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."
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 theorys 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 indeed "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. An inconsistent physical theory is "pure irrationality" for the same reason for which a mathematical theory involving the statement "two and two make both five and four" is "pure irrationality". Examples analogous to "two and two make both five and four":
1) The bug is both dead and alive:
hyperphysics.phy-astr.gsu.edu/Hbase/Relativ/bugrivet.html
2) The speed of light is both constant and variable:
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."
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
www.math.ucr.edu/home/baez/physics/Relat.../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."
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