The semantics of the Newtonian and relativity theories that Feyerabend says are incommensurable may be examined by considering their synthetic statements analytically.  By way of example consider one of the more famous empirical tests of Einstein's general theory of relativity, the 1919-eclipse test that had such a formative influence on Popper.  Two British astronomers undertook this test, Sir Arthur Eddington of Cambridge University and Sir Frank Doyle of the Royal Greenwich Observatory.  The test consisted of measuring the gravitationally produced bending of starlight visible during an eclipse of the sun that occurred on May 29, 1919, and then comparing measurements of the visible stars' positions with the different predictions made by Einstein's general theory of relativity and by New­ton's celestial mechanics.  The test design included the use of telescopes and photographic equipment for recording the telescopic images of the stars.  Firstly reference photographs were made during ordinary night darkness of the stars that would be visible in the proximity of the eclipsed sun.  These photographs were used for comparison with photographs of the same stars made during the eclipse.  They were made with the telescope at Oxford University several months prior to the eclipse, when these stars would be visible at night in England.
          Then the astronomers journeyed to the island of Principe off the coast of West Africa, in order to be in the path of the total solar eclipse.   During the darkness produced by the eclipse they photographed the stars that were visible in the proximity of the sun's disk.  They then had two sets of photographs: An earlier set displayed images of the stars unaffected by the gravitational effects of the sun.  A later set displayed images of the stars near the edge of the disk of the eclipsed sun and therefore produced by light rays affected by the sun's gravitational influence.  The stars in both sets of photographs that are farthest from the sun in the eclipse photographs are deflected only negligibly in the eclipse photograph.  And since different telescopes were used for making the two sets of photographs, reference to these effectively undeflected star images was used to determine an overall magnification correction.  But correction furthermore had to be made for distorting refraction due to atmospheric turbulence and heat gradients.  The distortions are large enough to be comparable to the effect being measured.  But they are also random from photograph to photograph, and the correction were made by averaging over the many photographs.  Such are the essentials of the design of the Eddington eclipse experiment.  The amount of deflection calculated with the general theory of relativity is 1.75 arc seconds.  Eddington's findings showed a deflection of 1.60 + 0.31 arc seconds.  The error in these measurements is small enough to conclude that Einstein's general theory is valid, and that the Newtonian celestial mechanics can no longer be considered valid.  Later experiments have reduced the error of measurement, thereby further validating the relativity hypothesis.  In this experiment the test design statements include description of the optical and photographic equipment and of their functioning, of the conditions in which they were used, and of the photographs of the measured phenomenon made with these measurement instruments.  These statements are universal, since they describe the repeatable experiment, and are presumed to be true characterizations of the experimental set up.  The theory statements are also universal, and each theory shares descriptive variables with the same set of test design statements.  If the test design statements are viewed as analytic statements, then any descriptive variable occurring both in a test design statement and in either theory has a univocal semantics with part of its meaning contributed by one or several test design statements. This semantics is shared by both theories, and it makes the theories semantically commensurable.
          Feyerabend maintained that theories are incommensurable, because there is no concept that is general enough to include both the Euclidian concept of space occurring in Newton's theory and the Reimannian concept occurring in Einstein's theory.  In fact the common part of the meanings in the semantics of the descriptive terms common to the two theories and to the test design statements, are not common meanings due to a more general geometrical concept.  There is a common meaning because the test design statements are silent about the claims made by either theory, even as both the theories claim to reference the same instances that the test design statements definitively describe.  Before the test this silence constitutes the vagueness in the common part of the meaning of the terms shared by the theory statements and defined by the test design statements.  In the case of the test design for Eddington's eclipse experiment, it may be said that before the test the meanings contributed by the test design statements are not properly called either Newtonian or Einsteinian.  For purposes of describing the experimental set up, their semantics have the status as Heisenberg's "everyday” concepts that are silent about the relation between parallel lines at distances much greater than those in the apparatus.
          After the test is executed, the nonfalsification of the relativistic theory and the falsification of the Newtonian theory are known outcomes of the test.  This acceptance of the relativity theory is a pragmatic transformation giving it the semantically defining status of an analytic statement, and the statements of the theory supply part of the semantics for each descriptive term common to the theory and the test design statements.  This semantical contribution by the nonfalsified theory to each of these common descriptive variables may be said to resolve some of the vagueness in the whole meaning complex associated with each of these common terms, and thus the terms may be said to have Einsteinian semantics.  But the semantics supplied to these terms by their test design statements is still vague, just as before the test.  However, if the test design statements are subsequently derived logically from the relativistic theory, then these common terms receive still more Einsteinian semantic values and additional structure from the accepted relativity theory.  In this case everyday concepts may still describe the phenomenon, but the Einsteinian concepts are resolutions of the vagueness in the everyday concepts in the descriptive terms in the test design statements.  In either case, regardless of whether or not the test design statements describing the experimental set up can be logically derived from the relativity theory, no resolution of the everyday concepts to Newtonian concepts is involved either before, during, or after the test, except for the convinced advocates of the Newtonian theory before the latter theory's falsification.  After the test outcome falsifying the Newtonian theory, even the most convinced advocates of the Newtonian theory must accept the semantically controlling role of the test design statements, or reconsider and reject the test design itself.
          Nonetheless some physicists inaccurately refer to the concepts in the test design statements of relativity theory as Newtonian concepts.  This is because any relativistic effects in the test equipment are too small to be detected or measured, and therefore do not jeopardize the conclusiveness of the test.  For example two different telescopes were used in the Eddington eclipse experiment to produce the photographs, one used before the eclipse and another used during the eclipse.  Since the resulting two sets of photographs were compared, a correction had to be made for dif­ferences in magnification.  But no correction was even con­sidered for the different deflections of starlight inside the telescopes due to the different gravitational effects of their different masses even by those who believed in the relativity theory, because such differential relativistic effects are not empirically detectable.  But the nonmeasur­ability or undetectability does not imply that the test design statements affirm the Newtonian theory.  For the test to have any contingency the test design statements must be silent about the tested theory and any alternative to it.  Consequently the concepts in the test design statements describing the phenomena were vague about any relativistic effect introduced by the different masses of the two telescopes, and the concepts in the test design statements are too vague to be described as Newtonian or Einsteinian.  This vagueness in the concepts in test design statements is indicated by a possible variation retrospectively called a measurement error that is not due to failure to execute the test in conformity with the test design, and that is recognized only after the test outcome is accepted.  There was such error in the Eddington experiment, but it was very small relative to the measured deflection of starlight by the sun's gravitational force through interstellar distances.  This inaccuracy due to vagueness is relative to the other concepts in the test design statements, and it must be distinguished from the vagueness relative to the concepts in the theory.  Before the test the meaning parts or semantic values defined by the test design statements are vague with respect to those defined by the theory statements, but this vagueness does not affect the measurement accuracy, since the condition of independence precludes the theory statements being used for measurement.
          In addition to Bohr's complementarity thesis and his own incommensurability thesis, Feyerabend is led to his radical historicism by the view that whether in philosophy of science or in any social science, cultural views and values including the criteria and research practices of empirical science are inseparable from historical conditions.  In its radical variant it says that particular historical circumstances do not function to supply initial conditions for universal theories describing recurrent aspects of human social behavior, but rather preclude the validity of universals altogether.  The persuasive objection to this historicism is that concepts are inherently universal (or as Popper says, all terms are disposition terms).   The metatheory, which proposes using synthetic universal statements analytically for semantical description, which also enables exhibiting semantical continuity through scientific change through history, is a variation on this old but valid objection to this old philosophy of historicism.  However, Feyerabend's historicism enjoys a novel plausibility that could not be admitted by philosophies from Platonism to Positivism, which advance a naturalistic philosophy of the semantics of terms.  Platonic Ideas, Aristotelian forms and simple apprehensions, Romantic intuitions, and Positivistic phenomena, sensations, sense data, and operationalist definitions are all variations on the myth of the given.  The scientific revolutions of the twentieth century have forced philosophers, and specifically Pragmatists, to affirm that meaning and belief are mutually conditioning, and in this sense are relativized to one another.  But universal statements used to describe the real world condition this relativism.  The real world is what imposes constraints on this mutual conditioning in language that makes falsification possible, and that reveals the real world to us.  Given any selected set of concepts, only some statements can be maintained; and conversely given any selected set of stated beliefs, only some concepts may be defined.  The selection of truths is negotiable among interested scientists.  But outside the narrow limits of measurement error and associated conceptual vagueness, truth conditioning expressed in universal statements linking initial conditions and test outcomes is not negotiable once test design statements are chosen.  New experiences anomalous to our universal beliefs force revisions of those universal beliefs and therefore of their semantics.  In empirical science the locus of the semantical revision is a proposed universal hypothesis conditioned upon chosen universal test design statements.  The empirical test is the window to new vision.
          The evolution of thinking from Conant's recognition of prejudice in science to Feyerabend's counterinduction thesis has brought to light an important limitation in Popper's falsificationist thesis of scientific criticism.   In this respect Feyerabend's philosophy of science represents a development beyond Popper, even after discounting Feyerabend's radical relativism.  Popper had rejected the Positivists' naturalistic philosophy of the semantics of language, and maintained that every statement in science can be revised.  But the paradigmatic status he accorded to Eddington's 1919 eclipse experiment as a crucial experiment had deflected Popper from exploring the implications of the artifactual semantics thesis, because he identified all semantical analysis with essentialism.  He saw that the decidability of a crucial experiment depends on the scientist sticking to his problem, which is to say that the scientist should not redefine his problem by reconsidering any experiment's test design, especially after the test outcome has been a falsification of the proposed theory.  Such reconsiderations in Popper's view have no contributing function in the development of science; they are objectionable because they are ad hoc content-decreasing stratagems, merely evasions.  But the prejudiced or tenacious response of a scientist to an apparently falsifying test outcome does have a contributing function in the development of science, as Feyerabend illustrates in his examination of Galileo's arguments for the Copernican cosmology.  Use of the apparently falsified theory as a detecting device by letting his prejudicial belief in the heliocentric theory control the semantics of observational description, enabled Galileo to reinterpret observations previously described with the equally prejudiced alternative semantics built into the Aristotelian cosmology.  This was also the strategy used by Heisenberg, when he reinterpreted the observational description of the electron in the Wilson cloud chamber experiment with the semantics of his indeterminacy relations pursuant to Einstein's anticipation of Feyerabend's Thesis I, i.e. that theory decides what the scientist can observe.  As it happens, the cloud chamber experiment was not designed to decide between Newtonian and quantum mechanics.  The water droplets suggesting discontinuity in the tracks are very large in comparison to the electron, and the produced effect admits easily to either interpretation.  The counterinduction strategy could also have been used by tenacious Newtonians who chose to reject the findings from Eddington's eclipse experiment.  The artifactual status of the semantics of language permits the dissenting scientists to view the falsifying test outcome as a refutation of one or several test design statements rather than as a refutation of the Newtonian theory, although such a dissenting Newtonian would likely be expected by his colleagues to offer an alternative test design.  In any event what some scientists view as definitive test design statements, others may decide to view as falsified theory.
          Feyerabend recognizes that there are semantical consequences to counterinduction.   In "Trivializing Knowledge" he states that the contents of theories and experiments are constituted by the refutation performed and accepted by the scientific community, rather than being the basis on which falsifiability can be decided and refutation can be carried out as Popper maintains.  He considers the stock theory "All ravens are black", and states that while a white raven falsifies the theory, the refutation depends on the reasons for the anomalous raven's whiteness.  Earlier in his "Popper's Objective Knowledge" he gives the same example, and says that the decision about the significance of the anomalously white raven depends on having a theory of color production in animals.  But his discussion by means of this stock theory pertains more to the factors that motivate a scientific community to decide between test design and theory statements, than to a description of the semantics resulting from that decision.  Feyerabend has no metatheory of semantical description for characterizing the contents of theories and experiments.  In this respect Feyerabend's philosophy suffers the same deficiency as Popper's.
          The conflicts between Popper and Feyerabend were struggles between giants in the philosophy of science profession.  Having started in the theatre before turning to philosophy, Feyerabend chose a theatrical writing style that offends the droll scholars of the profession, who tend to treat him dismissively.  But every profession has its pedantic slow learners.  Feyerabend stands above the academic crowd by an order of magnitude. He was an outstanding twentieth century philosopher of science, who advanced the frontier of the discipline, as it was turning from an encrusted Positivism to the contemporary Pragmatism.

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