of theories.
The only criterion for scientific criticism that is acknowledged by the contemporary pragmatist is the empirical criterion.
The philosophical literature on scientific criticism has little to say about the specifics of experimental design. Most often philosophical discussion of criticism pertains to the criteria for acceptance or rejection of theories and more recently to the decidability of empirical testing.
In earlier times when the natural sciences were called “natural philosophy” and social sciences were called “moral philosophy”, nonempirical criteria operated as criteria for the criticism and acceptance of descriptive narratives. Even today some philosophers and scientists have used their semantical and ontological preconceptions as criteria for the criticism of scientific theories including preconceptions about causality or specific causal factors. Such semantical and ontological preconceptions have misled them to reject new empirically superior theories. In his Against Method Feyerabend noted that the ontological preconceptions used to criticize new theories have often been the semantical and ontological claims expressed by previously accepted theories.
But what historically has separated the empirical sciences from their origins in natural and moral philosophy is the empirical criterion, which is responsible for the advancement of science and for its enabling practicality in application. Whenever in the history of science there has been a conflict between the empirical criterion and any nonempirical criteria for the evaluation of new theories, it is eventually the empirical criterion that ultimately decides theory selection.
Contemporary pragmatists accept scientific realism, relativized semantics and thus ontological relativity, and they therefore reject all prior semantical or ontological criteria for scientific criticism including the romantics’ mentalistic ontology requiring social-psychological reductionism.
4.15 Logic of Empirical Testing
An empirical test is a decision procedure consisting of a modus tollens deduction from a set of one or several universally quantified theory statements expressible in a nontruth-functional hypothetical-conditional schema proposed for testing together with an antecedent particularly quantified description of the initial test conditions. These statements jointly conclude to a consequent particularly quantified description of a produced (predicted) test-outcome event, which is compared with the observed test-outcome description.
In order to express explicitly the dependency of the produced effect upon the realized initial conditions in an empirical test, the universally quantified theory statements can be schematized as a nontruth-functional hypothetical-conditional statement, i.e., as a statement with the logical form “For every A if A, then C.” The hypothetical-conditional statement represents a system of one or several universally quantified related theory statements or equations that describe a dependency of the occurrence of an event described by “C” upon the occurrence of an event described by “A”. The dependency may be expressed as the range of stochastic boundary limits for the values of predicted probabilities. For advocates who believe in the theory, the hypothetical-conditional statement is the theory-language context that contributes meaning parts to the complex semantics of the theory’s constituent descriptive terms including the terms common to the theory and test design. But the theory’s semantical contribution cannot be operative in the test for the test to be independent of the theory.
The antecedent “A” also includes the set of universally quantified statements of test design that describe the initial conditions that must be realized for execution of an empirical test of the theory together with the description of the procedures needed for their realization. These statements are always presumed to be true or the test design is rejected as invalid. They contribute meaning parts to the complex semantics of the terms common to theory and test design, and do so independently of the theory’s semantical contributions. The universal logical quantification indicates that any execution of the experiment is but one of an indefinitely large number of possible test executions, whether or not the test is repeatable at will.
When the test is executed, the logical quantification of “A” is changed to particular quantification to describe the realized initial conditions in the individual test execution. In a mathematically expressed theory the test execution consists in measurement actions and assignment of the resulting measurement values to the variables in “A”. In a mathematically expressed single-equation theory, “A” includes the independent variables in the equation of the theory. In a multi-equation system whether recursively structured or simultaneous, the exogenous variables are assigned values by measurement, and are included in “A”. In longitudinal models with dated variables the lagged-values of endogenous variables that are the initial condition for a test and that initiate the recursion through successive iterations to generate predictions, must also be included in “A”.
The consequent “C” represents the set of universally quantified statements of the theory that describe the predicted outcome of every correct execution of a test design. Its logical quantification is changed to particular quantification to describe the predicted outcome in an individual test execution. In a mathematically expressed single-equation theory, “C” is the dependent variable in the equation of the theory. When no value is assigned to any variable, the equation is universally quantified. When the prediction value of a dependent variable is calculated from the measurement values of the independent variables, it becomes particularly quantified. In a multi-equation theory, whether recursively structured or a simultaneous-equation system, the solution values for the endogenous variables are included in “C”. In longitudinal models with dated variables the current-dated values of endogenous variables that are calculated by solving the model through successive iterations are included in “C”.
The conditional statement of theory does not say “For every A and for every C if A, then C”. It only says “For every A if A, then C”. In other words the conditional statement of theory only expresses a sufficient condition for the production of the phenomenon described by C upon realization of the test conditions given by “A”, and not a necessary condition. Alternative test designs described in “A” are sufficient to produce “C”. This may occur for example, if there are theories proposing alternative causal factors for the same outcome described in “C”. Or if there are equivalent measurement procedures or instruments described in “A” that produce alternative measurements falling within the range of their measurement errors, such that the errors are small relative to the predicted values described by “C”.
Let another particularly quantified statement denoted “O” describe the observed test outcome of an individual test execution. The report of the test outcome “O” shares vocabulary with the prediction statements “C”. But the semantics of the terms in “O” is determined exclusively by the universally quantified test-design statements rather than by the statements of the theory, and thus for the test its semantics is independent of the theory’s semantical contribution. In an individual predictive test execution “O” represents observations and/or measurements made and measurement values assigned after the prediction is made, and it too has particular logical quantification to describe the observed outcome resulting from the individual execution of the test. There are three outcome scenarios:
Scenario I: If “A” is false in an individual test execution, then regardless of the truth of “C” the test execution is simply invalid due to a scientist’s failure to comply with its test design, and the empirical adequacy of the theory remains unaffected and unknown. The empirical test is conclusive only if it is executed in accordance with its test design. Contrary to the logical positivists, the truth table for the truth-functional Russellian logic is therefore not applicable to testing in empirical science, because in science a false antecedent, “A”, does not make the hypothetical-conditional statement true by logic of the test.
Scenario II: If “A” is true and the consequent “C” is false, as
