can be closed by a reversible process (in
this case consisting of a "Reversible Adiabat", "Reversible Isotherm"
and "Reversible Adiabat") to become a cycle. Is the assumption
correct? If it is not, what remains of the concept of entropy?

This is one of the most dangerous questions in thermodynamics. For 140
years it has been asked only once, by Jos Uffink:

http://philsci-archive.pitt.edu/archive/00000313/
p.39: "A more important objection, it seems to me, is that Clausius
bases his conclusion that the entropy increases in a nicht umkehrbar
[irreversible] process on the assumption that such a process can be
closed by an umkehrbar [reversible] process to become a cycle. This is
essential for the definition of the entropy difference between the
initial and final states. But the assumption is far from obvious for a
system more complex than an ideal gas, or for states far from
equilibrium, or for processes other than the simple exchange of heat
and work. Thus, the generalisation to all transformations occurring in
Nature is somewhat rash."

That is, again, a possibly false premise has given a precious
conclusion. The answer to the dangerous question is implicit in
Uffink's statement:

http://philsci-archive.pitt.edu/archive/00000313/
Jos Uffink: "This summary leads to the question whether it is fruitful
to see irreversibility or time-asymmetry as the essence of the second
law. Is it not more straightforward, in view of the unargued
statements of Kelvin, the bold claims of Clausius and the strained
attempts of Planck, to give up this idea? I believe that Ehrenfest-
Afanassjewa was right in her verdict that the discussion about the
arrow of time as expressed in the second law of the thermodynamics is
actually a RED HERRING."

At the end of his career Clausius, just like Einstein, became somewhat
honest but it was too late:

http://philsci-archive.pitt.edu/archive/00000313/
"On many occasions Clausius was criticised by his contemporaries. I do
not know If, in his own time, he was criticised in particular for his
famous formulation of the second law as the increase of the entropy of
the universe. However, Kuhn (1978, pp. 13-15, p. 260) has pointed out
the remarkable fact that in the book (Clausius 1876) he eventually
composed from his collected articles, every reference to the entropy
of the universe and even to the idea that entropy never decreases in
irreversible processes in adiabatically isolated systems is deleted!
The most general formulation given to the second law in this book,
which may be regarded as the mature presentation of Clausius’ ideas,
is again the relation (10), where the system is supposed to undergo a
cycle, and entropy increase is out of the question."

Pentcho Valev

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

Pentcho Valev

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

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.

The 1824 pattern:

TRUE PREMISE: Perpetuum mobile of the first kind is impossible.

FALSE PREMISE: Heat is conserved (cannot be converted into work by the
heat engine).

FALSE BUT MIRACULOUS CONCLUSION: All reversible heat engines working
between two fixed temperatures have the same efficiency.

Einstein studied thermodynamics very carefully:

http://www.fourmilab.ch/etexts/einstein/specrel/www/
Albert Einstein 1905: "We will raise this conjecture [TRUE PREMISE]
(the purport of which will hereafter be called the "Principle of
Relativity") to the status of a postulate, and also introduce another
postulate [FALSE PREMISE], which is only apparently irreconcilable
with the former, namely, that light is always propagated in empty
space with a definite velocity c which is independent of the state of
motion of the emitting body.....From this there ensues the following
peculiar consequence [FALSE BUT MIRACULOUS CONCLUSION]. If at the
points A and B of K there are stationary clocks which, viewed in the
stationary system, are synchronous; and if the clock at A is moved
with the velocity v along the line AB to B, then on its arrival at B
the two clocks no longer synchronize, but the clock moved from A to B
lags behind the other which has remained at B by tv^2/2c^2 (up to
magnitudes of fourth and higher order), t being the time occupied in
the journey from A to B. It is at once apparent that this result still
holds good if the clock moves from A to B in any polygonal line, and
also when the points A and B coincide. If we assume that the result
proved for a polygonal line is also valid for a continuously curved
line, we arrive at this result: If one of two synchronous clocks at A
is moved in a closed curve with constant velocity until it returns to
A, the journey lasting t seconds, then by the clock which has remained
at rest the travelled clock on its arrival at A will be tv^2/2c^2
second slow."

http://kea.princeton.edu/che246/organization.htm
Albert Einstein wrote of thermodynamics: "A theory is the more
impressive the greater the simplicity of its premises is, the more
different the kinds of things it relates, and the more extended is its
area of applicability. Therefore, the deep impression which classical
thermodynamics made upon me. It is the only physical theory of
universal content concerning which I am convinced that, within the
framework of applicability of its basic concepts, it will never be
overthrown."

Pentcho Valev