Teknema 5 / "Energy and Chance"/ Fall 1999
Non-Epistemic Chance: Karl Popper’s Ontology
Howard Caygill
The true logic of this world is the calculus of probability.
—James Clerk Maxwell
In his 1973 essay "The World of Parmenides" Karl Popper made the provocative claim that "Parmenides was not an ontologist" and that the lesson of Parmenides’ poem was precisely the "impossibility of a non-empty ontology" (Popper 1998:114). Yet the rejection of ontology in terms of the traditional ontological categories of modality (possibility/impossibility) and quality (emptiness/fullness) indicates that Popper is not so free of ontology as he thinks, and invites the hypothesis that the bedrock of his work is ontological. Yet for Popper, ontological arguments—whether proposed by Plato, Marx or Heidegger—by stressing being as opposed to becoming are tendentially dogmatic and provide support for the enemies of the "open society." His work in the philosophy of science provides support for his political liberalism, both of which profess to be anti-ontological. If the appeal to an epistemological program based on a Kantian concept of experience in the Logic of Scientific Discovery of 1934 and the succeeding cosmological program in the Postscripts to that work, especially Quantum Theory and the Schism in Physics (1956/82), and the posthumously published The World of Parmenides: Essays on the Presocratic Enlightenment (1998), can be shown to be ontological, this will put in question not only his philosophy of science but also the concept of "openness" that grounds his political philosophy. The discovery of an ontology in Popper will have implications not only for the epistemological proposition of falsifiability but also for his cosmology and the non-epistemic theory of chance ratified in the propensity theory of probability and carried over into his political philosophy.
In "The World of Parmenides" Popper justifies his repudiation of ontology by means of a distinction between ontology and cosmology: the former is concerned with "being" the latter with "change." Popper extends Kant’s arguments for limiting the use of being as a predicate in "The One Possible Proof for the Existence of God" into a complete rejection of ontology as but a "verbal argument." In this residual gesture towards the anti-metaphysical program of the Vienna Circle he forgets Kant’s description of the "Transcendental Analytic" as an ontology and the theory of experience developed in it as "ontological." He focuses instead on the problem of change, which he claims is "not an ontological problem but a cosmological problem" (114). Parmenides’ proposition that being is one, undivided and ungenerated, is for him an ontological conjecture that opened the way for the cosmological refutation of Democritean atomism with the view of change as the movement of atoms in a void.
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The epoch of the allegedly cosmological theory of atomic change inaugurated by Democritus was for Popper closed with the discoveries of particle physics commencing in the mid 1930s: "The new particles, and especially the fact that they can decay into very different particles, represent the theoretically most important discovery since Democritus. For they have destroyed the fundamental research program of physics—the atomic theory of change" (198). Yet the scope of this revolution should not be restricted to "research programs" but extends to the understanding of the character of being itself, moving from an atomic to an electro-magnetic wave theory of matter and beyond. Popper’s response to this revolutionary change may be traced in the changing roles played by metaphysics and chance in the decades between the Logic of Scientific Discovery and its Postscripts, a period which coincided with the discovery of the elementary particles. This may be summarized in terms of a move from a broadly Kantian concept of experience allied with a frequency theory of probability to the rediscovery (led by Heisenberg) of the virtues of Aristotelian ontology and the propensity theory of probability. The Logic of Scientific Discovery
2 is divided into two parts: it begins with a short, two chapter introduction to "the logic of science" which is followed by eight chapters entitled "Some Structural Components of a Theory of Experience." The title of the largest section of the book betrays its Kantian origins, as does the insistent critique of induction in the name of temporal a prioris, the use of the de facto/de jure distinction and the single-minded pursuit of a transcendental deduction of valid knowledge through falsifiability.
Of like Kantian (or rather neo-Kantian) inspiration is the attempt to replace "metaphysical" ideas such as causality with "methodological rules," Popper’s term for Kant’s "regulative ideas."
3 Popper applies this Kantian structure to understanding the revolution in physics inaugurated by Maxwell in the previous century which developed into quantum mechanics. More ambitiously, the book is directed against the "Copenhagen Interpretation" of quantum mechanics which Popper understands as defending an epistemic or "subjective" concept of chance.
Popper summarizes the grounds for his dissent from the Copenhagen Interpretation in the 1982 preface to Quantum Theory and the Schism in Physics. He refuses to accept the assumption that a "fundamentally and irreducibly statistical physics has to be explained by a fundamental and irreducible barrier to our (subjective) knowledge" (Popper 1982:5). In this view, the elaboration of arguments based upon probability statements depends upon an epistemic concept of chance that understands random events as a reflection of the limits of the subjective understanding of reality. Popper traces this epistemic understanding of chance and its formulation in probability statements to Laplace, whose 1814 Philosophical Discourse on Probability defined probability statements in terms of subjective certainty, postulating an omniscient consciousness for whom all probabilities will be reduced to certainty or zero probability. Popper locates Heisenberg’s uncertainty principle within this tradition, with the proviso that for Heisenberg an omniscient consciousness is no longer an option, all that remains of Laplace is the necessary ignorance entailed by the uncertainty principle.
In the Logic of Scientific Discovery Popper describes the uncertainty principle in the following terms:
Every physical measurement involves an exchange of energy between the object measured and the measuring apparatus (which might be the observer himself) […] Any such exchange of energy will alter the state of the object which, after being measured, will be in a state different from before. Thus the measurement yields, as it were, knowledge of a state which has just been destroyed by the measuring apparatus itself. (Popper 1934, 218)
The impossibility of measuring both the position and momentum of a molecule or particle is regarded in the Copenhagen Interpretation as a consequence of the inevitable "subjectivity" of measurement. For this reason, in Popper’s words, "probabilistic considerations enter physics only because we cannot possibly know the precise positions and momenta of all molecules in a gas" (Popper 1982, 4). The structure of the argument is akin to certain moments in Kant’s Critique of Pure Reason where the "thing in itself" is by definition beyond the limits of possible experience. Here the apparently random movements of molecules and particles are defined by the limits of our experience and are not ontologically constitutive of those limits. The debate around the nature of probability statements that informs much of the Logic of Scientific Discovery is thus implicitly a debate in ontology, precisely the "no-man’s land that lies between logic and physics" where Popper expected to find "the solution of some of the still unsolved problems in quantum theory" (Popper 1934, 215).
The later editions of the Logic of Scientific Discovery betray not only the change in Popper’s appreciation of metaphysics but also a shift in his undeclared ontology from a Kantian analytic of experience to an Aristotelian conception of dúnamis or potentia. The argument is framed in terms of an analysis of probability statements, or in other words, in terms of a reflection upon the ontological character of chance. In 1934 Popper identified two tasks facing the theory of probability: the first involved providing "new foundations for the calculus of probability" and the second in elucidating "the relations between probability and experience" or addressing "the problem of decidability of probability statements" (146). The first project involved the discovery of an "objective" foundation to the calculus of probability, the second—following the spirit of the Kantian transcendental dialectic—consisted in limiting the extent of the statistical n-series in order to avoid illegitimate or "metaphysical" speculations.
The account of the calculus of probability presented in 1934 rejects subjective accounts of probability such as those of Laplace and Keynes in favor of an objective or "frequency interpretation." This is "objective" in so far that it replaces degrees of knowledge and ignorance by the "relative frequency with which an event of a certain kind occurs within a sequence of occurrences [or n-series]" (149). If an event in a possible sequences of occurrences or n-series of events recurs at every value of n, then its probability is 1; if it does not occur at all, then it is zero: intermediate frequencies between zero and one give probability statements of "observable regularities" of varying degrees of certainty. However, the danger with this "objective approach" consists in what may be described as its undisclosed subjective moment—the choice of the length of the n-series. If we make probability statements based on an n-series without introducing what Popper described as "special precautions" then we may become prone to statements of "speculative metaphysics" (197). By these Popper intends statements that so extend the n-series in order to explain "any regularity we please." Popper’s example is the proposition that the law of gravity is probabilistic, based on a number of chance events:
If we assume that the segment of the sequence has this very great length—or in other words, that the "world" lasts long enough—then our assumption of randomness entitles us to expect the occurrence of a cosmic period in which the law of gravity will seem to hold good, although "in reality" nothing every occurs but random scattering. This type of "explanation" by means of an assumption of randomness is applicable to any regularity we choose. In fact we can in this way "explain" our whole world, with all its observed regularities, as a phase in random chaos—as an accumulation of purely accidental occurrences. (197)
The objection to the illegitimate extension of the n-series is classically Kantian in its reluctance to extend the series of events beyond the limits of experience, a speculative metaphysics diagnosed by Kant in the cosmological antinomies of the Critique of Pure Reason which extend the series of events which make up the world of experience to their putative beginning beyond the limits of experience. However, while Kant opened a space within which the limits of experience could be argued ontologically through a Transcendental Analytic of finite appearances, Popper in his refusal of ontology is forced to establish the limits of experience by dictate or a posited "methodological decision" arbitrarily to limit the n-series. The resort to a decisionistic model of "special precautions" resulted from a fear of metaphysics manifest in the refusal to analyze the ontological character of the n-series and the operation of chance revealed in frequency statements. This meant no less than the re-introduction of subjective knowledge (of when to terminate the n-series) into probability statements.
Paragraph 67 of the Logic of Scientific Discovery on the critique of a "Probabilistic System of Speculative Metaphysics" concludes with a ratification of subjective decisions to determine the length of the n-series: "theories involving probability, therefore, if they are applied without special precautions, are not to be regarded as scientific. We must rule out their metaphysical use if they are to have any use in the practice of empirical science" (198). In his rush to exclude metaphysics, Popper leaves unexamined the question of the kind of knowledge that would allow the observer to determine what was the proper length of the n-series for scientific judgements as well as the conditions under which it might be determined when the use of a given series has become metaphysical. If the latter is not to be an unfounded decision based upon faith or prejudice then it must be grounded in a conception of the nature of the event and the series, that is, it must have an ontological foundation. Popper will later concede the need for a conception of the event, but insist that the event and the series be understood cosmologically as a sequence making up a series of related and directional changes.
Later in his discussion, Popper found himself forced to adopt a subjective definition of chance as that state "when our knowledge does not suffice for prediction" (206). This was necessary in order to avoid the speculative metaphysical claims for a universe made up of random events. Only if our predictions are corroborated can we speak of laws, and if they are not, then we must describe our ignorance as "chance." However, his uneasy rejection of the "metaphysical idea that events are, or are not, determined in themselves" is retracted in a footnote from a later edition where he claims that he "dismissed (because of its metaphysical character) a metaphysical theory that I am now, in my Postscripts, anxious to recommend because it seems to me to open new vistas, to suggest the resolution of serious difficulties, and to be, perhaps, true" (206). Later he similarly retracts the critique of the "metaphysical idea that not only can we deduce and test predictions, but that, in addition, nature is more or less ‘determined’ (or ‘undetermined’); so that the success (or failure) of predictions is to be explained not by the laws from which they are deduced, but over and above this by the fact that nature is actually constituted (or not constituted) according to these laws" (212). Popper’s footnote claim that "this somewhat disparaging characterization fits perfectly my own views […] under the name of the propensity interpretation of probability" is no less than a turn to ontology. What is at issue is the character of "nature"—whether it is determined or undetermined or constituted by laws or by chance. The propensity theory of probability is thus inseparable from a reflection upon the nature of being, or in other words, from "ontology."
Popper’s discussion of the propensity theory of probability is to be found in his Postscripts to the Logic of Scientific Discovery. In the third postscript—Quantum Theory and the Schism in Physics—he develops the subtle argument that the commitment to subjective probabilities of the Copenhagen Interpretation arises from a residual "determinism" or reluctance to accept non-epistemic or "objective" chance. A subjective concept of chance locates the aleatoric epistemologically in the limits of human knowledge while the objective concept argues for an ontology of chance, claiming that being itself is structured randomly. Popper argues not only that a commitment to subjective probability is compatible with objective determinism, but that "it is, in a way, the only reasonable possibility […] for objective physical probabilities are incompatible with determinism" (Popper 1982, 105). Popper illustrates the difference between the two views of chance with the example of the second law of thermodynamics, posing a choice between explaining the irreversible increase in the disorder of a system in terms of our ignorance or in terms of the system itself. The subjective theoreticians "instead of interpreting the ‘entropy’ of a system as a measure of its objective state of disorder or randomness, they interpret it as a measure of our own subjective state of ignorance of the system" (112). By this time he himself had come to subscribe to an objective concept of chance, defining its operation in terms of a propensity theory of probability.
The commitment to objective chance and the propensity theory of probability followed from Popper’s position in the ontological debate between wave and particle theories of matter. Indeed, his position is very close to that taken by Leibniz between atomism and Cartesian vortices,
4 understanding the waves as "mathematical propensities, or dispositional properties, of the physical situation (such as the experimental set-up), interpretable as propensities of the particles to take up certain states" (126). The compacting together of "mathematical propensities" and "dispositional properties" evident in this passage is unpacked later in the argument when Popper links the propensity interpretation of probability with objective dispositional tendencies. If the dispositions are "interpreted as tendencies to realize themselves, they lead to correspondingly statistical frequencies in a virtual (or real) aggregate or collective" (129-30). The dispositions in question not only are attributed "varying strengths or weights or intensities" whose degrees are measured in probability statements but they are also considered to be expressions of possibility.
Popper finds anticipations of the propensity theory of probability in the work of Born, Heisenberg and Schrodinger, but claims that they did not recognize the ontological implications of their statistical discoveries. His argument for a metaphysical reinterpretation of their work rested not only on "the fact that no propensity theory of probability existed at the time" but more broadly with "our Aristotelian and essentialist habit of expressing ourselves […] which suggests that relationist properties are not ‘real’ but ‘ideal’" (128). The second point exposes a fascinating inconsistency in Popper’s metaphysical convictions, one which goes to the heart of his avoidance of ontology. This involves the place of Aristotelian ontology in his thought. At first sight his critique of Aristotle’s "dogmatism" here (and elsewhere) seems implacable: Popper criticizes the Stagirite’s preference for "categorial, i.e., subject predicate statements" that he founds "relation" "only in our own thinking and ordering activities" (ibid.). Yet this surprising critique of Aristotle’s inauguration of epistemology in the Categories is accompanied by an equally unexpected alignment with Aristotle’s metaphysics, one which identifies the propensities with Aristotelian dúnamis (potentia).
The move towards the alignment of propensity and dúnamis was prepared by a comment in Heisenberg’s 1955 paper "The Development of the Interpretation of the Quantum Theory" which identified the "probability concept" of quantum mechanics as "a transformation of the old ‘potentia’ concept from a qualitative to a quantitative idea." Popper’s endorsement of this position in his phrase "the real potentialities of the potentia, i.e., of our propensity" (133) was not incidental. In the "Metaphysical Epilogue" Popper systematically phrases the propensity in terms of Aristotelian ontology, and in his rare light-hearted moments goes so far as to phrase the propensity theory in "the terminology" first of Ionian cosmology as "everything is a propensity" and then in that of Aristotle as "to be is both to be the actualization of a prior propensity to become and to be a propensity to become" (205).
In a more serious vein, Popper develops an historical analogy between the move from an Aristotelian notion of potentiality to his own propensity with the move from Newtonian central forces (such as gravity) to the field theories of force developed by Faraday and Maxwell. He first proposes that "the Aristotelian view of inherent potentialities and their actualization is developed into a relational theory in which relational structures, instead of inhering in each material thing, may be characterized by potentialities" (206). With this proposal Popper moves the site of potentia from substance to relation, a move consistent with Aristotle’s Metaphysics, which is far from providing any dogmatic argument for a metaphysics of substance. This change in the emphasis of Aristotelian metaphysics is then mapped onto the second scientific revolution of Faraday and Maxwell: "central forces (which correspond to the Aristotelian inherent potentialities) give place as with Faraday and Maxwell to fields of potentialities of a relational character" (206). These fields of potentiality are none other than Popper’s propensities.
Popper’s cosmology is revealed in the end to be a revised form of Aristotelian ontology. The bearer of potentiality is no longer the individual substance but the relation between the elements of a system and their past present and future. The Popperian dispositions and propensities arrive with all the properties of Aristotelian substance, allowing him "to interpret any real state of the world as both the actualization or realization of some of the potentialities or propensities of its preceding states and also a field of dispositions or propensities to realize the next state" (198). Whether potentia is located in an individual particle or atom or a in a field of forces is immaterial, the enterprise remains ontological. The escape from epistemic to non-epistemic conceptions of chance is only possible by way of ontology. In Popper’s ontology, being is neither unified in a single substance, nor dispersed into atoms, but is articulated in terms of the movement of particles and waves which locate it in its history but also open it to the chance of the future. Yet this openness is defined and articulated ontologically, suggesting that it is only in the context of ontological debate that a notion of chance can be defended. Without ontology chance remains a function of ignorance, leaving the field either to decisionism or to the claims to absolute knowledge characteristic of dogmatic ontology.