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Popper and Maxwell on Scientific Progress Leemon McHenry


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 Popper and Maxwell on Scientific Progress

Leemon McHenry

1. Introduction


Science is the supreme achievement of rationality, but does it make progress in a way in which other human endeavors do not?  In spite of its fallible and self-correcting nature, few would dispute the advances in our understanding of the cosmos, the electromagnetic spectrum, and the mapping of the human genome.  Yet others contend that this is naïve.   Science changes and develops, but it does not progress in the sense that it achieves truth or approximates truth.  In this regard, the detractors argue, science is just another ideology or social construction and not significantly different from art, morality, politics and religion.  The real question then is how does science make progress if indeed it does?  The whole enterprise of attempting to defend the idea of scientific advance involves us in theories of scientific progress, of which both Karl Popper and Nicholas Maxwell have made important contributions.

     At the beginning of Maxwell’s The Comprehensibility of the Universe, he describes the success of modern science beginning with Galileo and Kepler as “astonishing” and asks: “What is the methodological key to the unprecedented progressive success of modern science?”   His answer challenges what he calls “standard empiricism,” i.e., the orthodox conception that scientific theories are accepted or rejected solely with respect to the justice they do to the evidence, but not in a manner that explicitly recognizes any substantial thesis about the world as part of scientific knowledge.  Science does make progress, according to Maxwell, but it is not by the widely-accepted view of standard empiricism.  What is required, he argues, is a commitment to metaphysical principles underlying our notion that the universe is comprehensible.  But in addition to this criticism, Maxwell has devoted a great deal of his work to recognizing that science has the power to do as much harm as good, hence the theme of his life’s work--from knowledge to wisdom.  This raises a much larger question about progress when the consequences of a singled-minded quest for knowledge are not guided by the wisdom of sound judgment.  While my primary concern in this essay is the first question of how science makes progress, I shall also touch upon this second question raised by Maxwell’s work.  In particular, I wish to examine his critique of his philosophical mentor.  As Maxwell says in his Autobiographical Remarks, it was Karl Popper who opened a path in the philosophy of science and from this conceptual framework he developed his own critical evaluation.          

     Both Popper and Maxwell agree that science makes progress.  The question of scientific progress, however, requires an examination of how they view the aims of science, for the very notion of scientific progress depends upon a view of the aims of science.

2. Popper’s Falsification and Explanation


In Objective Knowledge, Popper says that the aim of science is satisfactory explanations, i.e., explanations advanced in terms of testable and falsifiable universal laws and initial conditions.  As he says:

the conjecture that it is the aim of science to find satisfactory explanations leads us further to the idea of improving the degree of satisfactoriness of the explanations by improving their degree of testability, that is to say, by proceeding to theories of ever richer content, of a higher degree of universality, and of higher degree of precision.  

Popper came to this view via his central problem of demarcation, namely, the problem of distinguishing between science and non-science.  In his classic work, The Logic of Scientific Discovery, he rejected the inductivist view of the growth of scientific knowledge and landed upon the one fundamental idea around which his philosophy is based.  Science progresses not by the accumulation of truths whereby later theories absorb what was correct in earlier ones, but rather by a curiously negative path of proving theories false, for the falsification of a theory is a decisive step forward in the sense that we have eliminated falsehood and can now substitute the old theory with a new one that has greater explanatory and predicative power.  This, Popper contends, is the great achievement of science that distinguishes its method from those of non-science, metaphysics, ideology, etc.  Rigor is achieved in science by proposing bold conjectures and then actively seeking out severely critical and risky empirical testing that can potentially refute the conjectures.  In other fields of human endeavor we have mere change, but rarely anything that approaches progress in science (and, of course, mathematics) by a clear method of detecting error.

     Science is guesswork, doxa rather than episteme.  In place of the old ideal (or rather idol) of science as the search for absolutely certain, demonstrable knowledge, Popper argues that the “demand for scientific objectivity makes it inevitable that every scientific statement must remain tentative for ever.”   Verification of scientific knowledge is replaced by falsification.  Accumulation of irrefutable facts is replaced by conjecture and refutation.

     Popper’s view of science as conjectural challenges the idea that the empirical base of science is an unchangeable and stable foundation from which we can measure progress.  As he says:

The empirical basis of objective science has thus nothing ‘absolute’ about it. Science does not rest upon solid bedrock.  The bold structure of its theories rises, as it were, above a swamp.  It is like a building erected on piles.  The piles are driven down from above into the swamp, but not down to any natural or ‘given’ base; and if we stop driving the piles deeper, it is not because we have reached firm ground.  We simply stop when we are satisfied that the piles are firm enough to carry the structure, at least for the time being.

Strictly speaking, the truth value of any scientific theory must be regarded as false.  If it has been falsified, it is false; if not, then it will at some future point be demonstrated false.  A theory is corroborated if it has withstood genuine attempts at falsification, but it is never anything more than a working hypothesis, never demonstrated true.  This is born out according to the logical asymmetry between verification and falsification.  While it is impossible to verify a universal law by reference to some putative confirming experience, a single counter-instance to the universal law conclusively refutes it.  We pursue truth, but at best, we can only have the expectation of finding our where our theories are mistaken and replacing them with better ones.

     A good scientific theory, for Popper, is one that puts itself at a genuine risk of being proved false due to its high informative content.  This has a rather paradoxical result especially if we are inclined to think that the more probable a theory, the better it is.   For Popper, we should not assume uncritically that high probability is an aim of science.  The more improbable a theory, the better it is as a scientific theory because probability and informative content vary inversely.  The higher the informative content of a theory, the lower the probability the theory will have.  This will be clear since the higher informative content means that scientists will have a better chance of demonstrating that the theory can be falsified.  The aim of science then is not high probability of theory turning out to be true, but rather high informative content leading to the demonstration of its falsehood.

     Still this may appear insufficient to describe the progress of science.  Does knowing what is false give us progress?  Popper seems to have recognized this point.  He writes:

…this picture of science--as a procedure whose rationality consists in the fact that we learn from our mistakes--is not quite good enough.  It may still suggest that science progresses from theory to theory and that it consists of a sequence of better and better deductive systems.  Yet what I really wish to suggest is that science should be visualized as progressing from problems to problems—to problems of ever increasing depth.

Popper viewed problem-solving as the hallmark of science but to account for a sequence of better and better deductive systems, he required an idea of truth.  He argued that the very idea of truth allows us to recognize mistakes and engage in the rational pursuit of eliminating mistakes.  The standard of an objective truth about the world, of which our empirical testing gives results, is the basis for the very idea of error.  What is needed for progress, however, is some explanation of how the succession of false theories constitutes progress.  The answer came in part with Popper’s attempt at the theory of verisimilitude--that later theories have a higher degree of verisimilitude or truth-likeness because though all are false, they get progressively closer to the truth.  That is, the truth-content is higher and the falsity-content is lower as we move from earlier to later theories.  In spite of the fact that Popper’s formal definitions of verisimilitude were demonstrated to be problematic, he maintained that the common sense notion that “science aims at truth in the sense of correspondence to the facts or to reality” remained a valuable heuristic device.  A well-corroborated successor to a falsified theory is a better approximation to truth provided that it has also met some new predicative success.

     So, for Popper, scientific progress is understood in terms of how theories replace others via the severely critical process of falsification.  A theory that has replaced a predecessor has a higher degree of testability and universality, richer content, greater precision and predicative power and deals with problems of ever-increasing depth that result in more satisfactory explanations.  Moreover, the idea of progress from theory to theory requires increasing fertility in that new conjectures will provide guidance in research to further problems and solutions.

     As Popper generalized his falsification theory to apply more broadly to problem solving in other areas of non-scientific inquiry, he extended his critical rationalism such that progress in metaphysics, politics and morality is achieved by the degree to which a discipline engages in rational discourse in advancing and criticizing theories.   The new criterion of demarcation is not between science and non-science, but rather between systems devoid of rational value and systems that are engaged in solving serious and interesting problems.  The boundary between science and metaphysics, or science and politics remains sharply drawn on the basis of falsifiability, but this does not mean metaphysics or politics is meaningless discourse as long as ideas are subjected to rigorous criticism and stand only as tentative and fallible solutions to problems.  Popper even recognizes that metaphysics is an inevitable precursor to science, as a sort of embryo in the development of scientific hypotheses.   The main obstacle to progress in these disciplines is not that they fail to be scientific but rather that they embrace dogma, i.e., ideological intolerance or simply become subject to intellectual fashion.

3. Maxwell’s Critique: Aim Oriented Empiricism


Maxwell sees the aim of science quite differently.  In place of Popper’s emphasis on satisfactory explanations, he first of all argues that science seeks explanatory truth in the sense that truth is presupposed to be explanatory by a substantial thesis about the world, and secondly that science aims at valuable truth.  With regard to the latter, Maxwell sees a larger social context in which science contributes, or should contribute, to the quality of human life.  The progress of science very broadly depends on what is of cultural and intellectual value.  Maxwell thus recognizes a broader telos in science. The aim is not just bare Truth as an abstract ideal of scientific objectivity but rather valuable truth that is put to concrete action.   In other words, Maxwell sees the very idea of progress is a normative or axiological concept.

     Popper’s view, Maxwell argues, is a primary example of standard empiricism or at least the view he held early in his career.  But the fact is that science does not practice this hard-nosed conception of its method; for if it did, he contends, science would come to a standstill.  This is an essential thesis of The Comprehensibility of the Universe -- that the official, orthodox view of science as advancing by strict adherence to the evidence is untenable and makes it impossible to understand how science makes progress.  Maxwell cites Popper: “in science, only observation and experiment may decide upon the acceptance and rejection of scientific statements, including laws and theories.” Given the existence of a number of competing hypotheses all empirically equivalent, there is no criterion for selection.  To make the point more strongly, Maxwell argues that there will be an infinite number of grossly ad hoc but equally (or even more) empirically successful rivals to a theory, yet if empirical considerations alone are supposed to justify the theory currently upheld, then there are no rational grounds for rejecting the infinitely many rivals to the theory.    So, in Popper’s terms, given a number of theories, all of which are equally falsifiable, it becomes difficult to understand which one becomes the accepted physical theory that provides guidance to a number of research programs.  Even the ones that are grossly ad hoc will satisfy Popper’s requirements for being superior theories to the ones currently accepted.  If falsification based on high empirical content alone is the criterion for the scientific status of a theory, the grossly ad hoc and even crackpot theories will have to be taken seriously as the best scientific theories because they will be immediately falsifiable.  Clearly this is not what actually happens in science.

     Maxwell calls Popper’s early falsification theory of The Logic of Scientific Discovery, “bare falsificationism,” that is, only empirical considerations and degrees of falsifiability determine what is to be accepted and rejected in science.  But he contends as Popper developed his view, he devised a modification that Maxwell calls “dressed falsificationism.”  According to the dressed version contained within a discussion of scientific progress in Conjectures and Refutations, simplicity is acknowledged as a meta-scientific criterion in addition to falsifiability for rational choice between theories.  Popper here recognized that a scientist seeking a new theory capable of explaining certain experimental facts must consider the requirement that the “new theory should proceed from some simple, new, and powerful, unifying idea about some connection or relation … between hitherto unconnected things or facts … or new theoretical entities.”  

      If Maxwell is correct in this interpretation, then Popper himself recognized that falsification remained the successful demarcation between science and non-science, but that falsification alone was inadequate to describe a good scientific theory and account for scientific progress.  According to dressed falsification then, falsification is a necessary but not sufficient condition for identifying progress in science.  A new theory could not simply be any theory, wildly speculative, ad hoc, or whatever taken out of the blue that is easily refuted; rather it has to have some connection or relation to its predecessors such that its success involves unification of previously disparate phenomena as well as greater explanatory and predicative power.     

     Maxwell has extended his argument against standard empiricism to make the radical claim that science so-conceived is guilty of, or suffers from, a “rationalistic neurosis,” for the claim of standard empiricism is that science aims at factual truths via adherence to the evidence whereas in reality science aims at improving our knowledge of the universe as unified and physically comprehensible.   This means that science must proceed with an assumption that the universe has an underlying unity that forbids consideration of grotesquely disunified theories, and the sharp boundary between metaphysics and science is eliminated.  For Maxwell, the scientist must be engaged in natural philosophy in the sense that untestable, substantial theses about the world are accepted as part of scientific knowledge.  Here we see a major difference from Popper’s theory, bare or dressed, since there was an element of positivism that lingered in Popper’s thought: metaphysical theses could not be admitted into the framework of scientific knowledge.

     Admitting that science cannot proceed without some basic assumption about the universe as comprehensible, the question is not whether science adopts a metaphysics but rather which metaphysics best suits our currently accepted fundamental physical theories, or does the best justice to the long-term development of physics.  This also opens the door to discussions about fundamental aims and methods.  Maxwell argues that the neurosis of science does not just involve the “repression” of problematic metaphysical assumptions about the comprehensibility of the universe; it also involves the repression of problematic assumptions concerning values and politics.  And more generally, academic inquiry as a whole represses problematic assumptions about what our aims ought to be in seeking social progress and civilization. What is needed most is a science, and a kind of rational inquiry more generally, that is devoted to articulating and helping to solve the real problems of humanity rather than merely adding to our stock of scientific facts.  We have made extraordinary strides in solutions to what Maxwell calls the “first great problem of learning,” namely, the acquisition of reliable knowledge of the world, but we have utterly failed to solve the second problem of global wisdom and civilization. The dogma of standard empiricism coupled with specialization instilled throughout the natural and social sciences and in our institutions of academic inquiry has the effect of preventing us from developing our aims and methods of problem-solving in such a way that humanity realizes that which is of fundamental importance.

     Maxwell suggests that the idea of the scientist as a dispassionate, disinterested, unbiased inquirer into objective truth is a myth, and once we own up to this fact by accepting the argument against standard empiricism, the fact/value distinction that separates science from the humanities must also be abandoned.  This is not to say that there isn’t a distinction between facts and values, but rather that science as a value-neutral inquiry simply does not exist and we can no longer excuse science from the failure to make positive contributions to the goal of civilization by appealing to the myth.  As Maxwell argues:

…values, of one kind or another, are inevitably, entirely properly and desirably, built into the scientific enterprise in influencing choice of research aims, in influencing what scientists seek to develop knowledge about…. I do not, then, argue against the value neutrality of science, for there is no such thing; what I do argue against, again, is the official philosophy of science of standard empiricism which, falsely and damagingly, denies that values do play any legitimate role within science.

     Just as Popper developed a philosophy of critical rationalism from his falsification theory, moving from philosophy of science to social and political theory, Maxwell likewise developed his aim-oriented rationalism as a generalization from aim-oriented empiricism.  Aim-oriented rationalism unlike critical rationalism, however, involves the idea of critically assessing our aims and methods in the attempt to contribute to the quality of human life.  The difference with Popper is clear for he is primarily concerned with problems of knowledge, whereas Maxwell shifts attention to problems of living.   Popper attempted to improve upon the Enlightenment ideal of learning from scientific progress how to make similar progress in the social sciences by focusing upon the rational, free and open society, but he conceived of progress entirely by way of the methods of social science imitating those of the natural sciences.  Maxwell instead focuses upon social inquiry in establishing and criticizing goals.  Social inquiry is not social science with a methodology similar to natural science.  Rather it gives priority to the needs of humanity, the goal of which is progress toward a sustainable, enlightened and civilized world.  Scientific progress falls under the purview of wisdom-inquiry rather than the more restricted knowledge-inquiry.  Aim-oriented rationalism embracing the former rather than the latter becomes a peoples’ civil service.  

4.  Evaluation


Maxwell contends that Popper’s view must result in the consequence that science is an infinite chain of false theories and caricatures the theory of falsification as a sort of blind mechanism whereby science staggers from one false theory to another.   As he explains: “When a theory is falsified, scientists must think up an even more falsifiable conjecture, which predicts everything its predecessor predicts, is not falsified by the experiment that falsified its predecessor, and predicts additional phenomena as well.  As a result of proceeding in this way, science is able to make progress because falsehood is constantly being detected and eliminated by this process of conjecture and refutation.”   However, he charges: “Not only does falsificationism fail to specify properly the methods that science makes progress in theoretical physics possible; it fails even to say what progress in theoretical physics means.  

         Let us take an example from physics in order to examine Maxwell’s position more carefully.  Alan Guth in his The Inflationary Universe says: “With the advent of the 1970s, . . . , particle physics went through a period of extraordinary progress, culminating in a theory that has come to be known as the standard model of particle physics.” Guth goes on to say that while this theory is not the ultimate theory, it is nonetheless the most successful theory that physicists have ever advanced, for here we have a theory that is well tested and has gone through a sequence of modifications in the unification of weak, electromagnetic, and strong interactions.  I take it both Popper and Maxwell would agree that the standard model of particle physics is an example of scientific progress, and according to the modified or “dressed” theory of Conjectures and Refutations, here we have a good theory in the sense that it has extraordinary explanatory power, has stood up against genuine testing, has unified into a simple theory what was previously disunified or fragmentary theories and has provided guidance to further research, theoretical and practical, however imperfect.  There still remains, of course, the question of ultimate unification sought in contemporary physics, the stumbling block with general relativity, and the potential refutation if string theory or some other grand hypothesis replaces the standard model in a scientific revolution, but here we have probably the best example of what progress is. 

     Maxwell’s admits that dressed falsificationism does better justice to scientific practice, but his main objection is that without an explicit, substantial metaphysical thesis that the universe is comprehensible and not-ad hoc corresponding to the assumption behind the simplicity thesis, Popper’s theory still fails.  In this case, adding simplicity to falsifability as a new criterion presents the difficulty that this presupposes that the universe is not grotesquely complex and disunified, which will clash with the requirement that this needs to be testable and potentially falsifable.  So, without admitting metaphysics into the framework of scientific knowledge, Popper allegedly violates his own requirement that substantial, influential, problematic assumptions need to be make explicit so that they can be subjected to criticism within science, yet these very metaphysical principles cannot be part of science because they are in principle irrefutable.

     I think Maxwell is correct in his assessment of the tension in Popper’s late theory, but this alone does not mean that he has failed to say what progress is or means, unless Maxwell has in mind Popper’s “bare” theory, i.e., falsifiability alone is insufficient to give a complete account of scientific progress, but even Popper recognized this.  For it seems that the real difference between Popper and Maxwell hangs on the status of metaphysics; Maxwell admits metaphysics into the framework of scientific knowledge while Popper rejected such a notion even in his very late work. 

     What role then did metaphysics play in the development of the standard model?  Surely Maxwell is right that the theory presupposes that the universe is comprehensible, simple and unified, that physicalism is always a premise in the most basic thinking and that some sort of ontology of the energy field as a unifying concept was crucial in the early development of the theory.  For Popper, however, all of this is important, “held unconsciously” in the minds of scientists and implicit in the theories they advance, but still not part of science per se.  As indicated above, the element of positivism that lingered in Popper’s thought prevented him from acknowledging metaphysical principles as part of science, for he could not retain the central importance of falsification and admit that metaphysics plays a role in the selection of theories.  Even when he considers simplicity and unity as part of the criteria, he does not spell out what this amounts to.  Maxwell, on the other hand, escapes Popper’s problem by proposing a hierarchy of ten levels introduced as central to his aim-oriented empiricism.   Falsification functions at levels one and two in terms of the relationship between theory and evidence.  And as one ascends the levels in his hierarchy, we find increasingly general metaphysical and epistemological principles, e.g., physicalism, comprehensibility, epistemological non-maliciousness, partial knowability.  This is, as he puts it, “some permanent assumption about the nature of the universe being made independently of empirical considerations.

     Steven Weinberg, who made a significant contribution to the standard model with his unification of the electromagnetic and weak forces in the electroweak force, seems to agree with Maxwell.  While expressing doubts about the positive influence of philosophy in science, he nonetheless claims that physics is not done without preconceptions, for without them “one could do nothing at all.”   Weinberg admits a rough-and-ready realism and a belief in the objective reality of the ingredients of our theories corresponding roughly to Maxwell’s notions of physicalism and comprehensibility presupposed in physical theory.  And as he expounds on the developments in twentieth century physics, particularly with regard to unification and simplicity in the quest for beautiful theories, it becomes clear that physics is not done without some basic commitment to ontology—an ontology that is developed by physicists in their experimental research rather than by following the lead of philosophy or thinking in traditional philosophical categories. Principles of symmetry, for example, are instances of simplicity in physical theories or laws of nature found in both the standard model and general relativity.  If I have understood Weinberg properly, he is arguing that these principles have a build-in assumption that the universe itself is so ordered or that they correspond to the intrinsic nature of the particles.  

     The failure to recognize the role of metaphysics as a part of science has produced some bizarre results, most notably, positivism’s influence on quantum theory and the resulting failure to solve fundamental problems of wave/particle duality and measurement.  The view that I have argued for, “naturalized metaphysics,” recognizes Maxwell’s point that a substantial commitment to metaphysical principles is essential to explaining how science works and also Weinberg’s concern about philosophy.  Instead of imposing philosophical categories onto science, metaphysics is the most abstract end of a continuum that develops out of scientific practice.  Metaphysics is ‘naturalized’ in the sense that our attempt to discover what there is does not arise above our scientific theories.   

     What is less clear is how Maxwell’s proposal for metaphysical foundations is connected to his more general philosophy of wisdom.  How is it, in his view, that theories in physics or any other branch of scientific investigation are connected to the goals of serving humanity?  Aim-oriented empiricism, he claims, accounts for scientific progress where standard empiricism fails.  The great scientists such as Einstein have been practicing aim-oriented empiricism or natural philosophy more generally all along.  So progress has been achieved in general relativity or the standard model despite the uncritical espousal of standard empiricism by the rank and file.  But aside from the sheer intellectual value of these developments, including the potential goal of complete unification, it remains unclear how Maxwell sees such theoretical success as contributing to the more general goal of solving problems of living or the achievement of global wisdom.  Would aim-oriented rationalism put into effect have altered the course of physics in the twentieth century such that our current theories would look entirely different and serve humanity in a way in which they are irrelevant at present?

     Maxwell has praised the standard model for its ability to account for all phenomena not associated with gravity, but has identified problems with the unification of forces and particles that are not determined by the theory itself.   Moreover, he spent a considerable part of his academic career attempting to demonstrate why orthodox quantum theory (following the Copenhagen interpretation) has failed to provide a complete theoretical framework.   These criticisms demonstrate why the theories fall short of the requirements of aim-oriented empiricism, but not his aim-oriented rationalism.  Aim-oriented empiricism, after all, cannot be just another version of what Maxwell calls “the philosophy of knowledge.”

5. Conclusion


Popper is widely acknowledged by scientists in a diversity of fields from physics to epidemiology as the champion of rigorous scientific method.  Genuine science is achieved not by seeking confirmation of the scientist’s cherished hypothesis, but rather by seeking to disprove the conjecture in a risky experiment.  Maxwell agrees citing Popper as the greatest philosopher of the twentieth century whose books “attack fundamental problems with ferocious integrity, clarity, simplicity, and originality.”   But Maxwell has also shown a major inconsistency in Popper’s philosophy of science.  Falsification alone cannot account for the progress of science.  The comprehensibility of the universe requires metaphysical principles as essential to scientific theory and practice.  Maxwell has thus offered an improvement on Popper by seeing falsification function within a larger structure of science, but as I have indicated above there is some question about the degree to which Maxwell’s proposed corrective to Popper would alter the course of science such that wisdom rather than knowledge becomes the primary goal.

     Both Popper and Maxwell rejected the conception of philosophy dominant in the twentieth century that treated problems as self-contained intellectual puzzles. They instead produced philosophical systems that are concerned with genuine scientific, social and political problems.  Their concern with defending the idea of scientific progress against detractors and offering clarification about its nature ranks amongst the most important of these problems.


Notes


I wish to thank Nicholas Maxwell for valuable criticism of an earlier draft of this paper, which is not to say that he would approve of any of its present contents.  I am also grateful to Donald Gillies for his peer review.

Paul Feyerabend, Against Method (London: Verso, 1975).

Nicholas Maxwell, The Comprehensibility of the Universe (Oxford: Clarendon Press, 1998), p. 1.

Nicholas Maxwell, “How Can Life of Value Best Flourish in the Real World” Chapter 1.

Karl Popper, Objective Knowledge: An Evolutionary Approach (Oxford: Clarendon Press, 1972), p. 193.

Thomas Kuhn described this traditional view as ‘incrementalism.”  Popper’s falsificationism shares with Kuhn an anti-incrementalism in that both espoused a view in which a change in scientific theory is not cumulative or continuous.

Karl Popper, The Logic of Scientific Discovery (New York: Basic Books, 1959), p. 280.

Ibid., p. 111.

Ibid., p. 218.

Karl Popper, Conjectures and Refutations (New York: Harper and Row, 1965), p. 222.

For criticisms of Popper’s verisimilitude, see David Miller, “Popper’s Qualitative Theory of Verisimilitude,” The British Journal for the Philosophy of Science 25 (1974), pp. 166-177 and P. Tichý, “On Popper’s Definition of Verisimilitude,” British Journal for the Philosophy of Science 25 (1974), pp. 155-160.

Karl Popper, Objective Knowledge, op. cit., p. 59. 

Karl Popper, The Open Society and Its Enemies, 2 volumes (London: Routledge, 1945).

Karl Popper, The Postscript to The Logic of Scientific Discovery, volume 3: Quantum Theory and the Schism in Physics (London: Routledge, 1992), especially pp. 199-211.

Nicholas Maxwell, The Comprehensibility of the Universe, op. cit., p. 3; Popper cited from Conjectures and Refutations, op. cit., p. 54.

Ibid., p. 3; also see Nicholas Maxwell, “Popper, Kuhn, Lakatos and Aim-Oriented Empiricism,” Philosophia 32/1-4, 2005, pp. 192-93.

Karl Popper, Conjectures and Refutations, op. cit., p. 241.

Nicholas Maxwell, Is Science Neurotic? (London: Imperial College Press, 2004), pp. 4-17.

Nicholas Maxwell, “Can Humanity Learn to Become Civilized? The Crisis of Science without Civilization,” Journal of Applied Philosophy, 17/1, 2000, pp. 29-44.

Nicholas Maxwell, From Knowledge to Wisdom: A Revolution for the Sciences and the Humanities, Second Edition (London: Pentire Press, 2007), p. 345.

Nicholas Maxwell, The Enlightenment Programme and Karl Popper, in Karl Popper: A Centenary Assessment. Volume 1: Life and Times, Values in a World of Facts, ed. I. Jarview, K. Milford and D. Miller, (eds) (London: Ashgate, 2006), pp. 177-90.

Nicholas Maxwell, The Comprehensibility of the Universe, op. cit., p. 24; also see From Knowledge to Wisdom, op. cit., p. 393.

Nicholas Maxwell, “The Enlightenment, Popper and Einstein,” in Y. Shi et al (eds) Advances in Multiple Criteria Decision Making and Human Systems Management (Amsterdam: IOS Press, 2007), p. 136.

Nicholas Maxwell, “Popper, Kuhn, Lakatos and Aim-Oriented Empiricism,” op. cit., p. 213.

Alan H. Guth, The Inflationary Universe (Reading, Mass: Helix Books, 1997), p. 119.

Nicholas Maxwell, “Popper, Kuhn, Lakatos and Aim-Oriented Empiricism,” op. cit., pp. 191-195.

Nicholas Maxwell, The Comprehensibility of the Universe, op. cit., p. 8.

Ibid., p. 4.

Steven Weinberg, Dreams of a Final Theory: The Scientist’s Search for the Ultimate Laws of Nature (New York: Vintage Books, 1992), p. 167. See also, Michael Redhead, From Physics to Metaphysics (Cambridge: Cambridge University Press, 1995).

Interestingly enough, Weinberg’s very point is addressed in Maxwell’s What is Wrong with Science? (London: Brian’s Head Books, 1976), pp. 70-71.

Steven Weinberg, Dreams of a Final Theory, op. cit., pp. 136, 138, 145.

Leemon McHenry, “Quine and Whitehead: Ontology and Methodology,” Process Studies, 26/1-2, 1997, pp. 2-12.

Nicholas Maxwell, The Comprehensibility of the Universe, op. cit., p. 139.

Nicholas Maxwell, “Particle Creation as the Quantum Condition for Probabilistic Events to Occur,” Physics Letters A, 187, 1994, pp. 351-355; “Quantum Propensiton Theory: A Testable Resolution of the Wave/Particle Dilemma,” British Journal of the Philosophy of Science, 39, 1988, pp. 1-50.



Nicholas Maxwell, “Karl Popper,” in P. B. Dematteis, P. S. Fosl and L. B. McHenry (eds) British Philosophers, 1800-2000 (Detroit: Thomson/Gale,  2002), p. 177.


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