Comment and Conclusion

          Mach and Duhem were not only Positivist philosophers of science; they were also practicing research physicists, who furthermore wrote histories of physics.  Carnap on the other hand was neither a practicing research physicist nor a historian of physics.  His philosophical work was remote from the physicists' research practices, because the Vienna Circle had an epistemological (i.e. metaphysical) agenda for scientific criticism, which did not actually operate in research physics.  Carnap aimed to construct a metalogic for science, but he did not apply his constructionalist tech­niques to the language used by scientists.  Instead he used the symbolic logic of Russell and Whitehead to substitute for the object language that he claimed he was investigat­ing.  But the symbolic logic is not useful to the physicist. Carnap and others such as Russell and Braithwaite hailed the development of the Ramsey sentence as a great philosophical achievement.  But it would be a rare physicist who would consider the Ramsey sentence at all con­sequential to either the practice or the history of physics.  The situ­ation is aptly stated by Radnitzky in the "Epilogue" in the first volume of his Contemporary Schools of Metascience (1968), where he says that the logical empiricists had not produced any metascience at all, because they did not study the producers of scientific knowledge or the production or even the results.  The post-Positivist philosophers rejected Positivism because they correctly recognized its irrelevance to research science and its inadequacy as a philosophy of science.
          When the post-Positivist philosophers rejected Positiv­ism, many of them also rejected its constructionalism.  Many Pragmatists in particular found their wholistic concept of the semantics of language incompatible with the mech­anistic and procedural character of logical constructionalism.  In the wholistic view the semantics of science makes the development of science a nonlogical process.  But they rejected too much, because the Logical Positivists' linguistic-analysis approach is more valuable than either the Russellian symbolic logic or the Logical Positi­vist philosophy of science, which used the logic.  In this age of the computerized discovery system Carnap's construc­tionalism and his metatheory of semantical systems may with certain noteworthy modifications be carried forward into contemporary and future methodology of science.  Some such modifications are as follows:

1.        A first important modification is that the object language that is constructed by a discovery system is not the Russellian symbolic logic; it is the mathematical equa­tions or other technical language actually used in the rele­vant science.  Scientists never use the Russellian symbolic logic for the expression of their theories, and Carnap’s use of the symbolic logic to express empirical science was never more than a caricature.  In his distinctive Primer of Quantum Mechanics Marvin Chester explicitly renders Dirac’s notational conventions as descriptive language.  Given Carnap’s interest in physics, his philosophical linguistic analyses would have been infinitely more interesting had he chosen Dirac’s operator calculus to illustrate the syntax, semantics, and pragmatics of an object language in science, especially with respect to his thesis of intensions and extensions.  Carnap’s philosophy might have evolved considerably in the process of developing such a linguistic analysis.

2.        A second modification of Carnap's work is the use of a computer language for the metalanguage.  The computer lan­guage gives the metalanguage a disciplined and procedural character that a colloquial metalanguage does not have.  The computer language in which the discovery system is written operates as a metalanguage in which the formation rules of the object language are expressed in computer instructions.  The discovery system in other words is a meta­language expressing a mechanized generative grammar.

3.         A third modification pertains to Carnap's concept of semantical rules that interpret a semantical system.  The semantical rules for interpreting a mechanically generated semantical system might be viewed as analogous to Carnap's meaning postulates, in that all of them are stated in the object language instead of the metalanguage, and are not like Carnap's rules of designation, which occur in the meta­language.  Two relevant types of semantical rules may be distinguished.  One type consists of those semantical rules that are the mechanically generated statements and equations.  These consist only of the statements constituting a mechanically generated and empirically acceptable theory, the outputted theory statements that are believed to be true.  But not all the semantical rules occurring in the object langu­age are mechanically generated.  A second type consists of test design statements, which are accepted independently of any statements of theory generated by the system, so that the generated theory is not tautological and can be tested independently.
       But the semantical rules for mechanically generated semantical systems are unlike Carnap's meaning postulates, because they are not just analytical sentences.  With Quine's rejection of any distinctively analytic truth it is possible to view sentences as both analytic and synthe­tic, and the semantical rules that describe the semantical interpretation of the object-language statements must be viewed as both analytic and synthetic sentences.  They are more like Quine's analytical hypotheses or discursive postulates.  These semantical rules might also be viewed as similar to Carnap's reduction sentences, which he says determine only "part" of the meaning of theoretical terms.  But Carnap has never explained how it is possible for the meanings of terms to have parts.  Viewing the sentences as both analytic and synthetic enables the empirical statements constituting the generated theory to exhibit the parts of the meanings of their constituent terms, just as analytic statements always have.  Test design statements and generated theory statements, both of which are believed to be true for empirical reasons and not due to the meanings of their con­stituent terms, are object-language statements functioning as semantical rules, each of which contribute parts to the meaning of each of their common descriptive terms.

4.         A fourth modification pertains to Carnap's idea of a state description.  The Carnapian state description is not a useful concept for describing the semantical systems genera­ted by mechanized discovery systems.  In fact it is not useful for science at all.  It consists of  "atomic" statements expressed in Russellian logic, and was conceived with the intent of explicating precisely the ideas of L-truth and A-truth.  The semantical systems gener­ated by the discovery systems contain only universal statements constituting the theories generated with the forma­tion rules in the computerized generative grammar.  In contrast to the semantical systems in Carnap's philosophy, which were devised for static analyses, the semantical systems in metascience are intended to describe the semantical changes occurring in the development of new theories, which is a dynamic procedure.  Accordingly the Carnapian idea of a state descrip­tion must be revised for describing the computer system in­put and output object language, in order to reveal the sem­antical changes produced by the discovery system.  The inputted information for the discovery system is drawn from the current cumulative state description consisting of the several theories that have been advanced to date by the particular scientific profession.  These theories supply the vocabulary inputted to the computerized discovery system.  This vocabu­lary has its semantics specified by semantical rules consis­ting of test design statements, which are common to both input and output state descriptions.   These test design statements are not changed by the discovery system, and they supply semantical continuity for identifying the subject of the theories independently of the theories.  The computerized discovery system generates a set of outputted state descriptions consisting of alternative empirically adequate theories, which are semantical rules describing the semantics of the new theor­ies.

5.        A fifth modification consists of replacing Carnap's theory of information with Shreider's semantical metatheory, if the concept of state description as revised in the manner described above is identified with Shreider's concept of thesaurus.  But unlike Shreider's theory there are actually two types of transformations involved.  Firstly there is the mechanized syntactical transformation, the generation of new theories which are the output messages.  And secondly there is also the semantical transformation on the part of the system users who communicate with the computer, when they attempt to interpret its output.  The computer system is a trans­mitter and information source that generates message texts consisting of new theories.  And the user receiving the message and having a thesaurus consisting of one of the input semantical systems, i.e. an old theory, must transform his thesaurus to conform to one of the output semantical systems, a new theory.  Thus the amount of information transmitted to a user depends on the degree of transformation between his initial thesaurus and the outputted theory that must transform his thesaurus for him to understand the new theory. The psycho­logical resistance might be large, if the amount of informa­tion communicated is large.  And there may also a philoso­phical resistance depending on the using-scientist's philosophy of science.  If the scientist is a Romantic, he will be philosophically ill disposed to accept the newly gener­ated theories containing large amounts of information, because he will find they are not "intuitively plausible" and do not "make sense.”   Romanticism retards the develop­ment of science, because it forbids the unfamiliar.  The Positivist like Mach will be less affected by such philosophical cog­nition constraints.   Positivists believe in the special importance of the familiar, which they call the "observable.”  But some, like Carnap, opposed "models" in which technologic­ally less accessible microphysical processes are explained on analogy with more familiar macrophysical processes.  The philosophy of science that offers the least impediment to the reception of new information is Pragmatism, according to which no ontology may even serve as a criterion for scientific criticism.