Aim of Science

          Popper's concept of scientific explanation and the rejection of the naturalistic theory of meaning implied by the falsificationist thesis of scientific criticism, in turn imply a new concept of the aim of science, which is very different from the views of the Positivists.  In his philo­sophical development two different types of statements of the aim of science may be distinguished, firstly the logical statement and then the later institutional statement.  As early as 1934 in his discussion of the degrees of testabil­ity in the Logic of Scientific Discovery he states that theoretical science aims to obtain theories that are easily falsifiable, because the theories have a large information content, a large class of potential falsifiers.  This con­cept of the aim of science is integral to Popper's view of the growth of scientific knowledge based on the idea of increasing empirical information content resulting from increasing falsifiability.  Similarly in "Truth, Rational­ity, and the Growth of Knowledge" he states that the task of science is a search for interesting truth in the sense of truth that has a high degree of explanatory power or empiri­cal information content.  In his later statements Popper added to these ideas of the aim of science the role of the historical problem situation with his idea of the metaphysi­cal research programme.  In the introductory chapter to Realism and the Aim of Science he describes science as a social institution, that results from human actions that are unforeseen and unintended.  He states that science grows through the institutionalized cooperation and competition of scientists, who are not only motivated by their own subjec­tive curiosity but also by their wish or aim to make a contribution to the growth of objective knowledge.  The phrases "social" and  "unforeseen and unintended" seem to refer to Popper's views on the nature of social science and to his rejection of all historical relativism.  Popper defines social science as the study of the unintended consequences of social behavior.  But what is unforeseen in the growth of science, is the new theories that result from conjectural scientific research.  The content of theories in future sci­ence is in principle unpredictable in Popper's view, and he rejects all historicisms that purport to predict history including the history of science.
          The strategic relevance of Popper's reference to the institutional character of science in the context of objec­tive knowledge becomes evident when contrasted with Kuhn's view that in the history of science the ontology of a pre­vailing theory assumes an institutional status.  It seems likely that Popper was led to think of the aim of sci­ence in institutional terms as a result of Kuhn's views.  Kuhn's thesis that the prevailing theory or paradigm assumes institutional status, means that the ontology of the preva­iling paradigm functions as the criterion for scientific criticism, and that therefore commonly recognized revolu­tionary developments in the history of science, which intro­duce a new theory and ontology into a science, must be viewed as institutional changes with no larger framework providing continuity.  In Popper's view this radical discon­tinuity is historical-relativist and irrational.  In his "Rationality of Scientific Revolutions" he paraphrases Marx, saying that the growth of science is "revolution in perma­nence", but Popper intends this phrase to mean that there exists criteria for scientific criticism that are invariant through even the most revolutionary developments, that make scientific change rational and meaningfully progressive.  Thus the force of Popper's statement that the growth of objective scientific knowledge is a social institution, is that the objective nature of science makes revolutionary scientific change a change within an enduring set of insti­tutional value standards, instead of a breakdown of the institution.  The criteria for scientific criticism that operate as the institutional values of the scientific community are in Popper's view independent of the semantics and ontology of the prevailing theory or paradigm.  As he says, science is “subjectless.”  In his 1982 "Introductory Comments" to Quantum Theory and the Schism in Physics Popper compares his idea of metaphysical research programmes to Kuhn's idea of paradigms, but nevertheless maintains that metaphysical research programmes can be rationally reconstructed and rationally criticized, even though they cannot yet be empirically tested.

Discovery

          Popper's rejection of the naturalistic theory of meaning had the interesting consequence of leading him to exclude consideration of the topic of scientific disco­very from philosophy of science, which he viewed as entirely a matter of logic and objective knowledge.  He believes that the topic of scientific discovery is exclu­sively a psychological and therefore subjective matter.  The conjec­tures resulting from the discovery process belong to world 3, but the discovery process itself belongs to world 2, and events in world 2 cannot determine the contents of world 3.  While this view offers very adequate recognition to the freedom in the creative discovery process, it also relegates a whole area of interest for philosophers to the empirical studies of the psychologists.  And as it happens, the topic of discovery has become a central concern of the emerging specialty of cognitive psychology, although Popper would reject the cognitive psychologists’ explicit psychologism.  Popper’s exclusion of discovery is perhaps due partly to his identification of traditional discussions of discovery with the "logic" of induction.  When he rejects inductive logic, he therefore rejects all logic from the discovery process.  He later modified this view, when he explained what he would admit to be possible with an "induc­tion machine.”  Considering the work done by contemporary information scientists working in artificial intelligence, Popper's later statements are more plausible.  Up to the present time at least, these information scientists would find it difficult to deny that the system designer of a discovery model must decide on what Popper calls "a repetition" of an event, which is to say the system designer must firstly conceptualize the input to the system.  The discovery systems are not unconditioned much less historicist, but must draw from the current state of the science under investigation for their input language.

Comment and Conclusion

          Popper`s philosophy was occasioned by Einstein's development of relativity theory, a milestone episode in the his­tory of science that Popper took to be paradigmatic of scientific progress.  And Popper's philosophy is also a mile­stone in the history of philosophy, because it represents a fundamental problem shift.  While Carnap and other Positiv­ists continued their efforts to establish theoretical sci­ence including Einstein's theory, on firm ontological foun­dations, Popper rejected the naturalistic theory of meaning that supposedly supplies such a foundation, and accepted the revision of scientific explanation as a matter of course.  Positivist foundational problems, such as the problem of the meaningfulness of theoretical terms, became pseudo problems as a result of Popper's problem shift, while the problem addres­sed by Popper, the rational growth of science without foun­dations, has become central to philosophy of science. 
          Popper's philosophy was not occasioned by the development of the modern quantum theory, and he spent much of his professional career attempting to reconcile his philosophy and the modern quantum theory.  It may be said that just as Carnap had attempted to reconcile Positivism and Einstein's relativity theory, so too Popper had attempted to reconcile his philosophy and the new quantum theory, except that Popper also presumed to revise the semantical interpretation of quantum theory.  In the meanwhile the Pragmatist philosophers have taken up a role relative to quantum physics, accepting it as the para­digm of modern physics, that Popper had taken up relative to Einstein's relativity theory.  As a result Popper's philosophy now represents the conservative position in the con­temporary professional literature of philosophy, a position that casts him in the role of more the defensive rear guard than the aggressive avant garde.
          One of the distinctive aspects of the historical development of quantum theory is the persistent plurality of semantical and ontological interpretations compatible with the same experimental measurements and mathematical formal­ism.  This plurality has caused lengthy controversies among the physicists; Lande's list of seven alternative interpre­tations may be taken as indicative of this plurality.  Pop­per's response to this situation in modern microphysics was to create still another interpretation for the quantum theory, his particle-propensity interpretation, because like Einstein, he rejects the schism in physics and believes that a uniform ontology for both microphysics and macrophysics is necessary. As it happens the history of physics has taken a different turn.  In 1968 Gabriel Veneziano resurrected an old mathematical formula called Euler’s beta function to develop what is now called string theory.  In 1974 Schwarz and Joel Scherk applied the string theory to incorporate gravitation, and in 1984 Green and Schwarz united gravitation with quantum theory, thereby starting the superstring revolution in physics.  However, the theory is not yet testable empirically.
          The Pragmatists reacted differently than Popper.  For them the quantum theory is the paradigmatic episode in the history of science, and their more accepting attitude has occasioned another problem shift in philosophy of science.  While some Pragma­tists express reason to advocate one or another particular interpretation of quantum theory as distinctively interest­ing from the viewpoint of philosophy of science, the reason is not the particular philosopher's prior ontological commit­ments.  Rather it often proceeds from a belief in the importance of the particular interpretation for scientific discovery (dis­covery is the topic that Popper did not consider even to be a part of philosophy of science).  The focus on the problem of scientific discovery has in turn occasioned the problem shift: philosophers have reconsidered the semantical and ontological pluralism represented by the different interpretations of quantum theory.  They have concluded that the pluralism is an outcome of certain properties of language, and that it is therefore a strategic condition for continu­ing the growth of science (growth is the topic that Popper considered to be central to philosophy of science).  In brief Popper's approach is to attempt to adjust the seman­tics and ontology of quantum physics to his philosophy of science, while the Pragmatists' approach has been to attempt to adjust philosophy of science to account for the phenomenon of semantical and ontological pluralism in science and to identify its function.
          As it happens, Popper's rejection of the naturalistic theory of meaning supplied philosophers with the point of departure for addressing this phenomenon of semantical pluralism, and they did so in ways that Popper did not accept.  The philosophical view that affirms an artifactual character of the semantics of language admits to a wholistic variation, that introduces an unresolvable cultural and historical relativism into science, which in turn makes problematic the intersubjective objectivity and rationality that Popper considers to be necessary for the growth of science.  The affirmation of this wholistic variation and its consequent linguistic relativism, is occasioned by the thesis that scientific change involves semantical change.  Popper's philosophy does not address the problem of semanti­cal change, because he identifies all attempts at semantical description or "meaning analysis" with essentialism.  As a result contemporary philosophers of science have moved on to new problems that Popper was unprepared and unwilling to address.
           Finally some comments are in order about Popper and the Positivists’ truth-functional logic. In addition to criticizing the Logical Positivists for their Positivism, Popper also refrained from using their favorite logic, the Russellian symbolic logic.  This logic is called a truth-functional logic, because the truth value of any compound statement, such as a conditional “material implication”, can be determined by reference to the truth values of its component elementary statements.  Therefore in the truth-functional logic the truth tables for all compound statements are complete for all combinations of truth values of the component statements, thus enabling the symbolic logic to have the closure of an algebra, which is very desirable for a mathematical system including a logic.  In contrast the nontruth-functional or Stoic conditional statement affirms the existence of a dependency connection between the truth values of the antecedent and consequent clauses, such that the truth of the compound statement is not determined by the truth values of the component clauses for most combinations of truth values.  The affirmed connection might for example be a logical one, as obtains between the premises and conclusion of the categorical syllogism.  The conditional statement expressing a syllogism would have an antecedent clause consisting of the conjunction of the major and minor premises and a consequent consisting of the conclusion.  As is well known, the conditional connection is the logical inference, which may be valid independently of the truth of its constituent statements - either in the conjunction of the premises in the antecedent clause or in the conclusion in the consequent clause.  The logical inference may be invalid such that the conditional statement is false, yet both of the premises in the antecedent and the conclusion may be true. Thus the conditional statement is not merely an oblique conjunction. Of greater interest in philosophy of science are those cases in which the nontruth-functional connection is an empirical hypothesis of a causal connection instead of a logical connection.  If the antecedent clause is false, then the truth of the conditional statement is unknown, because the empirical test is not valid when it is not executed in accordance with its test design.  If the antecedent is true, the test is valid, and the test outcome is not a falsification, then the theory can reasonably be believed for the time being, but its truth is not established.  The truth of the nontruth-functional conditional statement is known from the truth of its component statements only in the event of falsification.  The truth tables for truth-functional conditional and the corresponding nontruth-functional conditional logical forms are contrasted as follows, where T=”True” and F=”False”:

                    Truth-Functional                        Nontruth-Functional
                        Truth Table                                  Truth Table

                    A          B          A É B                 A          B          If A, then B.

        1.         T          T           T                       T          T           Not Falsified

        2.         T          F           F                       T          F           Falsified

        3.         F          T           T                       F          T           Invalid Test

        4.         F          F           T                       F          F           Invalid Test

            Consider the stereotypic universal “All ravens are black”, which Popper would consider a theory, since he considers all descriptive terms to be a type of theoretical term which the Positivists called “disposition terms.”  Then re-express the universal categorical proposition as a conditional statement in the form of a material implication, A É B, of the Russellian symbolic logic:

(x) (xRaven É xBlack).

This is conventionally rendered in English as “For all x, if x is a raven, then x is black”, or more colloquially as “For every thing, if a thing is a raven, then it is black.”  Popper’s falsificationist thesis of scientific criticism requires a nontruth-functional logic in which only the falsehood of the universally quantified conditional can be determined from knowledge of the truth values of its component elementary statements.  In this case the connection is a hypothesis or theory proposed for empirical testing. 
           The logic of the test resembles the modus tollens argument form, except that the truth of the conditional statement itself is in question rather than the truth of its component clauses.  The antecedent clause expresses the initial conditions of the experiment, and the clause is actually a rather complex description of the experiment.  When these conditions are realized in the execution of the experiment, then the antecedent clause is true.  The consequent clause expresses the predicted outcome of the test.  And the connection between the antecedent and consequent clauses is the universal hypothetical claim of the theory being tested.  If the description of actual test outcome described in the same terms as the consequent contradicts the consequent, such that the prediction is false, then the conditional hypothesis is falsified. This is the set of truth-values represented in the second line of the truth table displayed above for the nontruth-functional conditional compound statement. 
           The third and fourth lines of the nontruth-functional truth table represent those cases in which the antecedent is false, which is to say that the test was not executed correctly in accordance with its test design statements.  Nothing can be concluded about the theory expressed by the conditional statement from an invalid test execution.  The first line of the nontruth-functional truth table represents the case in which the test execution is valid, and in which the test outcome is as predicted by the expression constituting the consequent clause of the conditional hypothesis.  Scientists in the cognizant scientific profession may accept the tested and nonfalsified conditional hypothesis as what might be called a “working hypothesis”, which could be assumed as a test-design statement in a test of some other theory, but the conditional logic does not compel acceptance.  Nor does nonfalsification prohibit any scientist from reconsidering the hypothesis later, even though it has been tested and not been falsified.  Furthermore scientific theories are routinely more complex than the all-ravens-are-black stereotype.  There may be many alternative tested and nonfalsified theories with alternative antecedent clauses expressing alternative test designs from which a scientist may choose a working hypothesis for future research, because there may be multiple alternative sufficient conditions to produce the same predicted consequence.
          The Frege-Russellian “logistic” agenda to reduce mathematics to logic motivated the symbolic logicians to construct the truth-functional logic that firstly reduced logic to a closed mathematical algebra.  And the result has been a disservice to philosophy of science.  The Logical Positivist philosophers exercised themselves with their problem of so-called theoretical terms.  They believed that they are being very sophisticated and impressively technical by using the Russellian mathematical logic. Curiously the truth-functional truth table dictates that the truth of their so-called observation sentences occurring in the antecedent and consequent atomic sentences, guarantees the truth of the material implication connecting them, an implication which is a universal statement.  Yet even they did not maintain that material implications expressing empirical generalizations are eternal verities like the component observation sentences.  Nonetheless Philosophy of Science and British Journal of Philosophy of Science still contain enough Russellian chicken tracks to suggest that their pages have been trampled in a hen house of panicked birds convinced that the sky is falling.  Ironically for these philosophers of science who are still using the Russellian symbolic logic the sky has been falling for decades.  In due course even the lesser lights of the profession will recognize that the technical pretenses of the Russellian logic can no longer supply the façade of sophistication that had formerly masked its sophistic claim as the logic for science.

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