Rosenfeld then proceeds to discuss the formalization presented by von Neumann, which he regards as unnecessarily involving the mind of the human observer. This step should be avoided by basing the measurement description on the emergence of an indelible recording. To argue for the possibility of such an occurrence, he refers to the theory presented by Danieri, Loinger, (p.75) and Prosperi in 1962. This is a model which indeed is compatible with the Copenhagen approach as formulated by Bohr. Today, however, we know that there are many such possible schemes, but none of them will ultimately resolve the enigma of transferring quantum states into unambiguous human knowledge. As a contribution about the possibilities and limitations of axiomatization, the reference [51] presents an interesting discussion.

  The actual use of modern quantum theory is based on a rather involved and intricate mathematical structure. The interference of probabilities, the superposition of various states, and the nonclassical correlations implied by entanglement can only be incorporated in a linear space with correspondence rules relating its predictions to observations. However, this structure is well known and manifestly successful in describing ever‐new areas of physical investigations. This story is told in a comprehensive way in the reference [52]. This writing is not remarkable in any way, and to the extent it has not become outdated by the later developments, it still gives a simple and fair description of the quantum theory.

  In spite of the central role of the observer in the Copenhagen approach, Rosenfeld strongly argues against a positivistic approach to the description of physical reality. In [53] he reviews Werner Heisenberg's book Natural Law and the Structure of Matter. The whole review, however, becomes an eloquent but single‐ minded attack on Heisenberg's alleged “liquidation of dialectical materialism”. The text offers amusing reading, short as it is, but it does not further the understanding of quantum mechanics as understood by either Heisenberg or Rosenfeld.

  In the article [54], Rosenfeld analyzes the emergence of the concepts of classical dynamics in terms of the recent experiments about the formation of concepts in humans. Piaget and others are quoted to show how magnitude and motion become intuitive concepts. By using the possibility of mirages that deceive the eye, Rosenfeld argues that also the formal concepts, position, motion, and causality, are idealizations which have been abstracted from experience in a manner similar to the emergence of quantum theory.

  The limitations imposed on the classical concepts by the quantum of action allow us to use classically incompatible aspects in a complementary way.

  If one chooses to speak about “contradiction” in connection with mutual exclusion of complementary phenomena, then one may only mean a “dialectical” contradiction; in fact, one may regard the occurrence of complementary relations of quantum theory as a clear and precise example of what is implied by the general conception of “dialectical process”. The quantum theory, which comprehends the complementary aspects in a logically consistent whole, represents the synthesis resolving the dialectical opposition between these aspects.

  3.4. Copenhagen summarized

  For easy reference, I present a summary of the main points of Bohr's view of the science of physics:

  (p.76) 1. “Microscopic objects” exist and their properties can be investigated.

  2. The “quantum theory” is a system to order our empirical material.

  3. The difficulties in describing Nature derive from our dependence on language. Nature can only answer questions we can pose for it.

  4. The symbols of the theory mirror no intrinsic essence of reality.

  5. There is “no universal reality” restlessly described by quantum theory.

  6. Abstract mathematical symbols are tools to provide knowledge only.

  7. The correct description of empirical reality is the introduction of “phenomena” well described from their preparation to irreversible recordings of measurement results.

  8. In order to be able to communicate the performance of an experiment, we have to describe it in terms of classical physics (suitably extended by the tools of mathematics).

  9. The consistency of the process is guaranteed by the consistency of the mathematics used.

  10. The possibility to use classical concepts derives from the “correspondence principle” between massive quantum objects and their classical counterparts.

  11. All conceivable experiments are not simultaneously possible. This makes our concepts fuzzy and enforces indeterminacy on the interpretation of the observations.

  12. Quantum theory is a complete system where all classically introduced concepts can be selected for scrutiny. “Complementarity” guarantees that no aspect is omitted from the theory.

  3.5. Bohr's pragmatism

  Pragmatism of the American brand has not played a major role on the European stage of modern philosophy. It has, however, influenced the development of twentieth‐century philosophy of physics in a remarkable way. This is the more astonishing because there is no evidence that any of the actors of this scene has devoted himself to systematic study of the pragmatic classics. The influence seems to have been mainly indirect, based on the endeavor to define the concept of truth when it concerns the validity of scientific propositions.

  Above, I pointed out that Boltzmann clearly related scientific method to the procedure required to achieve “warranted assertibility”. The following excerpt from Boltzmann could have been written by James at about the same time:

  Of opinions sufficiently often confirmed by experience, we say that they are certain and that what they express belongs to our knowledge.

  What leads to correct deeds is true.

  Still there is no evidence that Boltzmann was acquainted with James's writings. On the other hand, it is obvious that Bohr knew about the philosophy of James, even if he never referred to him in his writings. As told above, Bohr's (p.77) philosophy mentor Høffding even corresponded with James. Thus even without reading any of the pragmatist texts, Bohr is very likely to know about their ideas. One may even claim that Bohr's philosophical outlook to a large extent derived from pragmatic influences.

  As explained earlier, a physical measurement can give meaning to a physical concept by defining the operations required to decide if an object falls under a concept or not. The outcome of the procedure constitutes existing information about a reality persisting independently of our perception of it. In this investigation there is no absolute meaning attached to the logical term “true”. Only referring to its third meaning (see Sec. 1.2.4 above), can we interpret the warranted assertibility as a substitute for true statements. All physical propositions are conditioned on insufficient evidence and consequently subject to change and corrections.

  Bohr did not necessarily assign the attributes “true” and “false” to empirical statements. Some cases are not decided (ambiguous). The existence of features of reality is independent of us but not of how we choose to act. The theory of physics is no mirror image of reality but only our tool to organize and master the terrain where we move and act out our lives. Here I remind the reader of the analogy with a map: It represents reality but only by utilizing arbitrarily chosen signs.

  Bohr's approach to epistemology is thus closely similar to the traditional pragmatism of James. No statement has got meaning if it “makes no difference” or implies no discernible “directions for actions”. The Copenhagen interpretation is often justifiably blamed for being positivist. Historically this contains some truth, but Bohr's approach is closer to pragmatism: Instead of regarding observability as criterion for existence (esse est percipi), he focusses attention on what we can do. Quantum mechanically what exists is what is “preparable”. This assigns the Heisenberg fuzziness of concepts not to the states but to the preparation procedure.

  As the influence on Bohr has been claimed to originate in James's attitudes, it is illuminating to consider these views.

  3.5.1. William James and pragmatism

  Early works:

  James acquired his fame originally from his comprehensive and innovative work on psychology [55]. This book seems to have been read by Bohr as well as by Wittgenstein. The book [56] defends the freedom to believe according to one's convictions. It has been pointed out that a more adequate title would have been “The right to believe”. Epistemologically this seems to follow from the fact that no amount of verified knowledge can uniquely determine the transcendental structure of reality.

  Also James's book [57] on personal religious experience had an influence on Wittgenstein. In spite of the strong Danish devotion to Gruntvig, Bohr did (p.78) only little to indicate any concern about religion even if his writings on culture occasionally touch on such issues.

  Pragmatism

  In the work [58], James introduces his concept of pragmatism. He starts from the conviction that no monistic rational method can dictate the image we use to describe reality. All information of value is based on empirical methods, i.e. our human experience. The multitude of our accumulating experience provides a pluralistic view of reality. Pragmatically, all conclusions drawn from the empirical material must make a difference because of their practical consequences.

  No empirical evidence can delete our personal experience of life but only add to it in accordance with new insights derived from empirically obtained results. These are not true; they simply come and persist. Their truth is of the first flavour (Sec. 1.2.4 above), and cannot be meaningfully denied. Truth is what we say about the experience. This “truth” is of the third flavour. The assertible is what has proved to be successfully applied.

  The concepts of the theoretical description, James compares to coordinates or logarithms, i.e. only tools to relate features of experience's flux. This reminds us of the map model of scientific theories. True ideas are those that we can assimilate, validate, corroborate, and verify. False ideas are those that we cannot. James summarizes his argument by writing ([58], p. 117):

  ‘Reality’ is in general what truths have to take account of, and the first part of reality from this point of view is the flux of our sensations. Sensations are forced upon us, coming we know not whence. Over their nature, order, and quantity we have as good as no control. They are neither true nor false; they simply are. It is only what we say about them, only the names we give them, our theories of their source and nature and remote relations, that may be true or not.

  The second part of reality, as something our beliefs must obediently take account of, is the relations that obtain between our sensations or between their copies in our minds.

  James, understandably, had no knowledge of quantum theory, but the quotation could have been adopted by Bohr. Epistemologically all our usable information about reality must derive from the empirical material. Only verifiable ideas and their relations can be assigned the epithet “true”. The pertaining facts are truth of the first flavour, they just are. Any conclusions from the material can be accepted only if they work. Already Boltzmann assigned Darwinian success to evolutionary surviving principles. We can accept no “idle wheels” (Wittgenstein). This truth is of the third flavour. James discusses some consequences of his views in [59], and elaborates his concept of truth in the sequel [60].

  The pragmatic concept of truth has suffered from several misconceptions: It has been confused with the transcendental concept of logical truth, which can only be applied to formal systems, i.e. within consistent logical frameworks.

  A second misconception is the application of pragmatic truth to moral issues; what works is good! Here most social systems hesitate to abandon the absolute (p.79) rules for human behavior. In addition, whose “good” is to determine what is true? Many Strebers would regard their economic progress as the “good” defining truth.

  As a purely epistemological principle, James's concept represents clearly “new name for old ideas”, with relevance even after the revolution caused by quantum mechanics. In its focussing on the empirical material and its carried evidence, it matches Bohr's declarations. In both cases, the structure offered carries only very limited knowledge about the “ontological” implications. We can ascribe some (probably) valid features to reality; its full framework is not available to us, and it may never be.

  Problems of Philosophy

  A very penetrating and pleasant overview of philosophy is provided by James in [61]. Here the stress is less on pragmatic truth and more on the empiricist approach to knowledge. Many of his fundamental views are elegantly exposed here.

  James started from the conviction that no logical introspection can create useful models of empirical reality. Thought implies mental images only:

  The importance attached by certain monistic writers to the fact that any chaos may become a universe by being merely named, is to me incomprehensible.

  The empirical program is to investigate “reality”. We thus need to define and delimit what this reality is:

  What is it to be “real”? The best definition I know is that which the pragmatist rule gives: “anything is real of which we find ourselves obliged to take account in any way.” Concepts are thus as real as percepts, for we cannot live a moment without taking account of them.

  Our inborn conceptual framework contains contributions from both observations and their role in our image of the ambience.

  The world we practically live in is one in which it is impossible, except by theoretic retrospection, to disentangle the contributions of intellect from those of sense.

  But our totality of knowledge and beliefs is always finite or denumerable. Thus in applying logic to the formal structures, we encounter the dangers attached to unlimited use of set theory for nondenumerable assemblies:

  The same things can always be taken either collectively or distributively, can be talked of either as “all”, or as “each”, or as “any”. Either statement can be applied equally well to what exists in finite number; and “all that is there” will be covered both times….

  But if we say that “all” must be fulfilled, and imagine “all” to signify a sum harvested and gathered‐in, and represented by a number, we not only make a requirement utterly uncalled for by the logic of the situation, but we create puzzles and incomprehensibilities that otherwise would not exist.

  (p.80) And this danger is real, because however much we learn about reality, there exists a multitude of things yet to learn:

  Conceptual knowledge is forever inadequate to the fullness of the reality to be known.

  What we know is to be collected like a map, an abstract representation of an aid helping us to find our way in the terrain of reality:

  This map of what surrounds the present, like all maps, is only a surface; its features are but abstract signs and symbols of things that themselves are concrete bits of sensible experience.

  In our network of theoretical constructs, one feature we try to capture is causality; without it no predictions whatsoever are possible. But without theory, there is no causality discernible because:

  It is plain that each moment of the universe must contain all the causes of which the next moment contains effects, or to put it with extreme consicision, it is plain that each moment in its totality causes the next moment.

  James does, however, consider the possibility of unpredictable, irrationally random events as conceivable.

  We imagine that in some respect at least the future may not be co‐implied with the past, but may be really addable to it, and indeed addable in one shape or another, so that the next turn in events can at any given moment genuinely be ambiguous, i.e. possibly this, but also possibly that.

  In 1911 he could have had no inkling of quantum uncertainties, but still he writes:

  …concepts current in physical science have also developed mutual oppugnancies which are beginning to make physicists doubt whether such notions develop unconditional “truth”.

  Here we have a clear warning that the concept of “truth” may not apply to physical reality.

  Radical empiricism

  In [62], James elaborates and completes his description of the pragmatic episte‐ mological framework. The essays are from different times. Here I only take up a few issues from this work.

  For James the real is all experienced in its multifarious plurality. The conception of reality is construed from all experience; no doubt James counts the outcomes of scientifically planned experiments as a part of “experience”.

  To be radical, an empiricism must neither admit into its constructions any element that is not directly experienced, nor exclude from them any element that is directly experienced. For such a philosophy, the relations that connect experiences must themselves be experienced (p.81) relations, and any kind of relation experienced must be accounted as “real” as anything else in the system.

  The totality of accumulated human knowledge is what forms our basis for living and acting. We have to accept it until we have empirical reasons to abandon cherished beliefs or correct common misconceptions. However, the totality of our experience cannot be captured and taught, but it can grow only at its edges.

  To continue thinking unchallenged is ninety‐nine times out of a hundred, our practical substitute for knowing in the completed sense. As each experience runs by cognitive transitions into the next one, and we nowhere feel a collision with what we elsewhere count as truth or fact, we commit ourselves to the current as if the port were sure. We live, as it were, upon the front edge of an advancing wave‐crest, and our sense of a determinate direction in falling forward is all we cover of the future of our path.

 

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