4.16 Test Logic Illustrated

For example consider the simple case of Gay-Lussac’s law for gasses in an enclosed container as a theory proposed for testing. The container’s volume is fixed throughout the experimental test, and 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 an experimental test.

The statement of the theory may be schematized in the hypothetical-conditional form “If A, then C”, where “A” includes (T’/T)*P, and “C” states the calculated prediction value of P’ after temperature is incremented from T to T’. The theory is universally quantified, because it claims to be true for every execution of the experimental test. And the semantics of T, P, T’ and P’ are mutually contributing to the semantics of each other for believers in the theory, since each variable can be expressed mathematically as a function of all the others.

The test-design statements are also included in “A”. They describe the experimental set up and initial conditions to be realized for execution of a test. These 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, such as the pressure units in atmospheres and the temperature units in degrees Kelvin. And they describe the procedure for performing the experiment. This test-design language is universally quantified and also contributes to the semantics of the variables P, T and T’ in “A”.

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 T = 200 degrees Kelvin and P is 1.6 atmospheres. Then the measurement value for T is incremented to T’, which might be 400 degrees Kelvin, and this incremented measurement value is recorded. A description of the execution of the procedure and the recorded magnitudes are expressed in particularly quantified language for this particular test execution.

The test outcome consists of measuring and recording the resulting observed incremented value of P’, which may be denoted P” and is represented by particularly quantified statement “O”. The universally quantified test-design statements also in “A” define the semantics of “O”. The test executions would also likely be repeated to estimate the range of measurement error in P, P’, T, T’ and P”. A mean average value would be calculated for each of these variables to estimate measurement errors. Deviations from the mean average value indicate the amounts of measurement error, and statistical standard deviations could summarize the dispersion of measurement errors about the means.

The mean average of the measures value P” is compared to the mean average of the value P’ to determine the test outcome. If the values of P’ and P” are within the estimated range of measurement error, i.e., are sufficiently close to 3.2 atmospheres as to be within the measurement errors, then “C” is deemed true, and the theory is sufficiently warranted empirically to be called a law, as it is today.


4.17 Semantics of Empirical Testing

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

Normally the semantics of a tested theory is such that if a test has a nonfalsifying outcome, then the semantics is unchanged for the developer and advocates of the tested theory. Prior to the test they had proposed the theory in the belief that it would not be falsified, and it consequently functions as a set of one or several semantical rules. Thus the universally quantified statements of both the theory and the test design are accepted as true, and after the nonfalsifying test outcome, each set of statements continues to contribute parts to the complex meanings of the terms common to both of them, 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 the 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

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

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 reconsidered the test-design statements or rejected the report of the test outcome. If he has rejected the outcome of the individual test execution, then he has merely questioned whether or not the test was executed in compliance with its agreed test design. Sometimes this is called “attacking the data”. If the test is repeatable at will, then repetitions of the test will likely answer the challenge to its validity.

But if he has challenged the test design itself, then he has thereby changed the semantics involved in the test in a fundamental way. This change amounts to rejecting the test design as if it were falsified, and letting the theory define the subject of the test and the problem under investigation – a role reversal in the pragmatics of test-design language and theory language. Then the theory’s semantics characterizes the problem, and the test design is deemed inadequate thus making the test design and the test execution irrelevant.

Popper rejects such a dissenting response to a test, calling it a “content-decreasing stratagem”, which is in fact what it is given the semantical outcome for the test design. He admonishes that that the fundamental maxim of every critical discussion is that one should "stick to the problem”. But the dissenting scientists may decide that the design of the falsifying test is a misconception of the problem that the tested theory is intended to solve, especially 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 terms common to the theory and test-design statements.

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


4.19 Empirical Underdetermination

An important factor affecting the decidability of empirical testing is the empirical underdetermination of language with the result that empirical criteria cannot always result in unambiguous theory-testing decisions. Two manifestations of empirical underdetermination are conceptual vagueness and measurement error. All concepts have vagueness that can be reduced indefinitely but never be eliminated completely. Mathematically expressed theories use measurement data that contain some measurement error in all but the simplest cases that are not typically found in science. Measurement error can be reduced indefinitely but never eliminated completely.

Scientists prefer measurements and mathematically expressed theories, because they can measure the amount of error in the theory, when the theory is tested. But separating measurement error from a theory’s prediction error can be problematic. Repeated execution of the measurement procedure enables estimation of the degree or range of measurement error. A test is conclusive to the extent that the measurement error is small relative to the predicted outcome.

Empirical tests are conclusive only to the extent that empirical underdetermination is manifestly small relative to the effect predicted in an empirical test.


4.20 Scientific Pluralism

All language is always empirically underdetermined by reality. Empirical underdetermination explains how two semantically alternative empirically adequate theories can have the same test-design language. It may occur that there are several semantically different theories yielding prediction errors that are different from one another but with differences that are small enough to be within the range of the estimated measurement error. In such cases empirical underdetermination due to the given test design has imposed undecidability on the choice among the alternative individual theories.

The problem of 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 geocentrist. Thus both these astronomers not only used the same test-design semantical contributions for the meanings in their observational concepts for identifying the planet Mars and for measuring its celestial movements, but they also used the same astronomical measurement data. In those days no test-design observations or measurements were informative enough to enable an empirical decision between the two cosmologies, and for many years both cosmologies were empirically adequate.

Kepler nonetheless believed in the heliocentric cosmology, and this belief made the semantic parts contributed by the heliocentric cosmology become for him component parts of the semantics of the language used for celestial observation, thus displacing the geocentric cosmology’s semantical contribution. Then hypothesizing with the heliocentric clarifying contributions to the celestial semantics, he developed his planetary laws for Mars.

Thus as Hanson said in Patterns of Discovery, observation language is “theory-laden”. And as Feyerabend noted in Against Method, Galileo practiced “counterinduction”. Galileo believed in the heliocentric cosmology, and counterinduction enabled him to create a new observation language, as did Kepler. By using heliocentric concepts in his Dialogue he revised and clarified apparently falsifying observational evidence alleged by the Aristotelian geocentrists. Similarly in 1926 Heisenberg had practiced counterinduction for describing the electron tracks in the cloud chamber, and he then developed his uncertainty relations.

But like geocentrism and heliocentrism in Galileo’s day, alternative empirically adequate theories due to excessive empirical underdetermination are all more or less true. An answer as to which theory is truer must await further development of additional observational information that clarifies the inadequate test-design concepts. But there is never any ideal test design with “complete” information, with no vagueness or no measurement error. Pragmatist recognition of undecidability among alternative empirically adequate scientific explanations due to empirical underdetermination is called the thesis of “scientific pluralism”.

Scientific pluralism is the coexistence of empirically adequate alternative explanations due to undecidability among alternative laws, permitted by test-design language that is too underdetermined empirically.


4.21 Scientific Truth

What is truth! Truth is a property of descriptive language. Furthermore as Jarrett Leplin maintains, truth and falsehood are properties admitting to more or less. They are not simply dichotomous, as they are represented in two-valued formal logic. Tested and nonfalsified statements are more empirically adequate, have more truth, and have ontologies that are more realistic than falsified statements. Falsified statements have recognized error, and may simply be rejected unless they are still useful for their lesser realism and lesser truth. As the classical pragmatists believed, what has utility has truth.

Popper said that the famous eclipse test of Einstein’s theory of gravitation in 1919 “falsified” Newton’s theory and thus “corroborated” Einstein’s. Yet the U.S. National Aeronautics and Space Administration (NASA) today uses Newton’s laws to navigate interplanetary rockets and satellites through our solar system. Thus it must be said that Newton’s “falsified” theory is not completely false or it could never be used, even for nineteenth-century ballistics.

Popper said that science does not attain truth. Contrary to Popper, contemporary pragmatists believe that with such an idea, truth has been misconceived. Theories are falsified by empirical tests, but it need not be said with Popper that truth is unattainable for scientists. Advancement in empirical adequacy is advancement in truth. And a theory with more truth is a theory with a more realistic ontology.


4.22 Nonempirical Criteria

Given the dilemma of having semantically alternative explanations that are tested and not falsified due to empirical underdetermination in the test designs, philosophers have proposed nonempirical criteria that they believe have been operative historically in explanation choice. But no such nonempirical criterion enables a scientist to predict reliably which alternative nonfalsified explanation will survive new empirical testing, when in due course the degree of empirical underdetermination is reduced by improved test design.

Test designs are improved by developing more accurate measurement procedures having less measurement error and/or by adding descriptive information that reduces the vagueness in the characterization of the subject for testing. Such test-design improvements refine the characterization of the problem addressed by the theories

When empirical underdetermination makes testing undecidable, different scientists may have personal reasons for preferring one alternative explanation to another. In such circumstances selection may be a decision for the career scientist rather than an investigative decision. The scientist is speculating on future science and also seeking professional acceptance. Knowing what a journal editor and his selected referees currently like to see in submissions helps getting a paper published in the peer-reviewed literature, which is an academic status symbol with the more prestigious journals paying out more brownie points for the accumulation of academic remuneration, promotion and tenure. Academic journal editors and their selected referees are nearly always the risk-avoiding rearguard rather than the risk-taking avant-garde. They are the established “authorities” who defend the received conventional wisdom in which they and their journals have a reputation-based vested interest.


4.23 The “Best Explanation” Criteria

As noted above, Thagard’s cognitive-psychology system ECHO developed specifically for theory selection has identified three nonempirical criteria. His simulations of past episodes in the history of science indicate that the most important criterion is breadth of explanation, followed by simplicity of explanation, and finally analogy with previously accepted theories. Thagard considers these nonempirical selection criteria as inferences to the “best explanation”.

The breadth of explanation criterion seems similar to Popper’s aim of maximizing information content. In any case there have been successful theories in the history of science, such as Heisenberg’s uncertainty relations, which do not have any of these characteristics. And as Feyerabend noted in criticizing Popper’s view in Against Method, Aristotle’s physics identified four causes, material, formal, efficient and final, while Newton’s only identified one kind of cause, the efficient cause. Aristotle’s explanations therefore may be said to have greater breadth, but his physics was less empirically adequate.

Contemporary pragmatists acknowledge only the empirical criterion. They exclude all nonempirical criteria from the aim of science, because while relevant to persuasion to make theories appear “convincing”, they are irrelevant to evidence. They are like the psychological criteria that trial lawyers use to select and persuade juries in order to win lawsuits in a court of law, but which are irrelevant to courtroom evidence rules for determining the facts of a case.


4.24 Nonempirical Linguistic Constraints

The constraint imposed upon theorizing by empirical test outcomes is the empirical constraint. It is a regulating institutionalized cultural value that is not viewed as an obstacle to be overcome, but rather as a condition to be respected for the advancement of science. The only other cultural constraint that must be respected is the moral constraint, which is a criterion external to the institution of science, and which cannot be judged either by science or by philosophy of science.

However, there are other kinds of constraints that are retarding impediments that must be overcome for the advancement of science. Some of these nonempirical impediments are purely circumstantial like those mentioned above. They are external to science. But there are two other nonempirical constraints that are internal to science in the sense that they are inherent in the nature of language, which science must use. These two constraints may be called the “cognition constraint” and the “communication constraint”.


4.25 Cognition Constraint

The cognition constraint inhibits a scientist’s ability to construct new theories, and it is manifested as what is often mundanely referred to as lack of imagination, creativity or ingenuity. Semantical rules are not just rules. They are also linguistic habits that enable fluency in both speech and thought.

As mentioned above, given belief in some universally quantified affirmative statement, the predicate in that affirmation determines part of the meaning complex of its subject term. Conversely given the conventionally established meaning of a descriptive term, certain related beliefs are sustained with the result that change of belief is made difficult by the need to change meanings that are reinforced by linguistic fluency. In his book Concept of the Positron Hanson identified what he called a “conceptual constraint” that operated as a semantical impediment to the discovery of the positron.

This thesis is opposed to the neutral-language thesis that language is merely a passive instrument for thought. Language is not merely a passive instrument for thought. It has a formative influence on thought. The formative influence of language on thought is recognized by the Sapir-Whorf hypothesis and specifically Benjamin Lee Whorf’s thesis of linguistic relativity set forth in his “Language, Mind and Reality” reprinted in Language, Thought and Reality.

Accordingly the more revolutionary the revision of beliefs, the more constraining the semantical structure and psychological conditioning on the creativity of the scientist who would develop a new theory. And if a new syntax is required such as an unfamiliar mathematics, then the semantical restructuring of the affected meaning complexes is all the more demanding.

It is noteworthy that the use of computerized discovery systems circumvents this problem, because the machines have no linguistic habits. They strategically yet mindlessly apply mechanized procedures to object-language syntactical inputs, which may be counted as one of their virtues.


4.26 Communication Constraint

The communication constraint is similar to the cognition constraint. It is the impediment to understanding a new theory relative to those currently conventional. The impediment is both cognitive and psychological. The scientist must cognitively learn the new theory well enough to restructure the composite meaning complexes associated with the descriptive terms common both to the old theory he already knows and to the new theory to which he is exposed. And this involves overcoming existing linguistic fluency enabled by psychological habit, which reinforces existing beliefs.

This learning process suggests the conversion experience described by Kuhn in revolutionary transitional episodes, because the new theory must firstly be accepted as true however provisionally for its semantics to be understood, since only statements believed to be true can operate as semantical rules. If testing demonstrates the new theory’s superior empirical adequacy, then the new theory’s acceptance will eventually make it the established conventional wisdom.

If the differences between the old and new theories are very great, some members of the affected scientific profession may be unwilling or unable to accomplish the required learning adjustment. They become the rearguard who cling to the received conventional wisdom, which is challenged at the frontier of research, where there is much conflict that produces confusion due to semantic dissolution. In the meanwhile the developer together with the more opportunistic and typically younger advocates of the new theory, who have been motivated to master the new theory’s language in order to exploit its perceived promise, assume the avant-garde role.

It is noteworthy that contrary to Kuhn and especially to Feyerabend the transition does not involve a complete semantic discontinuity much less any semantic incommensurability. And it is unnecessary to learn the new theory as though it were a completely foreign language. For the terms common to the new and old theories, the component parts contributed by the new theory replace those from the old theory, while the parts contributed by the test-design statements remain unaffected by the change. Thus the test-design language component parts shared by both theories constitute common and commensurating semantics providing semantical continuity and enabling characterization of the same subject of both theories independently of the distinctive claims of either theory. The shared semantics in the test-design language also facilitates learning and understanding the new theory, however radical the new theory may be. Or if excessive empirical underdetermination for the present prohibits a decisive test design, the currently vague characterizations of the subject of the theories enable semantical continuity, such as it is.

It may be noted that the scientist viewing the computerized discovery system output experiences the same communication impediment with the machine output that he would were the outputted theories developed by a fellow human scientist.

In summary both the cognition constraint and the communication constraint are based on the following semantical fact:

Given the conventionally established meaning of a descriptive term, certain implied beliefs are reinforced by habitual linguistic fluency with the result that the term’s conventional meaning impedes a change in those beliefs.


4.27 Scientific Explanation

Explanation is the ultimate aim of basic science. There are other types such as the historical explanation, but only explanation in basic science is of interest in philosophy of science. When some course of action is taken in response to an explanation such as a social policy, a medical therapy or an engineered product or structure, then the explanation is utilized in applied science.

The logical form of the explanation in basic science is the same as that of the empirical test. The universally quantified statements constituting a set of one or several scientific laws in an explanation can be schematized as a nontruth-functional hypothetical-conditional statement in the logical form “If A, then C”. But while the logical form is the same for both the test and the explanation, the deductive arguments are different.

The deductive argument of the explanation is the modus ponens argument instead of the modus tollens logic used for testing. In the modus tollens argument the hypothetical-conditional expressing the proposed theory is falsified, when the antecedent clause is true and the consequent clause is false. On the other hand in the modus ponens argument for explanation both the antecedent clause and the hypothetical-conditional statements are accepted as true, such that affirmation of the antecedent clause concludes to a valid affirmation of the consequent clause.

The schematic form of an explanation is: “If A, then C.” “A is affirmed.” “Therefore C is affirmed.” The statement “If A, then C” represents the universally quantified law statements. “A is affirmed.” is the particularly quantified statements describing the realized initial conditions that cause the explained phenomenon. “Therefore C is affirmed.” is the particularly quantified statements affirmed deductively and describing the explained individual effect, which may be a prediction of the event.

In the explanation the statements in the hypothetical-conditional schema express scientific laws accepted as true due to their empirical adequacy as demonstrated by nonfalsifying tests. The antecedent statements describing the initial conditions in the explanation together with the law statements jointly constitute the explicans or explaining language. And the logically consequent language is the explicandum describing the explained phenomenon.

A scientific explanation is a modus ponens deduction with one or several explaining universally quantified law statements expressible as a nontruth-functional hypothetical-conditional schema together with particularly quantified antecedent language describing initial conditions, which jointly conclude to particularly quantified consequent language describing the explained event.

It has also been said that theories “explain” laws. Neither untested nor falsified theories occur in an explanation. Explanations consist of laws, which are formerly theories that have since been tested with nonfalsifying outcomes. Proposed explanations are merely untested theories.

Since all the universally quantified statements in the nontruth-functional hypothetical-conditional schema of an explanation are laws, the “explaining” of laws means that a set of logically related laws forms a deductive system partitioned into dichotomous subsets of explaining antecedent axioms and explained consequent theorems.




Note: BOOK I is available as an ebook titled Philosophy of Science: An Introduction.
 

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