Clausius' famous conclusion "Entropy always increases", a conclusion
that holds, according to Arthur Eddington, "the supreme position among
the laws of Nature", was also deduced from an "indispensable false
axiom":

http://philsci-archive.pitt.edu/archive/00000313/
Jos Uffink: "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."

Uffink is too lenient here - the fact that irreversible processes
don't have reversible replicas is obvious. I used to fuss vigorously
over the issue ( http://link.aip.org/link/?APCPCS/643/430/1 ) but in
the end I realized I was alone - even Uffink had abandoned the
dangerous (for one's career) topic. In the era of Postscientism
indispensable false axioms eventually become obsolete and the
conclusion starts living all on its own. "Who cares about Clausius'
archaic deduction?" - would reply the mainstream theoretician - "After
all, the law of entropy increase has proved empirically correct. You
don'y expect air molecules to spontaneously assemble in the corner of
the room do you?"

Sometimes indispensable false axioms produce absurd conclusions but
the absurdities automatically become "paradoxes" that gloriously
illustrate the scope of the respective "theory". In the era of
Postscientism there is nothing embarrassing about an 80m long object
safely trapped inside a 40m long container, or about a bug that is
both dead and alive:

http://math.ucr.edu/home/baez/physic...barn_pole.html
"These are the props. You own a barn, 40m long, with automatic doors
at either end, that can be opened and closed simultaneously by a
switch. You also have a pole, 80m long, which of course won't fit in
the barn. Now someone takes the pole and tries to run (at nearly the
speed of light) through the barn with the pole horizontal. Special
Relativity (SR) says that a moving object is contracted in the
direction of motion: this is called the Lorentz Contraction. So, if
the pole is set in motion lengthwise, then it will contract in the
reference frame of a stationary observer.....So, as the pole passes
through the barn, there is an instant when it is completely within the
barn. At that instant, you close both doors simultaneously, with your
switch. Of course, you open them again pretty quickly, but at least
momentarily you had the contracted pole shut up in your barn. The
runner emerges from the far door unscathed.....If the doors are kept
shut the rod will obviously smash into the barn door at one end. If
the door withstands this the leading end of the rod will come to rest
in the frame of reference of the stationary observer. There can be no
such thing as a rigid rod in relativity so the trailing end will not
stop immediately and the rod will be compressed beyond the amount it
was Lorentz contracted. If it does not explode under the strain and it
is sufficiently elastic it will come to rest and start to spring back
to its natural shape but since it is too big for the barn the other
end is now going to crash into the back door and the rod will be
trapped in a compressed state inside the barn."

http://hyperphysics.phy-astr.gsu.edu.../bugrivet.html
"The bug-rivet paradox is a variation on the twin paradox and is
similar to the pole-barn paradox.....The end of the rivet hits the
bottom of the hole before the head of the rivet hits the wall. So it
looks like the bug is squashed.....All this is nonsense from the bug's
point of view. The rivet head hits the wall when the rivet end is just
0.35 cm down in the hole! The rivet doesn't get close to the
bug....The paradox is not resolved."

Pentcho Valev