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where the alternative operations produce overlapping results.

      On the contemporary pragmatist philosophy a theory that has been tested is no longer theory, once the test outcome is known and the test execution is accepted as compliant with the test design. The nonfalsifying test outcome makes the theory empirically warranted, and it is thus deemed a scientific law until it is tested again at some future time and possibly falsified. The law is still hypothetical because it is empirical, but it is less hypothetical than it had been as a theory proposed for testing. The law may thereafter be used either in an explanation or in a test design for testing some other theory. But if the theory has been falsified, it is merely rejected language, although it may still be useful in application for its lesser empirical adequacy, realism and truth.

      For example the elaborate engineering documentation for the Large Hadron Collider at CERN, the Conseil Européen pour la Recherche Nucléaire, is based on previously tested science. After installation of the Collider is complete, the science in that engineering is not what is tested when the particle accelerator is operated for the microphysical experiments, but rather is presumed true and contributes to the test-design language for experiments performed with the accelerator.

      4.16 Test Logic Illustrated

      Consider the simple case of Gay-Lussac’s law for a fixed amount of gas in an enclosed container as a theory proposed for testing. The container’s volume is constant throughout the experimental test, and therefore is not represented by a variable. The theory is (T'/T)*P = P', where the variable P means gas pressure, the variable T means the gas temperature, and the variables T' and P' are incremented values for T and P in a controlled experimental test, where T' = T ± ΔT, and P' is the predicted outcome that is produced by execution of the test design.

      The statement of the theory may be schematized in the hypothetical-conditional form “For every A if A, then C”, where “A” includes (T'/T)*P, and “C” states the calculated prediction value of P', when temperature is incremented by ΔT from T to T'. The theory is universally quantified, and thus claims to be true for every execution of the experimental test. And for proponents of the theory, who are believers in the theory, the semantics of T, P, T' and P' are mutually contributing to the semantics of each other, a fact that could be made explicit in this case, because the equation is monotonic such that each variable can be expressed mathematically as a function of all the others by simple algebraic transformations.

      “A” also includes the test-design statements. These statements describe the experimental set up, the procedures for executing the test and initial conditions to be realized for execution of a test. They include description of the equipment used including the container, the heat source, the instrumentation used to measure the magnitudes of heat and pressure, and the units of measurement for the magnitudes involved, namely the pressure units in atmospheres and the temperature units in degrees Kelvin (K). And they describe the procedure for executing the repeatable experiment. This test-design language is also universally quantified and thus also contributes meaning components to the semantics of the variables P, T and T' in “A” for all interested scientists who accept the test design.

      The procedure for performing the experiment must be executed as described in the test-design language, in order for the test to be valid. The procedure will include firstly measuring and recording the initial values of T and P. For example let T be 200°K and P be 1.6 atmospheres. Let the incremented measurement value be recorded as ΔT = 200°K, so that the measurement value for T' is made to be 400°K. The description of the execution of the procedure and the recorded magnitudes are expressed in particularly quantified test-design language for this particular test execution. The value of P' is then calculated.

      The test outcome consists of measuring and recording the resulting observed incremented value for pressure. Let this outcome be represented by particularly quantified statement O using the same vocabulary as in the test design. Only the universally quantified test-design statements define the semantics of O, so that the test is independent of the theory. In this simple experiment one can simply denote the measured value for pressure by the variable O. The test execution would also likely be repeated to enable estimation of the range of measurement error in T, T', P and O, and the error propagated into P'. A mean average of the measurement values from repeated executions would be calculated for each of these variables. Deviations from the mean are estimates of the amounts of measurement error, and statistical standard deviations could summarize the dispersion of measurement errors about the mean averages.

      The mean average of the test-outcome measurements for O is compared to the mean average of the predicted measurements for P' to determine the test outcome. If the values of P' and O are within the estimated ranges of measurement error, i.e., are sufficiently close to 3.2 atmospheres as to be within the measurement errors, then the theory is deemed not to have been falsified. After repetitions with more extreme incremented values with no falsifying outcome, the theory will likely be deemed sufficiently warranted empirically to be called a law, as it is today.

      4.17 Semantics of Empirical Testing

      Much has already been said about the artifactual character of semantics, about componential semantics, and about semantical rules. In the semantical discussion that follows these concepts are brought to bear upon the discussion of empirical testing and test outcomes.

      If a test has a nonfalsifying outcome, then the semantics of the tested theory is unchanged for the theory’s developer and advocates. Since they had proposed the theory in the belief that it would not be falsified, their belief in the theory makes it function for them as a set of semantical rules. Thus for them both the theory and the test design are accepted as true, and after the nonfalsifying test outcome both sets of statements continue to contribute parts to the complex meanings of the descriptive terms common to both theory and test design, as before the test.

      But when the test outcome is a falsification, there is a semantical change produced in the theory for the developer and advocates of the tested theory who accept the test outcome as a falsification. The unchallenged test-design statements continue to contribute semantics to the terms common to the theory and test design by contributing their parts to the meaning complexes of each of the common terms. But the component parts of those meanings contributed by the falsified theory statements are excluded from the semantics of those common terms for the proponents who no longer believe in the theory due to the falsifying test outcome.

      4.18 Test Design Revision

      Empirical tests are conclusive decision procedures only for scientists who agree on which language is proposed theory and which language is presumed test design, and who furthermore accept both the test design and the test-execution outcomes produced with the accepted test design.

      The decidability of empirical testing is not absolute. Popper had recognized that the statements reporting the observed test outcome, which he called “basic statements”, require prior agreement by the cognizant scientists, and that those basic statements are subject to future reconsideration.

      Theory language is relatively more hypothetical than test-design language, because the interested scientists agree that in the event of a falsifying test outcome, revision of the theory will likely be more productive than revision of the test-design language.

      For the scientist who does not accept a falsifying test outcome of a theory, a different semantical change is produced than if he had accepted the test outcome as a falsification. Such a dissenting scientist has either rejected the report of the observed test outcome or reconsidered the test design. If he rejects the outcome of the individual test execution, he has merely questioned whether or not the test was executed in compliance with its agreed test design. Repetition of the test with greater fidelity to the design may answer such a challenge to the test’s validity one way or the other.

      But if in response to a falsifying test outcome the dissenting scientist has reconsidered the test design itself, then he has thereby changed the semantics involved in the test in a fundamental way. Reconsideration of the test design amounts to rejecting the test design as if it were falsified, and letting the theory define the subject

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