then the theory is falsified, because the hypothetical conditional “For every A if A, then C” is false. Falsification occurs when the statements “C” and “O” are not accepted as describing the same thing within the range of vagueness and/or measurement error, which are manifestations of empirical underdetermination. The falsifying logic of the test is the modus tollens argument form, according to which the conditional-hypothetical statement expressing the theory is falsified, when one affirms the antecedent clause and denies the consequent clause. This is the falsificationist philosophy of scientific criticism advanced by Charles S. Peirce, the founder of pragmatism, and later advocated by Karl Popper. Readers seeking more on Popper are referred to BOOK V below.
The response to a falsification may or may not be attempts to develop a new theory. Scientists will not simply deny a falsifying outcome of a test, if they have accepted its test design and test execution. Characterization of falsifying anomalous cases is informative, because it contributes to articulation of a new problem that a new and more empirically adequate theory must solve. Some scientists may, as Kuhn said, simply believe that the anomalous outcome is an unsolved problem for the tested theory without attempting to develop a new theory. But such a response is either an ipso facto rejection of the tested theory, a de facto rejection of the test design or a disengagement from attempts to solve the problem. And contrary to Kuhn this procrastinating response to anomaly need not imply that the falsified theory has been given institutional status, unless the science itself is institutionally retarded. Readers seeking more on Kuhn are referred to BOOK VI below.
Scenario III: If “A” and “C” are both true, the hypothetical-conditional statement expressing the tested theory is validly accepted as asserting a causal dependency between the phenomena described by the antecedent and consequent clauses. The hypothetical-conditional statement does not merely assert a Humean constant conjunction. Causality is an ontological category describing a real dependency, and the causal claim is asserted on the basis of ontological relativity due to the empirical adequacy demonstrated by the nonfalsifying test outcome. Because the nontruth-functional hypothetical-conditional statement is empirical, causality claims are always subject to future testing, falsification, and then revision. This is also true when the conditional expresses a mathematical function.
Furthermore if the test design is modified such that it changes the characterization of the subject of the theory, then even a nonfalsifying test outcome should be reconsidered and the theory should be retested for the new definition of the subject. If the retesting produces a falsifying outcome, then the new information in the modification of the test design has made the terms common to the two test designs equivocal and has contributed parts to alternative meanings. But if the test outcome is not falsification, the new information is merely new parts added to the univocal meaning of the terms common to the old and new test-design language. Such would be the case if the new information were what the positivists called a new “operational definition”, as for example a new and additional way to measure temperature for extreme values that cannot be measured by the old operation, but which yields the same temperature values within the range of measurement errors, 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
