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 empirical underdetermination of language may make empirical criteria incapable of producing decisive theory-testing outcomes. Two manifestations of empirical underdetermination are conceptual vagueness and measurement error. All concepts have vagueness that can be reduced indefinitely but can never be eliminated completely. Mathematically expressed theories use measurement data that always contain measurement inaccuracy. Measurement error can be reduced indefinitely but never eliminated completely.
Scientists prefer measurements and mathematically expressed theories, because they can measure the amount of prediction error in the theory, when the theory is tested. But separating measurement error from a theory’s prediction error can be problematic. Repeated careful execution of the measurement procedure, if the test is repeatable, enables statistical estimation of the degree or range of measurement error. A test is conclusive to the extent that the estimated measurement error is manifestly small relative to the produced effect in the test. But as in economics, repeated measurement is not always possible.
4.20 Scientific Pluralism
Scientific pluralism is recognition of the coexistence of empirically adequate alternative explanations due to undecidability permitted by the empirical undetermination in test-design language.
All language is always empirically underdetermined by reality. Empirical underdetermination explains how two or more semantically alternative empirically adequate theories can have the same test-design language. This means that there are several theories yielding accurate predictions that are alternatives to one another, while having differences that are small enough to be within the range of the estimated measurement error. In such cases empirical underdetermination due to the current test design imposes undecidability on the choice among the alternative explanations.
Econometricians are accustomed to alternative empirically adequate econometric models. This occurs because measurement errors in aggregate social statistics are large in comparison to those in natural sciences. Each such model has different equation specifications, i.e., different causal variables, and makes different forecasts for some of the same prediction variables that are accurate within the relatively large range of estimated measurement error. And discovery systems with empirical test procedures routinely proliferate empirically adequate alternative theories for output. They produce what Einstein called “an embarrassment of riches”. Logically this multiplicity of alternative theories means that there may be alternative empirically warranted nontruth-functional hypothetical conditional statements in the form “For all A if A, then C” having alternative antecedents “A” and making different but empirically adequate predictions that are the empirically indistinguishable consequents “C”.
Empirical underdetermination is also manifested as conceptual vagueness. For example to develop his three laws of planetary motion Johannes Kepler, a heliocentrist, used the measurement observations of Mars that had been collected by Tycho Brahe, a type of geocentrist. Brahe had an awkward geocentric-heliocentric cosmology, in which the fixed earth is the center of the universe, the stars and the sun revolve around the earth, and the other planets revolve around the sun. But Kepler used Brahe’s astronomical measurement data, so measurement error was not the operative underdetermination permitting the alternative cosmologies. But Kepler was a convinced Copernican placing the sun at the center of the universe.
Kepler’s belief in the Copernican heliocentric cosmology made the semantic parts contributed by that heliocentric cosmology become for him component parts of the semantics of the language used for celestial observation, thus displacing Brahe’s complicated combined geocentric-heliocentric cosmology’s semantical contribution. Then hypothesizing with the simpler Copernican heliocentrism’s clarifying contributions to the observational celestial semantics, he developed his three laws after deciding that the orbit is elliptical.
Alternative empirically adequate theories due to empirical underdetermination are all more or less true. An answer as to which theory is truer must await further development of additional observational information or measurements that clarify the empirically inadequate test-design concepts. But there is never any ideal test design with “complete” information, i.e., with no vagueness or no measurement error. Pragmatist recognition of possible undecidability among alternative empirically adequate scientific explanations due to unavoidable
