The propensity interpretation is consistent with Popper's particle interpretation of the quantum theory, that he had advanced years before in Logic of Scientific Disco­very.  According to Popper`s particle interpretation the Heisenberg uncertainty relations are statistical scatter relations that describe the lower limits of the dispersion of particles; they are not the upper limits of the accuracy of measurements, as Heisenberg maintains.  The uncertainty relations apply only to the magnitudes that belong to the particle after the disturbing measurement has been made.  The particle always has position and momentum, and both position and momentum up to the instant of measurement can be ascertained in principle with unlimited accuracy.  It is not the impossibility of precise measurement, but the statistical scatter that makes it impossible to predict the path of the particle after the disturbing measurement oper­ation.  The scatter relations are statistical predictions about paths, and the paths must be measurable in order to test the statistical theory.  For these reasons Popper rejects Heisenberg's view, as Popper sees it, that the uncertainty relations express limits to our subjective know­ledge instead of expressing objective statistical scatter relations, and that measurements are impossible due to the nonexistence of the entities measured.  What is impos­sible is producing scatter-free, dispersion-free quantum states.  The statistical laws add to our knowledge.  They do not set limits to our knowledge; they set limits to the scatter relations and tell us that the scatter is an objec­tive reality that cannot be suppressed.
          The propensity interpretation solves the problem of the relationship between particles and their statistics, and between particles and waves.  Popper calls the Copenhagen wave-particle dualistic interpretation the "great quantum muddle.”  The great quantum muddle results from the mistake of taking the probability distribution function as a physi­cal property of the elements of the population.  Popper believes that this mistake is historically due to the fact that the works of de Broglie and Schrödinger led physicists to view the wave as the structure of the particle, and thus to view the particle as a "wave packet" or a "wavicle.”  Popper maintains that the statistical wave function is a property characterizing a sample space and not a property of the elements of the sample space.  The elements have the proper­ties of a particle.  The propensity interpretation achieves the application of probability theory to single cases, but it does not do this by speaking about single electrons or protons; it speaks about propensities, which are properties of each instance of the whole repeatable experimental situa­tion involving a single particle.
          Propensity statements in physics describe properties of the situation, and are testable if the situation is typical.   Popper accepts Lande's explanation of the two-slit experi­ment, and he references what he calls the Duane-Lande space periodicity formula.  The two-slit experiment is a space periodicity experiment, in which the particle interacts with the whole experimental situation including the crystal.  More specifically from the viewpoint of the propensity interpretation, it is the whole experimental arrangement that determines the propensities.  The possible results of any one experiment are different in the case of both slits being open from the case where only one is open; propensi­ties are dependent on possibilities, such that the results will differ with different experimental arrangements, one slit or two.  Thus in the two-slit arrangement the particle will pass through only one of the slits and in a sense will remain unaffected by the other slit.  What the other slit influences are the propensities of the particle relative to the entire experimental arrangement and not relative to the particle itself: the propensities for reaching the one point or the other point on the screen with the two slits.  The Schrödinger wave equation enables the physicist to determine the propensities, and it entails the Heisenberg scatter relations, which limit the possible predictions.
          Popper states that Schrödinger had anticipated one of the most important aspects of the propensity interpretation, namely the objectivity and reality of the waves in configu­ration space.  One of the features of Popper's propensity interpretation is his thesis that the propensities are real, just as forces are real, and he speaks of propensity fields, just as contemporary physicists are accustomed to speak of force fields.  The propensities are dispositional relational properties of the experimental set up.  The waves are pro­pensities of the particles to take up certain states under the conditions of the experimental set up, and the propen­sity waves are therefore no less real than electromagnetic waves.  Lande believes that if he admitted to the reality of the Schrödinger wave, then like Born he would have to make what he called "concessions" to the Copenhagen dualistic thesis.  Therefore Lande maintains that the Schrödinger wave function interpreted as a probability wave is merely a statistical function that is no more real than a mortality table, which Lande did not view as real.  But Popper uses Lande's criterion of interaction, and argues that because the proba­bility waves can interact to produce interference, they must be real, and are not merely mathematical tables.  Popper sup­ports Lande's rejection of the Copenhagen dualism, but contrary to Lande, Popper says that he prefers to speak of the particle and its associated propensity fields, instead of speaking of the particle and its associated mathematical probability function.
          In the 1982 introduction to Quantum Theory and The Schism in Physics Popper proposes a crucial experiment for deciding between the Copenhagen interpretation and his propensity interpretation of the uncertainty relations.  At issue is the subjective interpretation in the Copenhagen view: whether knowledge alone is sufficient to create uncertainty, or whether it is the physical situa­tion that is responsible for the statistical scatter.  The experimental situation involves two slits in two opposing screens, through which electrons pass, one electron through each screen.  The sizes of the two slits are greatly different, while the degree of inaccuracy in the knowledge of the size of a slit is presum­ably small relative to the difference in the slit sizes.  Popper expects different statistical scatters from each of the slits, while the accuracy with which the size of the slits is known, and is the same for each slit.

On Crucial Experiments and Scientific Revolutions

          Unlike the Positivist philosophy of science, which has been interred to its resting place in the history of philosophy, Popper’s philosophy of science is still a living philosophy in the sense that it is still accepted and debated in the professional literature.  Popper has addressed more than one generation of philosophers during his lifetime.  Initially his philo­sophy was a critique of the Positivists, who viewed his philosophy as an unconventional novation, while today his philosophy is criticized by the contemporary Pragmatists, who view his philosophy as the conventional wisdom.  The central issue in which Popper represents the conservative position is the problem of the decidability of scientific criticism including most notably the decidability of crucial experiments.  The origin of the problem is the thesis shared by both Popper and the Pragmatists, and also enunciated by Einstein, that theory determines what is observed.  To the Pragmatists this thesis implies that the description of the observed results from an experimental test cannot be under­stood in the same way by different scientists who maintain alternative theories in an experimental test that is crucial in the sense that it purportedly decides between the alter­native theories.  If theory determines what is observed, then scientists maintaining different theories do not observe the same thing, and the observed outcome from the crucial exper­iment cannot decide between the alternative theories.  To Popper on the other hand, Eddington’s 1919 eclipse experiment, which is widely regarded as the historic crucial experiment deciding on behalf of Einstein's theory of relativity, demonstrates conclusively that crucial experiments are decisive.
          It should be noted at the outset that even in his earliest writings Popper maintained that falsification is never finally and permanently conclusive, because the singular basic statements that are potential falsifiers may be revised, thus occasioning the revision of a falsifying test outcome.  The empirical test may be said to be conclu­sive only to the extent that interested scientists agree to accept certain basic statements.  Popper states that in some cases it has taken scientists a long time before a falsifi­cation is accepted, and that it is usually not accepted until a falsified theory is replaced by the proposal of a new and more adequate theory.  But Popper does not find this historical fact to be problematic, even though in his view it is responsible for having led the Pragmatists to accept irrationalism and relativism in philosophy of science.  In his introduction to Realism and the Aim of Science he gives several examples of successful falsifications, that furthermore have led to important scientific revolutions. 
          If the development of Einstein's relativity theory can be said to be the formative influence in Popper's philosophy of science, then the development of the quantum theory can be said to be the formative influence in the contemporary Pragmatist phil­osophy of science.   The topic of crucial experiments has assumed its controversial status in the professional litera­ture due to the Copenhagen interpretation of quantum theory.  The Copenhagen interpretation denies that a crucial experiment can decide between the wave and particle interpretations of microphysics, because the electron has the properties of both wave and particle.  Quine invoked Duhem's philosophy of physical theory not only due to Duhem rejection of the decidability of crucial experiments, but also more fundamentally due to Duhem's thesis of the organic character of the semantics of theory language in physics.  In his "Two Dogmas of Empiricism" Quine extended Duhem's thesis of the organic or wholistic character of the seman­tics of physical theory, to make it a general theory of the semantics of language as such, including the language used by physicists to describe observed experimental test outcomes.  As a result of this extended thesis, which is now conventionally called the Duhem-Quine thesis, the wholistic character of the semantics of language explains why crucial experiments are undecidable not only in the wave-particle issue in quantum theory, but also more generally for all scientific criticism.  Even where one of the alternatives is the Copenhagen dualistic interpretation, as in Lande's list of seven interpretations, the crucial experiment cannot effectively decide among them, according to the contemporary Pragmatist philosophy.  The issue of crucial experiments has become a focal point in philosophy of science for the larger issues of the decidability of scientific criticism and of the nature of the semantics of language in general.  The historic transition from the Positivists' naturalistic phil­osophy of the semantics of language to the contemporary artifactual philosophy of the semantics of language has thus resulted in two alternative artifactual philosophies of the semantics of language: The one is the organic or wholistic thesis advocated by the Pragmatists, which they use to attack the decidability of crucial experiments and of scien­tific criticism in general.  The other is the logical or mechanistic thesis advocated by Popper, which he uses to defend the decidability of crucial experiments and the rationality of scientific criticism in general.
          In his "Three Views Concerning Human Knowledge" (1956) reprinted in his Conjectures and Refutations Popper discus­ses Duhem's views on crucial experiments.  He notes that Duhem shows that crucial experiments cannot establish a the­ory by refuting its alternatives, and emphasizes that Duhem does not say that theories cannot be refuted in crucial experiments.  Popper maintains that crucial experiments can be used to decide between alternative theories, as occurs when a new theory in proposed as a superior alternative to an older theory.  The new theory is tested by applying it to cases for which it yields results that are different from what is expected from the older theory.  He says that such cases are "crucial" in the Baconian sense that they indicate the crossroads between two or more theories, but not in the Baconian sense that any theory can be established.  Popper then turns to Duhem's thesis that in every test it is not only the theory under investigation that is tested, but also the whole system of assumptions made by the theory, such that it is never possible to be certain which of the assump­tions is refuted by the test.  Popper states that if the scientists consider each of the two theories in the crucial test together with all the background knowledge assumed by both theories, then the scientists decide between the two systems, which differ only over the two alternative theories in the test.  Popper adds that scientists do not assert the refutation only of one of the theories by the test, but rather the theory together with the background assumptions.  By this he does not mean that every statement in the theory and its assumed background is refuted, but only that there is at least one statement that is erroneous, and that it may be in either the theory or the assumed common background.  Thus he also says that in future tests parts of the background knowledge may be rejected as responsible for the falsification of the theory in the current crucial test.
          Popper then proposes to "characterize the theory under investigation" in the crucial test precisely as that part of the vast system of knowledge for which the scientist has an alternative in mind, and for which he has therefore designed the crucial test.  This may be taken as Popper's basis for individuating theories: theory a is distinguished from the­ory ß, because a makes a claim or statement than is an alternative to that made by ß, and because a consists in the language that makes it an alternative to ß.  Thus it may be said that Popper individuates theories by reference to the theories' semantical properties as manifested in the crucial test situation.  However, Popper does not define theory lan­guage by reference to the crucial test situation as such; he often states that the background knowledge includes theories other than the tested one.  In his philosophy, therefore, theory language is any testable general statement regardless of whether or not it is being tested, which is to say that he defines theory by reference to its syntactical property of universal quantification and not by reference to its pragmatic properties.  Further­more Popper's concept of theory language may be contrasted with that of the Positivists, who believed that it is possible to define theory in terms of its semantical properties by means of their distinction between theoretical and obser­vation terms; Popper rejects this distinction.
          In his "Truth, Rationality, and the Growth of Know­ledge" (1961) reprinted in Conjectures and Refutations Popper turns to Quine's use of Duhem's philosophy.  Quine maintains a wholistic view of empirical testing, and in his "Two Dogmas of Empiricism" in From A Logical Point of View he states that our statements about the external world face the tribunal of experience not individually but as a corporate body.  Popper replies that this wholistic view of tests, even if it were true, would not create a serious problem for the falsificationist philosopher of science.  He repeats his thesis that the fact that scientists take a vast amount of background knowledge for granted, is not to say that the scientist must uncritically accept it; the background knowledge too may be challenged and tested.  Even though all of the back­ground assumptions may be challenged, it is quite impossible to challenge all of the assumptions at the same time.  All criticism must be "piecemeal", which Popper says is only another way of saying that the fundamental maxim of every critical discussion is that one should "stick to the problem", because the misguided attempt to question all background assumptions merely leads to a breakdown of critical debate.  Critics such as Feyerabend will view this thesis as the Achilles heel of Popper’s philosophy of science, its parallel postulate to be replaced with the new Pragmatist philosophy of language. 
          Furthermore even though the falsification of a theory does not reveal where the error is, nevertheless it is still possible to find the hypothesis that is responsible for the refutation, i.e. to find which hypothesis is responsible for the refuted prediction.  The fact that such logical depen­dencies may be discovered is established by the existence of independence proofs for axiomatized systems; these are proofs that show that certain axioms of a system cannot be derived from the rest.  Popper argues that the existence of such proofs shows that Quine's wholistic view of the global character of all empirical tests is untenable, and that it explains why even without axiomatized physical theories, the scientist may still have an inkling of what has gone wrong with the theory.  In Realism and the Aim of Science Popper affirms as historical fact, that scientists are sometimes highly succes­sful in attributing to a single hypothesis the responsibil­ity for the falsification of a complex theory or of a system of theories, and he argues that this success remains to be explained if one adopts the wholistic view of empirical testing.
          In 1962 Thomas Kuhn wrote Structure of Scientific Revolutions in which he used the wholistic thesis to inter­pret the history of science.  And in 1970 he defended his whol­istic interpretation against critics in Criticism and the Growth of Knowledge.  The leading critic in this later book was Popper, who contributed "Normal Science and its Dangers.”  In his earlier statements in defense of the decidability of crucial tests Popper did not explicitly address the basis of the wholistic view of testing, namely the thesis that the semantics of language is wholistic.  The wholistic thesis of the semantics of language means that the meanings of terms are mutually determined in the context of the discourse in which they occur, such that alternative contexts consisting of alternative theories produce a semantic ambiguity or equivocation that is propagated through all of the related language.  Therefore when considering the alternative theo­ries investigated in a crucial test, all that constitutes the background assumptions is ambiguous.  In other words there is really no common background, because one semantical interpretation is given to the language expressing the background assumptions by one of the theories in the test and another interpretation is given by the other theory in the test.  Often the two alternative semantical interpretations are spoken of as two different languages, and there is said to arise a problem of translation from one to the other.  This thesis is strategic to Kuhn's critique of the Positivists, because the lack of any common semantics for alterna­tive theories that makes impossible a common background for crucial tests, also makes impossible a common observation language.
          Kuhn maintains that the kind of scientific progress that Popper describes with its crucial experiments and fal­sifications can occur only within a linguistic framework, and he calls this type of scientific progress "normal sci­ence", which Kuhn opposes to another type which he calls "extraordinary science" or "revolutionary science.”  Revolu­tionary science is a transition from one language framework to another, where the term "framework" in the discussion refers to discourse having a univocal semantical interpreta­tion and associated ontology.  Popper rejects this theory of scientific revolution as irrational, when he criticizes Kuhn in Criticism and the Growth of Knowledge.  While admitting that "normal science" in Kuhn's sense does exist, Popper argues that such normal science is dogmatic.  He says that science is essentially critical, that it consists of bold conjectures controlled by criticism, and that it may be called revolutionary in this rational sense.  He rejects Kuhn's relativism, the thesis that the linguistic framework cannot be critically discussed, and he calls this "the myth of the framework.”  Comparison of different frameworks is always possible on Popper's view, and so is critical discus­sion therefore.  Even totally different languages are not untranslatable.  And it would be simply false to say that the transition from Newton's theory of gravitation to Ein­stein's theory is an irrational leap, and that the two are not rationally comparable; the transition to Einstein's theory was genuine progress in comparison with Newton's.  Popper concludes that the myth of the framework is in our time the central bulwark of irrationalism, and that it exaggerates a difficulty with communication and criticism into an impossibility.  In place of criticism as is found in Popper's falsification thesis, Kuhn proposes turning for enlightenment concerning the aim of science to psychology and sociology.  But Popper rejects this proposal, and states that compared with physics, sociology and psychology are riddled with fashion and with uncontrolled dogmatism.  He believes that such a proposal is a backward regression that cannot solve the difficulty.

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