Pragmatics and Theory Language

         Pragmatics is the fourth and the most inclusive of the metalinguistic perspectives.  Pragmatics pertains to the language user’s use of his language understood as semantically interpreted syntax and associated ontology.  The controlling pragmatics of basic science is described in the statement of the aim of science: to create explanations by the development and empirical testing of theories that are laws because they are not falsified when tested.  Explanations and laws are accomplished science; theories are work in process at the frontier of development.
         Scientific theories are universally quantified semantically interpreted syntactical structures proposed for testing.  This is the definition of theory language in the contemporary Pragmatist philosophy of science.  It contains the traditional idea that theories are hypotheses, but the reason for their hypothetical status is not due to the Positivist observation-theory dichotomy. The Positivist observation-theory dichotomy is based on the semantical thesis that observation sentences have a naturalistic semantics acquired by observation, and that theory language has no semantics unless and until it is logically related to observation statements with reduction sentences. But when the observation-theory dichotomy falls, so too must the semantical basis for identifying theory language.
         Today the contemporary Pragmatists have replaced the semantical basis for identifying theory language with a pragmatic one: theories are hypothetical because they are untested and are proposed for testing.  Actually all universally quantified statements are hypothetical in the sense that they cannot be incorrigibly true and beyond revision.  But theories are those statements that are selected as relatively more hypothetical and more likely to be revised when testing shows revision is needed.  Empirical testing is the pragmatics of theory language in science.  After its test outcome is known, the theory is no longer a theory.  The test outcome transforms the theory into either a law or a falsified discourse.  Furthermore at some later time a law may revert to a theory to be tested again.  For about three hundred years Newtonian mechanics had been received as paradigmatic of scientific law in physics.  But Newton’s theory of gravitation was tested again in the famous Eddington eclipse experiment of 1919, after Einstein had proposed his alternative general relativity theory.  For a brief time early in the twentieth century Newton’s “theory” was actually a theory again. 
         The term “theory” is thus ambiguous in contemporary usage.  Both the traditional and the pragmatic meanings continue to be used.  In the traditional sense we still speak of Newton’s “theory” of gravitation.  In the pragmatic sense it is now falsified physics in basic science, although it is still used by engineers whose applied-science purposes can accept its known error.  But this knowledge of the error means that Newtonian mechanics is no longer either a hypothesis for testing or our law-based explanation of the physical universe.  Hanson recognized this difference between the pragmatic and traditional meanings of “theory” in his distinction between “research science” and “almanac science.”

Pragmatic Definition of the Language of Test Design and Observation

         Accepting or rejecting the hypothesis that there are red ravens presumes a prior agreement about the semantics needed to identify a bird’s species.  Similarly the empirical test of a scientific theory presumes a prior agreement about the semantics needed to identify the test subject, to set up the test apparatus, to perform the test operations, and to characterize the test’s initial conditions and outcome.  This is done with the test design language.  Pragmatically theory is universally quantified language that is proposed for testing, and test-design language is universally quantified language that is presumed for testing.  Both types of language are believed to be true, but for different reasons.  Test-design statements are presumed true with definitional force for executing the test, while the advocates of the theory propose the theory statements as true with sufficient plausibility for testing with an expected nonfalsifying outcome. The descriptive terms common to both the test-design statements and the theory statements thus have their semantics determined jointly by both sets of universally quantified statements. 
         Observation sentences are test-design sentences and test-outcome sentences with their logical quantification changed from universal to particular quantification for executing the test and for reporting its observed outcome.  To describe an individual test execution, the test-design statements have their quantification changed from universal to particular, and are then called observation statements for describing the concrete test.  This is a pragmatic sense of observation language, because it depends on the use of the language and not on the semantics.  Unlike the Positivists the Pragmatists recognize no inherently observational semantics.  The statement predicting the test outcome is a statement of the tested theory with its quantification made particular for the individual test.  After the test is performed, the statement reporting the test outcome also has particular quantification for the individual test and is observation language.  Whether or not the actual test outcome agrees with the theory’s prediction, both the prediction statement and test-outcome statement have the same vocabulary, and their semantics are the same in so far as their descriptive semantics is definable by reference to the universally quantified test-design statements.  Herein lies independence of the test from the theory.  Herein also lies the semantical continuity throughout the test for each of the terms common to the test design and the theory regardless of the test outcome, because the parts of the complex semantics defined by the test-design statements are unchanged throughout the test.  The statement reporting the test outcome is an observation statement describing what was observed in the test execution.  But the prediction statement is not as such an observation statement; it is only incidentally an observation statement when the test outcome is nonfalsifying, such that the prediction is the same as the test-outcome statement. All scientists define the semantics of their observation language when they formulate and accept test designs.  Feyerabend had hit upon an important historical insight when he said that in defending the Copernican heliocentric theory Galileo had created his own observation language.

Semantic Individuation of Theories

         Theory language is defined pragmatically, but theories are individuated semantically.  Theories may be individuated in either of two ways. Firstly different theory expressions are different theories because they address different subjects.  Theory expressions may be different theories, because they are unrelated; their subjects individuate them. Different theory expressions having different test designs are different theories, because the test-design language identifies the subject of the test. Secondly different theory expressions are different theories because each makes contrary claims about the same subject, where different claims usually means different predictions. They have different semantics.  Occasionally there is more than one theory proposed for empirical testing with the same set of test-design statements.  Since the proposals are all universally quantified and are proposed for testing, they are all instances of theory language. While they have the same test-design statements and therefore all address the same subject, they are not the same theory, because they make contrary claims about the same subject.

Diachronic Comparative Static Semantical Analysis

         There has been much confusion due to philosophers’ failure to recognize principles for the individuation of theories.  Many philosophers state that theories are not falsified by empirical tests, because all theory choice is comparative, and because scientists retain a falsified theory until a better theory is developed and tested with a nonfalsifying outcome.  But when it is said that scientists retain a falsified theory, the response of the scientists is not adequately described.  What should be said is that when the scientist tries to save the theory by making adjustments to it, he has made a new theory.  When the adjustments are not merely ad hoc, but are attempts to modify the universal claims of the theory even in relatively minor ways, in order to enable it to survive a previously falsifying test design, then the original theory has been discarded and a new theory developed. 
         Theories modified to produce improved predictions while retaining the same test design are different theories.  If a change of the test-design has the effect of reducing semantical vagueness or measurement error, the outcome of the empirical test with the modified design may or may not be a falsification of the previously tested and nonfalsified theory.  But modified test designs that produce improved predictions produce different theories, which in turn results in a new state description.  When the universal statements or equations in either the new theory or test design are used as semantical rules for semantical analysis, the change in meaning of the descriptive terms common to both state descriptions are exhibited by comparison between the two successive state descriptions.  Universal statements that are the same in both state descriptions exhibit semantical continuity, while those that have changed or replaced exhibit semantical change.  As noted above, such comparison is not possible with a wholistic (or “holistic”) view of semantics.

Mathematical Language in Science  

         The stereotypic “All ravens are black” categorical type of statement is not typically the form used explicitly in the object languages of science.  The object language of science is more often expressed either in colloquial language or in mathematical language.  Colloquial discourse is often implicitly universal with universality intended.  In such cases the grammatical form may lack definite articles or quantifiers, and may be without a copula explicitly containing a form of the verb “to be.”  Colloquial language is often called the “informal” language of science.  The informal colloquial expressions can be transformed into the categorical form although usually at the expense of awkward style.
         A mathematical language for science is an object language for which the syntax is supplied by mathematics. The syntax includes the notational symbols and the formation and transformation rules.  Whenever possible the object language of science is mathematical rather than colloquial.  This preference is not due to an aesthetic appreciation for deductive elegance.  Mathematical syntax is preferred, because measurement quantification of the subject of discourse enables the scientist to quantify the error in his theories, after estimates are made for the measurement errors by repetition of the measurements.

Universal Quantification in Mathematical Language in Science

         Mathematical language in science is universally quantified when descriptive variables have semantics but no associated numerical values.  It is particularly quantified when numeric values are associated with the descriptive variables either by measurement or by calculation from measurement values.  Like the categorical statements, the mathematically well formed formulas, usually equations, are explicitly quantified logically as either universal or particular, even though the explicit indication is not with such logical quantifiers as “every”, “all”, or “no.”  Universal quantification is changed to particular quantification in mathematical language, when measurements are made for an ongoing empirical test situation and are associated with the descriptive variables in the equation.  When an equation is particularly quantified logically by association with measurement values, it may be said to describe a numerical measurement instance.  In the case of quantum theory the situation is distinctive by the fact of duality, which means that not all the variables such as those representing momentum and position can have specific values simultaneously.  But realizing a value for any one of them makes the logical quantification particular.  Quantification is also changed similarly, when numeric values are associated with descriptive variables by computation with the equation and measurement values. When an equation is particularly quantified logically by association with such computed values, it may be said to describe a numerical empirical instance, since the referenced instance has not been measured.  This occurs when an equation is used to make a quantitative prediction, and the numerical empirical instance is the predicted value intended to be compared with a measurement value for the same phenomenon in an empirical test.

Semantics of Mathematical Language in Science

         The semantics for a descriptive variable is determined by the context consisting of statements and/or equations believed to be true.  The semantics-determining statements include measurement language describing the subject measured and the measurement procedures and any employed apparatus.  Like the Positivist “operationalist definitions” the statements setting forth the measurement procedures and apparatus contribute meaning to the descriptive term.  But unlike the operationalist definitions, each statement does not constitute a separate definition for the measured subject, thereby making the term equivocal.  Instead different measurement procedures contribute different parts to the one univocal meaning of the descriptive term, unless and until the different procedures are found to produce different measurement values, where the differences are greater than estimated measurement error.  Semantics for the descriptive variables in the theory is also supplied by the equations of the theory itself, such that the structure of their meaning complexes is in part mathematical.

Ontology of Mathematical Language in Science

         In the categorical proposition the quantified subject term references individual instances and also describes the attributes that enable identifying the instances, while the predicate term only describes attributes.  In an older vocabulary the same idea is expressed by saying that the subject term has personal supposition, while the predicate has only simple supposition.  Both categorical statements and colloquial discourse have been called the “thing language”, because the instances referenced are “things” or “instantiated entities.”  Attributes manifest the things of which they are aspects, and enable classification of the manifested things into kinds.  The things thus classified and the attributes thus manifested the ontology of the categorical proposition believed to be true.  The ontological claim is made explicit by the term “is” in the copula. 
         However, the ontological claim made by the mathematical equation is not about instances that are things or entities.  The individual instances referenced by the mathematical equation are numerical measurement instances.  The measurement instances are related to thing instances and their attributes by the colloquial statements describing the measured subject, the metric, and the measurement procedures including any apparatus, which typically occur in the test design language.

Aside on the Ontological Issue in Quantum Theory

         An ontological issue in modern quantum theory in microphysics is about whether or not microphysical waves and particles are two aspects of the same entity.  The affirmative view is called the “duality” thesis.  Its advocates cite the de Broglie equation relating both wave and particle properties, and also note that the mathematical expression for the wave function can be transformed into the mathematical expression for the matrix mechanics.  One version of the negative view is called the “pilot wave” thesis, which affirms the separate reality of wave and particle, and says that they always found together as exhibited in the Young two-slit experiment.  Other versions deny the reality of either the wave or the particle.  This ontological issue cannot be resolved by appeal to the mathematically expressed theory, because the mathematics says nothing about entities.  It only references numerical measurement instances.  Bohm was correct in maintaining that the interpretation issue of the quantum theory is in the informal language of physics, and not in the theory’s mathematics.  The issue about entities is supplementary to the mathematically expressed and empirically tested quantum theory.  This ontological issue has therefore continued for many decades, as each side advocates its preferred informal language and associated ontology to address the question of individual entities.  The issue is a variation on the ontological problem of the red raven.

Dynamic Diachronic Metalinguistic Analysis

         Turn next to the dynamic diachronic metalinguistic analysis, the examination of the processes of how the language of science changes through time from one language state to a later one.  Language changes in science result from the two basic types of research functions: theory development and theory testing.  The linguistic changes are not merely incidental to the performance of basic research, since the product of basic science is new language consisting of theories hopefully yielding laws and explanations.  A change of state description is produced whenever a new theory is proposed, and whenever a proposed theory is tested by the most critically empirical test that can be applied at the current time.  If the test outcome is a falsification, the proposed theory is eliminated from the current state description.  When the test outcome is not a falsification a theory has become a new law in the state description.   

Pages [1] [2] [3] [4] [5] [6]
NOTE: Pages do not corresponds with the actual pages from the book