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Newton's equations of motion tell us that a mass at rest at the apex of a dome with the shape specified here can spontaneously move. It has been suggested that this indeterminism should be discounted since it draws on an incomplete rendering of Newtonian physics, or it is “unphysical,” or it employs illicit idealizations. I analyze and reject each of these reasons.

Various fault modes of determinism in classical physics are outlined. It is shown how quantum mechanics can cure some forms of classical indeterminism.

A recent proposal by Norton (2003) to show that a simple Newtonian system can exhibit stochastic acausal behavior by giving rise to spontaneous movements of a mass on the dome of a certain shape is examined. We discuss the physical significance of an often overlooked and yet important Lipschitz condition the violation of which leads to the existence of anomalous nontrivial solutions in this and similar cases. We show that the Lipschitz condition is closely linked with the time reversibility of certain solutions in Newtonian mechanics and the failure to incorporate this condition within Newtonian mechanics may unsurprisingly lead to physically impossible solutions that have no serious metaphysical implications.

I examine different arguments that could be used to establish indeterminism of neurological processes. Even though scenarios where single events at the molecular level make the difference in the outcome of such processes are realistic, this falls short of establishing indeterminism, because it is not clear that these molecular events are subject to quantum mechanical uncertainty. Furthermore, attempts to argue for indeterminism autonomously (i.e., independently of quantum mechanics) fail, because both deterministic and indeterministic models can account for the empirically observed behavior of ion channels.

The ubiquitous probabilities of evolutionary theory (ET) spark the question: Which interpretation of probability is the most appropriate for ET? There is reason to think that, whatever we take probabilities in ET to be, they must be consistent with both determinism and indeterminism. I argue that the probabilities used in ET are objective in a realist sense, if not in an indeterministic sense. Furthermore, there are a number of interpretations of probability that are objective and would be consistent with deterministic evolution and indeterministic evolution. However, I suggest that evolutionary probabilities are best understood as propensities of population-level kinds.

I argue that results from foraging theory give us good reason to think some evolutionary phenomena are indeterministic and hence that evolutionary theory must be probabilistic. Foraging theory implies that random search is sometimes selectively advantageous, and experimental work suggests that it is employed by a variety of organisms. There are reasons to think such search will sometimes be genuinely indeterministic. If it is, then individual reproductive success will also be indeterministic, and so too will frequency change in populations of organisms employing such search.

In “The Indeterministic Character of Evolutionary Theory: No ‘Hidden Variables Proof’ But No Room for Determinism Either,” Brandon and Carson (1996) argue that evolutionary theory is statistical because the processes it describes are fundamentally statistical. In “Is Indeterminism the Source of the Statistical Character of Evolutionary Theory?” Graves, Horan, and Rosenberg (1999) argue in reply that the processes of evolutionary biology are fundamentally deterministic and that the statistical character of evolutionary theory is explained by epistemological rather than ontological considerations. In this paper I focus on the topic of mutation. By focusing on some of the theory and research on this topic from early to late, I show how quantum indeterminism hooks up to point mutations (via tautomeric shifts, proton tunneling, and aqueous thermal motion). I conclude with a few thoughts on some of the wider implications of this topic.

Recent discussion of the statistical character of evolutionary theory has centered around two positions: (1) Determinism combined with the claim that the statistical character is eliminable, a subjective interpretation of probability, and instrumentalism; (2) Indeterminism combined with the claim that the statistical character is ineliminable, a propensity interpretation of probability, and realism. I point out some internal problems in these positions and show that the relationship between determinism, eliminability, realism, and the interpretation of probability is more complex than previously assumed in this debate. Furthermore, I take some initial steps towards a more adequate account of the statistical character of evolutionary theory.

We argue that Brandon and Carson's (1996) “The Indeterministic Character of Evolutionary Theory” fails to identify any indeterminism that would require evolutionary theory to be a statistical or probabilistic theory. Specifically, we argue that (1) their demonstration of a mechanism by which quantum indeterminism might “percolate up” to the biological level is irrelevant; (2) their argument that natural selection is indeterministic because it is inextricably connected with drift fails to join the issue with determinism; and (3) their view that experimental methodology in botany assumes indeterminism is both false and incompatible with the commitment to discoverable causal mechanisms underlying biological processes. We remain convinced that the probabilism of the theory of evolution is epistemically, not ontologically, motivated.

In this paper we first briefly review Bell's (1964, 1966) Theorem to see how it invalidates any deterministic “hidden variable” account of the apparent indeterminacy of quantum mechanics (QM). Then we show that quantum uncertainty, at the level of DNA mutations, can “percolate” up to have major populational effects. Interesting as this point may be it does not show any autonomous indeterminism of the evolutionary process. In the next two sections we investigate drift and natural selection as the locus of autonomous biological indeterminacy. Here we conclude that the population-level indeterminacy of natural selection and drift are ultimately based on the assumption of a fundamental indeterminacy at the level of the lives and deaths of individual organisms. The following section examines this assumption and defends it from the determinists' attack. Then we show that, even if one rejects the assumption, there is still an important reason why one might think evolutionary theory (ET) is autonomously indeterministic. In the concluding section we contrast the arguments we have mounted against a deterministic hidden variable account of ET with the proof of the impossibility of such an account of QM.

In a number of publications, John Earman has advocated a tertium quid to the usual dichotomy between substantivalism and relationism concerning the nature of spacetime. The idea is that the structure common to the members of an equivalence class of substantival models is captured by a Leibniz algebra which can then be taken to directly characterize the intrinsic reality only indirectly represented by the substantival models. An alleged virtue of this is that, while a substantival interpretation of spacetime theories falls prey to radical local indeterminism, the Leibniz algebras do not.I argue that the program of Leibniz algebras is subject to radical local indeterminism to the same extent as substantivalism. In fact, for the category of topological spaces of interest in spacetime physics, the program is equivalent to the original spacetime approach. Moreover, the motivation for the program—that isomorphic substantival models should be regarded as representing the same physical situation—is misguided.

Carl G. Hempel's doctrine of essential epistemic relativization of inductive-statistical explanation seems to entail the unintelligibility of the notion of objective homogeneity of reference classes. This discussion note explores the question of whether, as a consequence, essential epistemic relativization also entails the unintelligibility of the doctrine of indeterminism.

The intuitive notion of a statistical explanation has been explicated in different ways; recently it has even been claimed that there are no statistical explanations at all. In an attempt to clarify the disputed issue, the approaches adopted by Hempel, by Jeffrey, Salmon and Greeno, and by Stegmüller are analyzed critically, as far as they are concerned with the explanation of particular events. A solution of the controversy is proposed on the basis of a concept of explanation which refers essentially to a causal analysis of the explanandum. The possibility of statistical explanations, then, becomes contingent upon the existence of indeterministic causation. In conclusion, therefore, a conception of causality is sketched which shows that indeterminism and causal connection are compatible, at least from an epistemological point of view, so that statistical explanation can be seen to represent a specific and possibly irreducible scientific activity.

In this paper I wish to argue that counterfactual analyses of causation are inadequate. I believe the counterfactuals that are involved in counterfactual analyses of causation are often false, and thus the theories do not provide an adequate account of causation. This is demonstrated by the presentation of a counterexample to the counterfactual analyses of causation. I then present a unified theory of causation that is based upon probability and counterfactuals. This theory accounts for both deterministic and indeterministic causation, and is not subject to many of the traditional problems facing theories of causation.

Two initially different arguments for indeterminism are often based either upon the Uncertainty Relations or the statistical interpretation of the wave equation of quantum mechanics. Both arguments ultimately involve three factors: (1) the assumption that elementary entities are enough like classical particles for it to make sense to say they are either determined or indetermined, (2) the fact that no exact measurements are possible of quantities supposed to characterize elementary entities, (3) the pragmatic supposition that determinism is false unless exact predictions are theoretically possible.If it is legitimate to use (3) to prove indeterminism, then an equally legitimate argument can be based upon (2) which denies (1). Thus, it is doubtful that quantum mechanics supports indeterminism, though it may show that the concepts of ‘determined’ and ‘indetermined’ are inapplicable to the world.

The historical origin and the experimental basis of the concept of physical determinism indicate that this basis was removed with the acceptance of the kinetic theory of matter, while its difficulties are increased by the admission that human nature, in its entirety, is a product of natural causation. An indeterministic view of causation has the advantages (a) of unifying the concept of natural law in different spheres of human experience and (b) of a greater generality, which precludes the acceptance of the special case of completely deterministic causation, so long as this is an unproved assumption. It is not inconsistent with the orderliness of the world, or with the fruitful pursuit of natural knowledge. It enriches rather than weakens the concept of of causation. It possesses definite advantages with respect to the one-sidedness of human memory, and to the phenomena of aiming and striving observable in man and other animals. Among biological theories it appears to be most completely in harmony with the theory of natural selection, which in its statistical nature resembles the second law of thermo-dynamics.In an indeterministic world natural causation has a creative element, and science is interested in locating the original causes of effects of special interest, and not merely in pushing a chain of causation backwards ad infinitum. These contrasting tendencies are illustrated by a critique of the mutation theory, and by an attempt more closely to define the sense in which indeterministic causation should be thought of as creative.

Scientists with creative imaginations are ever confronted by two opposing forces. One tempts them to soar into the realm of fancy, and the other cautions them to keep their feet on the ground. These conflicting influences play a significant part in the search for fundamental truth.The complementary value of philosophical reasoning and matter-of-fact experimentation in the complete fulfillment of science is illustrated by many an epochal discovery. Von Laue had the brilliant thought that the symmetrical distribution of atoms in a crystal presents a lattice sufficiently fine to scatter the exceedingly small waves of X-rays. The idea appeared to be scientifically sound, at least to von Laue, but to certain of his colleagues, classicists all, it was untenable. The kinetic energy or heat-movement of the atoms would, they said, disturb the diffraction phenomena and obscure the picture. Von Laue had confidence in his hypothesis and the courage to see it through, but he also knew that the validity of a scientific theory lies in experimental verification. There were in his laboratory two assistants, both able experimenters, and they proved the truth of von Laue's dream.

I Physicalism, and the weak identity theory deny, while physicalism2 and the radical identity theory assert, that raw feels can be accomodated in a purely physicalistic framework.II A way of interpreting the claim of physicalism1 is that raw feels are emergents.III The doctrine of emergence asserts that: (i) there are different levels of existence, (ii) these levels of existence are distinguishable on the basis of the behaviour of entities of that level, and (iii) an adequate scientific explanation of a lower level is inadequate for a higher level.IV The criteria of emergence are novelty and a priori unpredictability.V Either qualities or laws or both may be regarded as emergents.VI If the alleged impossibility of explaining higher level phenomena on the basis of explanation adequate for lower level phenomena is logical, then the impossibility is either trivial or it implies indeterminism.Consideration of theories of emergence: VII Semantic emergence. On this view emergence is theory-bound, analogous to indefinability or indemonstrability.VIII Methodological emergence. On this view what we regard as emergents depends on the theory we construct.IX Nomological emergence. On this view emergence is an empirical problem.Conclusion: if there are emergents, physicalism2 and the radical identity theory probably have to be abandoned. However, unless actual examples of emergents are produced both theories hold. The logical possibility of falsification is not an objection against physicalism2 and the radical identity theory; it is one of their merits.

Prompted by Alfred Landé's appraisal of individual indeterminacy in both ordinary and quantum games of chance [Mind, n.s. 67: 174-181 (April, 1958)], this paper suggests an alternative assessment in terms of the model-structure of physical theory. Whereas Landé explains such indeterminacy by appeal to “the Leibnitzian principle” of causal continuity, the author sees no need for such a special explanation. Instead, he indicates how the partial interpretation of the kinetic and quantum models limits us to statistical generalities—to limited “areas of relative chance.” The alleged indeterminism of physics thus resides in the model and its partial interpretation in the sense that the statistical nature of statements about “the next throw” or about individual particles is built into the model that enables the scientist to talk at all about such outcomes or entities.

Heisenberg's (3) principle of indeterminacy or uncertainty has led most theoretical physicists and philosophers to two important steps: 1) the denunciation of the law of physical causality; 2) the decision of biological and psychological problems in favor of indeterminism. One of the few opponents to this far-reaching application of the principle is Niels Bohr (1). He is "far from sharing. . . the widespread opinion that the recent development in the field of atomic physics could directly help us in deciding such questions as 'mechanism or vitalism' and 'free will or causal necessity' in favor of the one or the other alternative. Just the fact that the paradoxes of atomic physics could be solved not by a one-sided attitude towards the old problem of 'determinism or indeterminism,' but only by examining the possibilities of observation and definition, should rather stimulate us to a renewed examination of the position in this respect in the biological and psychological problems of the issue." Such an examination is attempted in the present article. 1. Heisenberg's Principle. Heisenberg's principle denies the accurate prediction of the course of an electron (or other elementary particles) due to the fact that, "the product of the average errors of two mechanical values, (canonically conjugated and measured simultaneously) cannot be smaller than the quantum of action" (Planck's constant h). Heisenberg considers the impossibility of determining the accurate state of an elementary particle as of such principal importance that he concludes his fundamental paper with the categoric statement (translated): "Since all experiments are subjected to the laws of quantum mechanics, the latter establishes definitely the untenability of the law of causality." 2. Physical Criticism. While Heisenberg's principle has found almost universal acceptance in theoretical physics, three very prominent physicists have criticized its validity: Bohr does not permit the formulation of Heisenberg's law: "The position and momentum of a particle cannot simultaneously be measured with arbitrary accuracy." While Heisenberg attributes the inaccuracy to the disturbance of the elementary particle through the process of observation (e.g. by means of a light beam), Bohr applies his principle of complementarity to the problem, according to which it is evident that different measurements require different experimental methods. In case of elementary particles one has to "use two different experimental arrangements of which only one permits an unambiguous use of the concept of position, while only the other permits the application of the concept of momentum." Heisenberg's indeterminacy appears thus as a special application of the principle of complementarity which also explains such a dilemma as the double appearance of electrons either as individual elementary particles or as an extended wave formation. According to these considerations its seems inadvisable to attribute the impossibility of our measurements or observations to the object