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of test-design language and theory language. Then the theory’s semantics characterizes the problem for the dissenter, and the test design is effectively falsified, because it is deemed inadequate thus making the test design and the test execution irrelevant.

      If a scientist rejects a test design in response to a falsifying test outcome, he has made the theory’s semantics define the subject of the test and the problem under investigation.

      Popper rejects such a dissenting response to a test, calling it a “content-decreasing stratagem”. He admonishes that the fundamental maxim of every critical discussion is that one should “stick to the problem”. But as James Conant recognized to his dismay in his On Understanding Science: An Historical Approach the history of science is replete with such prejudicial responses to scientific evidence that have nevertheless been productive and strategic to the advancement of basic science in historically important episodes. The prejudicially dissenting scientists may decide that the design for the falsifying test supplied an inadequate description of the problem that the tested theory is intended to solve, often if he developed the theory himself and did not develop the test design. The semantical change produced for such a recalcitrant believer in the theory affects the meanings of the terms common to the theory and test-design statements. The parts of the meaning complex contributed by the test-design statements are then the parts excluded from the semantics of one or several of the descriptive terms common to the theory and test-design statements. Such a semantical outcome for a tested theory can indeed be said to be “content-decreasing”, as Popper said.

      But a scientist’s prejudiced or tenacious rejection of an apparently falsifying test outcome may have a contributing function in the development of science. It may function as what Feyerabend called a “detecting device”, a practice he called “counterinduction”, which is a discovery strategy that he illustrated in his examination of Galileo’s arguments for the Copernican cosmology. Galileo used the apparently falsified heliocentric theory as a “detecting device” by letting his prejudicial belief in the heliocentric theory control the semantics of observational description. This enabled Galileo to reinterpret observations previously described with the equally prejudiced alternative semantics built into the Aristotelian geocentric cosmology. Counterinduction was also the strategy used by Heisenberg, when he reinterpreted the observational description of the electron track in the Wilson cloud chamber using Einstein’s thesis that the theory decides what the physicist can observe, and he then developed his indeterminacy relations using quantum concepts.

      Another historic example of using an apparently falsified theory as a detecting device is the discovery of the planet Neptune. In 1821, when Uranus happened to pass Neptune in its orbit – an alignment that had not occurred since 1649 and was not to occur again until 1993 – Alexis Bouvard developed calculations predicting future positions of the planet Uranus using Newton’s celestial mechanics. But observations of Uranus showed significant deviations from the predicted positions.

      A first possible response would have been to dismiss the deviations as measurement errors and preserve belief in Newton’s celestial mechanics. But astronomical measurements are repeatable, and the deviations were large enough that they were not dismissed as observational errors. They were recognized to be a new problem.

      A second possible response would have been to give Newton’s celestial mechanics the hypothetical status of a theory, to view Newton’s law of gravitation as falsified by the anomalous observations of Uranus, and then attempt to revise Newtonian celestial mechanics. But by then confidence in Newtonian celestial mechanics was very high, and no alternative to Newton’s physics had been proposed. Therefore there was great reluctance to reject Newtonian physics.

      A third possible response, which was historically taken, was to preserve belief in the Newtonian celestial mechanics, propose a new auxiliary hypothesis of a gravitationally disturbing phenomenon, and then reinterpret the observations by supplementing the description of the deviations using the auxiliary hypothesis of the disturbing phenomenon. Disturbing phenomena can “contaminate” even supposedly controlled laboratory experiments. The auxiliary hypothesis changed the semantics of the test-design description with respect to what was observed. In 1845 both John Couch Adams in England and Urbain Le Verrier in France independently using apparently falsified Newtonian physics as a detecting device made calculations of the positions of a disturbing postulated planet to guide future observations in order to detect the postulated disturbing body. In September 1846 using Le Verrier’s calculations Johann Galle observed the postulated planet with the telescope at the Berlin Observatory.

      Theory is language proposed for testing, and test design is language presumed for testing. But here the status of the discourses was reversed. In this third response the Newtonian gravitation law was not deemed a tested and falsified theory, but rather was presumed to be true and used for a new test design. The new test-design language was actually given the relatively more hypothetical status of theory by supplementing it with the auxiliary hypothesis of the postulated planet characterizing the observed deviations in the positions of Uranus. The nonfalsifying test outcome of this new hypothesis was Galle’s observational detection of the postulated planet, which Le Verrier named Neptune.

      But counterinduction is after all just a discovery strategy, and Le Verrier’s counterinduction effort failed to explain a deviant motion of the planet Mercury when its orbit comes closest to the sun, a deviation known as its perihelion precession. He presumed to postulate a gravitationally disturbing planet that he named Vulcan and predicted its orbital positions in 1843. But unlike Le Verrier and most physicists at the time, Einstein had given Newton’s celestial mechanics the hypothetical status of theory language, and he viewed Newton’s law of gravitation as falsified by the anomalous perihelion precession. He had initially attempted a revision of Newtonian celestial mechanics by generalizing on his special theory of relativity. This first attempt is known as his Entwurf version, which he developed in 1913 in collaboration with his mathematician friend Marcel Grossman. But working in collaboration with his friend Michele Besso he found that the Entwurf version had clearly failed to account accurately for Mercury’s orbital deviations; it showed only 18 seconds of arc each century instead of the actual 43 seconds.

      In 1915 he finally abandoned the Entwurf version with its intuitive physical ideas carried over from Newton’s theory, and under prodding from the mathematician David Hilbert turned to mathematics exclusively to produce his general theory of relativity. He then developed his general theory, and in November 1915 he correctly predicted the deviations in Mercury’s orbit. He received a congratulating letter from Hilbert on “conquering” the perihelion motion of Mercury. After years of delay due to World War I his general theory was vindicated by Arthur Eddington’s famous eclipse test of 1919. Some astronomers reported that they observed a transit of a planet across the sun’s disk, but these claims were found to be spurious when larger telescopes were used, and Le Verrier’s postulated planet Vulcan has never been observed.

      Le Verrier’s response to Uranus’ deviant orbital observations was the opposite to Einstein’s response to the deviant orbital observations of Mercury. Le Verrier reversed the roles of theory and test-design language by preserving his belief in Newton’s physics and using it to revise the test-design language with his postulate of a disturbing planet. Einstein viewed Newton’s celestial mechanics to be hypothetical, because he believed that the theory statements were more likely to be productively revised than the test-design statements, and he took the deviant orbital observations of Mercury to be falsifying, thus indicating that revision was needed. Empirical tests are conclusive decision procedures only for scientists who agree on which language is proposed theory and which is presumed test design, and who furthermore accept both the test design and the test-execution outcomes produced with the accepted test design.

      4.19 Empirical Underdetermination

      Vagueness and measurement error are manifestations of empirical underdetermination that permit scientific pluralism.

      Empirical underdetermination can be reduced indefinitely but never completely eliminated.

      Empirical tests are conclusive only when empirical underdetermination is small relative to the effect predicted in a test.

      The

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