Popper's philosophy of scientific knowledge is a sus­tained attack on Positivism, but it is not just a critical rejection; he has his own alternative philosophy of observa­tion.  The Positivists maintained that there is a clear dis­tinction between theory and observation, such that one could separate the language of theory from the language of obser­vation with each containing its own distinctive vocabulary and its own class of universal of statements.  The universal statements containing only observation terms are produced by inductive generalization, while those containing theoretical terms are invented by the scientist's creative imagination.  However, with the recognition that theory determines what is observed, the separation between theory language and obser­vation language can no longer be sustained, and the ideas of theory and observation must be reconceptualized.  And since the existence of an observation language was thought to be the empirical basis for science, the empirical basis for science also must be reconsidered.
          The Positivists had attempted to base empirical science on "atomic statements", "protocol statements" and "judgments of perception" stated in the observation language.  Popper rejects these ideas with his rejection of the naturalistic philosophy of meaning.  Instead he proposes the idea of the  "basic statement", which he defines as a singular statement which together with the universal statements of theory can serve as a premise in an empirical falsification of a the­ory.  The basic statement is fundamentally different in con­cept from Carnap's protocol statement.  The protocol statement is thought to be justified by perceptual experiences and thereby to constitute a foundation for science.  But Popper maintains that this is a confusion between the sub­jective psychological aspect of knowledge and the objective logical aspect.  Perceptual experiences are subjective and psychological; they can motivate a decision and hence an acceptance or a rejection of a statement, but a basic state­ment cannot be justified by them any more than it can be justified by thumping on a table.  Basic statements are objective in the sense that they can be intersubjectively tested by repetition of the conditions that occasioned them.  And they can be falsified, since they operate as premises from which other statements can be deduced, which in turn can be tested.  As a result there can be no ultimate state­ments in science, as the Positivists believed; all state­ments in empirical science can be refuted by falsifying some of the conclusions that may be deduced from them.
          But it is not necessary that a basic statement should be tested in order for it to be accepted; it is only neces­sary that the basic statement be testable.  The function of basic statements is to test theories.  Every test of a the­ory must stop at some basic statement, which the scientists have agreed to accept at least for the present time.  To the extent that the basic statements are accepted on the basis of agreement, they are conventional.  But the agreement is not arbitrary or capricious; the decision is made by refer­ence to a theory and the problem that the theory is proposed to address.  Theory dominates experimental work from its initial planning to its completion in the laboratory.  Pop­per summarizes his views on the empirical basis of science by means of a memorable metaphor: There is nothing absolute about science; it does not rest upon solid bedrock, as it were.  The bold structure of its theories rises as it were above a swamp like a building erected on piles, which in turn are driven down to whatever depth is found to be satis­factory to carry the structure for the time being.
          Popper's reconceptualization of the empirical basis of science is also a reconceptualization of the concept of theory in science.  Unlike the Positivists, Popper does not define the concept of scientific theory in terms of theore­tical terms.  Instead he views theories as universal state­ments, and rejects any distinction between empir­ical laws and theories, since there is no longer any dis­tinction between theory language and observation language based on a distinction between theoretical terms and observation terms.  All the universal statements in science are conjectures that are testable and falsifiable, and these conjectures are invented by the human mind; none of them are produced by inductive generalization.  To give a causal explanation of an event means to deduce a statement which describes the event using as premises of the deduction one or more universal laws as theories together with singular basic statements that describe the initial conditions.  Popper's ideas for such terms as "theory", "law", and "cause” are fundamentally different from the Positivists' ideas for these terms, because Pop­per's ideas are separated from the subject matter or onto­logies described by the sciences.
          Empirical science is not purely formal like mathematics or logic, but neither is it defined in terms of certain sub­stantive concepts about reality as it is described by sci­ence today.  Future science may have revised the substantive content of today's science and yet science will still be science as Popper has defined it.  As Popper says in reply to Kuhn's concept of science in "Normal Science and Its Dangers" in Criticism and the Growth of Knowledge (1970), science is "subjectless.”  Such could not be said of science by the Positivists, for whom the naturalistic philosophy of the semantics of language requires that certain substantive concepts permanently established by observation must always be retained as definitive of the empirical character of sci­ence.  The rejection of the naturalistic philosophy of the semantics of language implies the reconceptualization of such metascientific terms as "theory", "law", "explanation", and "cause" in a manner that disassociates these ideas from any particular ontology that the semantics of science may describe at any point in history.  Empirical science becomes a sequence of alternative ontologies instead of a specific ontology.  And with his criterion of increasing information content Popper believes that the sequence of ontologies is not a disconnected random sequence, but rather is one that reveals objective and rational scientific progress.  Curiously Popper himself did not follow through on these ideas when he sup­ported Einstein's criticism of the Copenhagen interpretation of quantum theory, and advanced his own "commonsense realism" ontology.

On Computers, Induction Machines, and Scientific Discovery

          In his Logical Foundations of Probability and elsewhere Carnap proposed using a computer to make empirical general­izations with inductive logic.  Throughout his career Popper has rejected the idea of inductive logic, but in Realism and the Aim of Science (1982) he admits to induction machines of a certain type.  For such a machine he postulates a simple universe containing individuals and a limited number of pro­perties that the individuals can have.  This universe fur­thermore operates with a number of so-called "natural laws.”  Popper says that for this universe a machine can be created, such that in some reasonable period of time it will discover the laws that are valid in the postulated universe during the time period.  If the laws of its universe are modified, the machine will show its capacity for finding a new set of laws.  It would be capable of drawing up statistics about various distinguishable occurrences and of calculating aver­ages.  If the postulated universe is complicated further to include among its natural laws, the laws of succession, the general or conditional frequencies having a certain degree of stability, etc., then the machine can be enhanced to be able to formulate hypotheses, to test the hypotheses, and to eliminate those that should be eliminated.  Such a machine can learn from experience.
          But this inductive machine is limited to the universe that its architect has created for it.  The architect of the universe decides what are to be individual events, and what constitutes a property or a relation.  In general it is the architect of the machine who decides what the machine can recognize as a repetition.  And even more fundamentally it is the architect of the machine who decides what kinds of questions the machine is to answer.  All these considerations mean that the more important and difficult problems are already solved by the human designer, when he constructs the machine and the universe it can recognize.  Things that Positivists such as Carnap had thought to be simply given by nature, the meanings that according to the naturalistic theory of the semantics of language are delivered by the natural operation of human perception, are in Popper's view the product of the creative and imaginative powers of the human designer.  These powers enjoy a freedom that is permitted by the artifactual character of objective knowledge, and that is necessary for the creation of the hypotheses and theories that have characterized the growth of knowledge by science.  The basis of this freedom is the nondeterministic relation between world 3 on the one hand and worlds 1 and 2 on the other.  Carnap had admitted that an induction machine cannot create hypotheses, and that theories are inventions created by the human mind.  But Popper does not admit to the Positivists' separation between empirical generalizations on the one hand and theories on the other; he maintains that there is no observation without theory.  He also argues that no human or computer can pre­dict the future growth of scientific knowledge by scientific methods without committing the fallacy of historicism. In his Poverty of Historicism (1975) as well as in Realism and the Aim of Science he maintains that historicism involves unconditional predictions, and he says that such predictions are impossible, because prediction in science requires universal laws, which are always condi­tional.
          As it happens, the computerized development of hypo­theses and conjectures is precisely what information scien­tists attempt to accomplish by their artificial-intelligence computer systems, which Herbert Simon calls "discovery systems.”  These computer systems are instrumental to the scientist's development of hypotheses.  They are not historicist, but are conditioned upon inputs that require the same kind of preparation or initial conditions that Popper says are needed for what he calls an “induction machine.”

The Schism in Physics and Metaphysical Research Programmes

          The term "schism" in the context of the philosophical discussions of the quantum theory did not originate with Popper; Heisenberg introduced it.  In his "Recent Changes in the Foundations of Exact Sciences" (1934) in Philosophical Problems of Quantum Mechanics Heisenberg notes a "peculiar schism", that he says is inescapable in the investigation of atomic processes.  He is not referring to a sociological phenomenon in the physics profession or to an issue that must be resolved; he views the schism positively as a development in physics.  As Heisenberg uses the term "schism", it refers to the different concepts used by clas­sical physics and quantum physics and to the different ontolo­gies they describe.  On the one hand there is the need for macrophysical classical concepts of space and  time, which are used in quantum physics for the description of experiments and of the appa­ratus of measurement in experiments.  On the other hand there is the mathematical expression suitable for the representation of microphysical reality, the wave function in multidimensional configuration spaces, that allow of no easily comprehensible interpretation.  Heisenberg says that the dividing line between the classical and the quantum physics is the statistical relation.
          Popper's earlier views on quantum theory are set forth in his Logic of Scientific Discovery and his more mature statement is set forth in his Postscript to the Logic of Scientific Discovery (1982).  The latter work is a collection of three volumes: Realism and the Aim of Science, The Open Universe: An Argument for Indeterminism, and Quantum Theory and the Schism in Physics.  Popper brings to statistical quantum theory a prior ontological commitment, which he calls "com­monsense realism.”  In Popper's view physics has historic­ally developed out of one or another metaphysical view which he calls a "metaphysical research programme.”  A metaphysi­cal research programme is a set of ideas that are currently untestable, and therefore are called “metaphysical.”  In Pop­per's philosophy the demarcation between science and meta­physics is testability thus giving metaphysics a residual status relative to science.  The metaphysical research programme supplies the physicist both with a metaphysical view or ontology about the general structure of the world and with a metascientific view about such things as the criteria for a satisfactory scientific explanation based on the ontology contained in the metaphysical research programme.  Science needs metaphysical research programmes, because they largely determine its problem situations.  Popper cites Einstein's way of looking at the Lorentz transformation as an example of how a metaphysical research programme can sup­ply a new way of looking at things, that may change science completely.  Metaphysical research programmes change and are replaced as some parts become testable and are incorporated into science.  The relation between the testable theory and the research programme is part of the history of problem situations of the science, along with the problems arising from inconsistency among theories and empirical falsifica­tions of theories.
          Unlike Heisenberg, Popper views the schism in physics in more sociological terms and in terms of the issues that have given rise to the schism.  And unlike Heisenberg, he does not view the current schism in physics favorably.  In his opinion the acceptance of the Copenhagen interpretation and the rejection of what he calls the Faraday-Einstein- Schrödinger metaphysical research programme have left physics without any unifying picture of the world, without any theory of change, and without any general cosmology.  The current schism in physics is a clash between two meta­physical research programmes, neither of which in his view seems to be doing its job.  In Quantum Theory and the Schism in Physics he summarizes the current schism in terms of three issues: (1) indeterminism vs. determinism, (2) realism vs. instrumentalism, and (3) objectivism vs. subjectivism.  All three issues are closely related to one another and to the interpretation of the probability function in the sta­tistical quantum theory.  The schism has its orthodox group, and it has a variety of dissenters.  On the dissenting side of the schism he locates the views of Einstein, de Broglie, Schrödinger and Bohm, which he characterizes together as determinist, realist and subjectivist.  On the orthodox side of the schism he locates the Copenhagen school including Bohr, Heisenberg, Pauli and Born, which he characterizes together as indeterminist, instrumentalist and objectivist.  He does not consider Heisenberg's views to be realist, and he effectively lumps Heisenberg together with Bohr, who was explicitly instrumentalist in his view of the formalism of quantum theory.  This amounts to a misrepresentation of Heisenberg.  Popper proposes a new and unifying metaphy­sical research programme that he says offers a consis­tent ontology for both macrophysics and microphysics.  Such an ontology has been the Holy Grail of nearly every critic of the Copenhagen school.  In his autobiography he states that his views on quantum theory were greatly influenced by those of the physicist Alfred Lande, and he states in the Postscript that Lande antici­pated his own interpretation of the quantum theory.  There­fore, a brief examination of Lande's interpretation of the statistical quantum theory is in order before proceeding further in the discussion of Popper's particle-propensity interpretation.

Lande's New Foundations of Quantum Physics

          A brief biography of Alfred Lande (1888-1975) can be found in an obituary published in Physics Today (May 1976).  Lande was a German-born American physicist, who received a doctorate in physics in 1914 from the University of Munich, where he studied under Sommerfeld.  In 1918 he co-authored a paper with Born, that refuted Bohr's model of coplanar electronic orbits.  In 1931 he immigrated to the United States, where he taught theoretical physics at Ohio State University until his retirement in 1960.  Lande originally advocated the Copenhagen interpretation of quantum theory, but pub­licly disassociated himself from it with the publication of his Foundations of Quantum Theory (1955).  His most mature statement of his views is his New Foundations of Quantum Mechanics (1965), which includes ideas published in his previous papers.
          As a physicist Lande had his own agenda: the solution of what he calls "The Quantum Riddle", which is the deriva­tion of the laws of quantum mechanics from a nonquantal and nondeterministic basis without the ad hoc assumptions that he finds in the Copenhagen interpretation.  In his deductive explanation of quantum laws from three nonquantal postulates, he maintains that uncertainty is a physical principle for both classical and quantum physics, and he advances and defends a particle interpreta­tion of both Heisenberg's uncertainty relations and Schrödinger's wave function.  Both of these views were central to Popper's philosophy of science twenty years before Lande rejected the Copenhagen interpretation of quantum theory, and Lande references Popper's views in his own literary corpus.  However, Lande maintains a contrary ontology with respect to the reality of the waves associated with the Schrödinger wave function.
          In "Probability in Classical and Quantum Theory" in Scientific Papers Presented to Max Born (1953) Lande argues that classical thermodyna­mics cannot be reduced to deterministic mechanics, and that it is futile to search for hidden causes behind any distribution that satisfies the rules of probability either in classical or quantum physics.  To illustrate his thesis he describes an experiment in which ivory balls are dropped through a tube onto the center of a steel blade, resulting in an observed 50:50 average ratio of balls falling to the left or right.  On the determinist view the 50:50 ratio is possible only if it is already contained in the initial conditions, which in turn either implies an infinite regress to still prior conditions, or is left unexplained.  Lande rejects both these options.  Instead he concludes that random distribution is a physical reality, and that determinism is a purely academic construction, because a program of giving a deterministic theory of statistically distributed events leads nowhere.  Statistical theory can only reduce one prob­ability distribution to another, and when there are ensembles of events conforming to error theory, these events are not reducible to deterministic mechanics.
          In New Foundations he states that the belief in deter­minism is as much beyond the domain of physics as the belief in indeterminism, because both ideas are metaphysical theses.  Observation only shows that equal preparation, as far as equality can be achieved, always leads to unpredictably different results.  Lande elevates this general insight to the physical prin­ciple of uncertainty.  In contrast to ordinary experience, classical mechanics was deterministic, while on the other hand ordinary experience and quantum mechanics agree.  Unpredictabil­ity understood as the acausality of individual events must be seen as an irreducible feature of natural science.  Sta­tistical mechanics can describe predictable averages for unpredictable individual events.  In quantum mechanics it is Heisenberg's great merit that he established quantitative limits for the uncertainty of prediction, but Lande also states that unpredictability of future events does not pre­clude the reconstruction of past individual cases using a deterministic theory.
          Lande rejects Heisenberg's thesis that between two observations in atomic physics the electron is nowhere.  In his discussions of uncertainty and measurement in New Foun­dations he admits that while in classical physics a measure­ment value can be attributed to the object immediately before, during, and after the measurement, in quantum phys­ics there is an active, unpredictable, and unavoidable par­ticipation of the instrument or "meter" in producing the result, in which the microphysical object is thrown from its previous state into a new state.  Therefore in quantum phys­ics the measured value can be ascribed to the atomic object only immediately after the measurement is completed, and any subsequent measurement erases all traces of the first state and produces an entirely new situation.  Nevertheless Lande maintains that it is always possible to reconstruct one and only one path between the two space-time positions according to the laws of classical mechanics post factum, even though the path cannot be predicted.  He distinguishes between direct and indirect measurements; the former are coinciden­ces in space and time, and are the basis for all other measurements, which are indirect measurements.  Energy, momen­tum, and velocity are relevant examples of indirect measure­ments; velocity by definition requires measuring two adja­cent positions at two adjacent times.
          Lande rejects the Copenhagen thesis that effectively equates "indirectly observed" with "not observed", and then with "not observable", and finally with "nonexistent" and "meaningless.”  The Copenhagen school wrongly maintains that only direct measures count as observation.  To say as they do, that position and momentum cannot be measured simultane­ously is only a half-truth.  If one includes "directly", then it is trivial because momentum can never be measured directly.  And without the word "directly" the statement is wrong, because the momentum value acquired within a given position increment can be determined by reconstruction of space-time data with the help of theory.  The root of the difficulty with reconstructing values of indirect observ­ables is the ambiguity of their definition, which always requires theory.  Lande maintains that classical theory can be used to make the indirect measurements needed to describe the path of an electron.  The controversy about the meaning of an atomic measurement is due to an erroneous connecting of the first measurement with a set of possible future measurements.  When the wave function is used as a mathe­matical representation of just one physical state, there is no confusion.  But when it is used to connect one measurement with a set of future possible measurements, misunderstanding occurs which results in different interpretations of the wave function, including the Copenhagen dualistic thesis that the wave function describes a physical state of matter which is spread out in space and time, and which suddenly contracts to one point when the particle is measured.

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