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W. H. Newton-Smith, The rationality of science, Routledge, London,
1981, p. 229: "A theory ought to be internally consistent. The grounds
for including this factor are a priori. For given a realist construal
of theories, our concern is with verisimilitude, and if a theory is
inconsistent it will contain every sentence of the language, as the
following simple argument shows. Let 'q' be an arbitrary sentence of
the language and suppose that the theory is inconsistent. This means
that we can derive the sentence 'p and not-p'. From this 'p' follows.
And from 'p' it follows that 'p or q' (if 'p' is true then 'p or q'
will be true no matter whether 'q' is true or not). Equally, it
follows from 'p and not-p' that 'not-p'. But 'not-p' together with 'p
or q' entails 'q'. Thus once we admit an inconsistency into our theory
we have to admit everything. And no theory of verisimilitude would be
acceptable that did not give the lowest degree of verisimilitude to a
theory which contained each sentence of the theory's language and its
negation."

http://www.lip.uns.edu.ar/cmsra/bueno.pdf
Otavio Bueno: "The traditional approach to scientific rationality
presupposes that consistency is a necessary condition for rational
theory change in science (see, for example, [13] or [10]). This
presupposition has been adopted for an obvious reason: given the
assumption that classical logic is the underlying logic of scientific
theories, the inconsistency of a particular theory immediately
establishes its triviality. That is, presupposing classical logic, if
a given theory is shown to be inconsistent, then every sentence in the
theory’s language is true. But this traditional approach faces a
serious difficulty. The fact that inconsistencies have often been
entertained in science (as well as in mathematics) makes this approach
to scientific rationality quite unlikely. After all, according to this
approach, substantial and significant parts of scientific practice are
turn into pure irrationality."

An inconsistent PHYSICAL theory IS "pure irrationality", that is, it
SHOULD be given the "lowest degree of verisimilitude", but not because
it contains "each sentence of the theory's language and its negation".
Newton-Smith's proof involves the inference:

" from 'p' it follows that 'p or q' "

which is PHYSICALLY unacceptable. In physical sciences, an
inconsistent theory is "pure irrationality" for the same reason for
which "two and two make five; two and two make four" is pure
irrationality. Examples analogous to "two and two make five; two and
two make four":

1) The bug is dead; the bug is alive:

http://hyperphysics.phy-astr.gsu.edu/Hbase/Relativ/bugrivet.html

2) The speed of light is constant; the speed of light is variable:

http://www.astronomynotes.com/relativity/s4.htm
"Prediction: light escaping from a large mass should lose energy---the
wavelength must increase since the speed of light is constant.
Stronger surface gravity produces a greater increase in the
wavelength. This is a consequence of time dilation. Suppose person A
on the massive object decides to send light of a specific frequency f
to person B all of the time. So every second, f wave crests leave
person A. The same wave crests are received by person B in an interval
of time interval of (1+z) seconds. He receives the waves at a
frequency of f/(1+z). Remember that the speed of light c = (the
frequency f) (the wavelength L). If the frequency is reduced by (1+z)
times, the wavelength must INcrease by (1+z) times: L_atB = (1+z)
L_atA. In the doppler effect, this lengthening of the wavelength is
called a redshift. For gravity, the effect is called a gravitational
redshift."

http://helios.gsfc.nasa.gov/qa_sp_gr.html
"Is light affected by gravity? If so, how can the speed of light be
constant? Wouldn't the light coming off of the Sun be slower than the
light we make here? If not, why doesn't light escape a black hole?
Yes, light is affected by gravity, but not in its speed. General
Relativity (our best guess as to how the Universe works) gives two
effects of gravity on light. It can bend light (which includes effects
such as gravitational lensing), and it can change the energy of light.
But it changes the energy by shifting the frequency of the light
(gravitational redshift) not by changing light speed. Gravity bends
light by warping space so that what the light beam sees as "straight"
is not straight to an outside observer. The speed of light is still
constant." Dr. Eric Christian

http://www.math.ucr.edu/home/baez/physics/Relativity/SpeedOfLight/speed_of_light.html
"Einstein went on to discover a more general theory of relativity
which explained gravity in terms of curved spacetime, and he talked
about the speed of light changing in this new theory. In the 1920 book
"Relativity: the special and general theory" he wrote: ". . .
according to the general theory of relativity, the law of the
constancy of the velocity of light in vacuo, which constitutes one of
the two fundamental assumptions in the special theory of relativity
[. . .] cannot claim any unlimited validity. A curvature of rays of
light can only take place when the velocity of propagation of light
varies with position." Since Einstein talks of velocity (a vector
quantity: speed with direction) rather than speed alone, it is not
clear that he meant the speed will change, but the reference to
special relativity suggests that he did mean so."

http://www.physlink.com/Education/AskExperts/ae13.cfm
"So, it is absolutely true that the speed of light is not constant in
a gravitational field [which, by the equivalence principle, applies as
well to accelerating (non-inertial) frames of reference]. If this were
not so, there would be no bending of light by the gravitational field
of stars....Indeed, this is exactly how Einstein did the calculation
in: 'On the Influence of Gravitation on the Propagation of Light,'
Annalen der Physik, 35, 1911. which predated the full formal
development of general relativity by about four years. This paper is
widely available in English. You can find a copy beginning on page 99
of the Dover book 'The Principle of Relativity.' You will find in
section 3 of that paper, Einstein's derivation of the (variable) speed
of light in a gravitational potential, eqn (3). The result is,
c' = c0 ( 1 + V / c^2 )
where V is the gravitational potential relative to the point where the
speed of light c0 is measured."

Pentcho Valev
pvalev@yahoo.com