Determinism is the thesis that the state of the world at any time uniquely determines the state of the world at all future times. Our best scientific theories seem inconclusive as to whether our world is deterministic. Our world could very well be either partially or completely deterministic. But determinism is not as innocuous as it seems; the truth of determinism seems to come into conflict with many intuitive concepts. One such concept is objective chance. Our intuitive notions of objective (...) chances are tied to the belief that events could have turned out differently than the way they actually occurred. Though many philosophers have declared that this conception of objective chance is incompatible with deterministic worlds, some have tried to provide accounts that render the two compatible. In this thesis I investigate what a theory of deterministic chance could be. Working within certain metaphysical constraints on chance, I craft out a new dispositional account of chance grounded in properties that objects have. (shrink)

The big news about chaos is supposed to be that the smallest of changes in a system can result in very large differences in that system's behavior. The so-called butterfly effect has become one of the most popular images of chaos. The idea is that the flapping of a butterfly's wings in Argentina could cause a tornado in Texas three weeks later. By contrast, in an identical copy of the world sans the Argentinian butterfly, no such storm would have arisen (...) in Texas. The mathematical version of this property is known as sensitive dependence. However, it turns out that sensitive dependence is somewhat old news, so some of the implications flowing from it are perhaps not such “big news” after all. Still, chaos studies have highlighted these implications in fresh ways and led to thinking about other implications as well. -/- In addition to exhibiting sensitive dependence, chaotic systems possess two other properties: they are deterministic and nonlinear (Smith 2007). This entry discusses systems exhibiting these three properties and what their philosophical implications might be for theories and theoretical understanding, confirmation, explanation, realism, determinism, free will and consciousness, and human and divine action. (shrink)

Philosophical discourse traditionally distinguishes between ontology and epistemology and generally enforces this distinction by keeping the two subject areas separated. However, the relationship between the two areas is of central importance to physics and philosophy of physics. For instance, many measurement-related problems force us to consider both our knowledge of the states and observables of a system and its states and observables independent of such knowledge. This applies to quantum systems in particular. This contribution presents an example showing the importance (...) of distinguishing between ontic and epistemic levels of description even for classical systems. Corresponding conceptions of ontic and epistemic states and their evolution are introduced and discussed with respect to aspects of stability and information flow. These aspects show why the ontic/epistemic distinction is particularly important for systems exhibiting deterministic chaos. Moreover, this distinction provides some understanding of the relationships between determinism, causation, predictability, randomness, and stochasticity. (shrink)

The concept of randomness has been unjustly neglected in recent philosophical literature, and when philosophers have thought about it, they have usually acquiesced in views about the concept that are fundamentally flawed. After indicating the ways in which these accounts are flawed, I propose that randomness is to be understood as a special case of the epistemic concept of the unpredictability of a process. This proposal arguably captures the intuitive desiderata for the concept of randomness; at least it should suggest (...) that the commonly accepted accounts cannot be the whole story and more philosophical attention needs to be paid. 1. Randomness in science1.1Random systems1.2Random behaviour1.3Random sampling1.4Caprice, arbitrariness and noise2. Concepts of randomness2.1Von Mises/church/martin-löf randomness2.2KCS-randomness3. Randomness is unpredictability: preliminaries3.1Process and product randomness3.2Randomness is indeterminism?4. Predictability4.1Epistemic constraints on prediction4.2Computational constraints on prediction4.3Pragmatic constraints on prediction4.4Prediction defined5. Unpredictability6. Randomness is unpredictability6.1Clarification of the definition of randomness6.2Randomness and probability6.3Subjectivity and context sensitivity of randomness7. Evaluating the analysis[R]andomness … is going to be a concept which is relative to our body of knowledge, which will somehow reflect what we know and what we don't know. Henry E. Kyburg, Jr ([1974], p. 217)Phenomena that we cannot predict must be judged random. Patrick Suppes ([1984], p. 32). (shrink)

Kellert (In the Wake of Chars, University of Chicago press, Chicago, 1993) has argued that Laplacean determinism in classical physics is actually a layered concept, where various properties or layers composing this form of determinism can be peeled away. Here, I argue that a layered conception of determinism is inappropriate and that we should think in terms of different deterministic models applicable to different kinds of systems. The upshot of this analysis is that the notion of state is more closely (...) tied to the kind of system being investigated than is usually considered in discussions of determinism. So when investigating determinism corresponding changes to the appropriate notion of state – and, perhaps, the state space itself – also need to be considered. (shrink)

Chaos-related obstructions to predictability have been used to challenge accounts of theory validation based on the agreement between theoretical predictions and experimental data. These challenges are incomplete in two respects: they do not show that chaotic regimes are unpredictable in principle and, as a result, that there is something conceptually wrong with idealized expectations of correct predictions from acceptable theories, and they do not explore whether chaos-induced predictive failures of deterministic models can be remedied by stochastic modeling. In this paper (...) we appeal to an asymptotic analysis of state space trajectories and their numerical approximations to show that chaotic regimes are deterministically unpredictable even with unbounded resources. Additionally, we explain why stochastic models of chaotic systems, while predictively successful in some cases, are in general predictively as limited as deterministic ones. We conclude by suggesting that the way in which scientists deal with such principled obstructions to predictability calls for a more comprehensive approach to theory validation, on which experimental testing is augmented by a multifaceted mathematical analysis of theoretical models, capable of identifying chaos-related predictive failures as due to principled limitations which the world itself imposes on any less-than-omniscient epistemic access to some natural systems. (shrink)

This paper considers definitions of classical dynamical chaos that focus primarily on notions of predictability and computability, sometimes called algorithmic complexity definitions of chaos. I argue that accounts of this type are seriously flawed. They focus on a likely consequence of chaos, namely, randomness in behavior which gets characterized in terms of the unpredictability or uncomputability of final given initial states. In doing so, however, they can overlook the definitive feature of dynamical chaos--the fact that the underlying motion generating the (...) behavior exhibits extreme trajectory instability. I formulate a simple criterion of adequacy for any definition of chaos and show how such accounts fail to satisfy it. (shrink)

Recent developments in nonlinear dynamics have found wide application in many areas of science from physics to neuroscience. Nonlinear phenomena such as feedback loops, inter-level relations, wholes constraining and modifying the behavior of their parts, and memory effects are interesting candidates for emergence and downward causation. Rayleigh–Bénard convection is an example of a nonlinear system that, I suggest, yields important insights for metaphysics and philosophy of science. In this paper I propose convection as a model for downward causation in classical (...) mechanics, far more robust and less speculative than the examples typically provided in the philosophy of mind literature. Although the physics of Rayleigh–Bénard convection is quite complicated, this model provides a much more realistic and concrete example for examining various assumptions and arguments found in emergence and philosophy of mind debates. After reviewing some key concepts of nonlinear dynamics, complex systems and the basic physics of Rayleigh–Bénard convection, I begin that examination here by (1) assessing a recently proposed definition for emergence and downward causation, (2) discussing some typical objections to downward causation and (3) comparing this model with Sperry’s examples. (shrink)

Recent work in the Philosophy of Mind has suggested that alternatives to reduction are required in order to explain the relationship between psychology and biology or physics. Emergence has been proposed as one such alternative. In this paper, I propose a precise definition of emergence, and I argue that chaotic systems provide concrete examples of properties that meet this definition. In particular, I suggest that being in the basin of attraction of a strange attractor is an emergent property of any (...) chaotic nonlinear dynamical system. This shows that non-reductive accounts of inter-theoretic relations are necessary, and that non-reductive accounts of the mental are possible. Moreover, this work provides a foundation for future work investigating the nature of explanation, prediction, and scientific understanding of non-reductive phenomena. (shrink)

If the laws of nature are deterministic, then it seems possible that a Laplacean intelligence that knows the initial conditions and the laws would be able to accurately predict everything that will ever happen. However, it would be easy to construct a counterpredictive device that falsifies any revealed prediction about its future behavior. What would then occur if a Laplacean intelligence encountered a counterpredictive device? This is the paradox of predictability. A number of philosophers have proposed solutions to it, though (...) part of my aim here is to argue that the paradox is more pernicious than has thus far been appreciated, and therefore that extant solutions are inadequate. My broader aim is to argue that the paradox motivates Humeanism about laws of nature. (shrink)

The fact that there exist in nature thoroughly deterministic systems whose future behavior cannot be predicted, no matter how advanced or fined-tune our cognitive and technical abilities turn out to be, has been well established over the last decades or so, essentially in the light of two different theoretical frameworks, namely chaos theory and (some deterministic interpretation of) quantum mechanics. The prime objective of this paper is to show that there actually exists an alternative strategy to ground the divorce between (...) determinism and predictability, a way that is older than—and conceptually independent from—chaos theory and quantum mechanics, and which has not received much attention in the recent philosophical literature about determinism. This forgotten strategy—embedded in the doctrine called “emergent evolutionism”—is nonetheless far from being a mere historical curiosity that should only draw the attention of philosophers out of their concern for comprehensiveness. It has been indeed recently revived in the works of respected scientists. (shrink)

From the beginning of chaos research until today, the unpredictability of chaos has been a central theme. It is widely believed and claimed by philosophers, mathematicians and physicists alike that chaos has a new implication for unpredictability, meaning that chaotic systems are unpredictable in a way that other deterministic systems are not. Hence, one might expect that the question ‘What are the new implications of chaos for unpredictability?’ has already been answered in a satisfactory way. However, this is not the (...) case. I will critically evaluate the existing answers and argue that they do not fit the bill. Then I will approach this question by showing that chaos can be defined via mixing, which has never before been explicitly argued for. Based on this insight, I will propose that the sought-after new implication of chaos for unpredictability is the following: for predicting any event, all sufficiently past events are approximately probabilistically irrelevant. (shrink)

In a rarely quoted paper, published in 1958 in the American Journal of Physics, T. Ehrenfest-Afanassjewa introduced the idea that the concept of chance as employed in physics is subject to what she called a ‘Limited Belief in Chance’. In this paper I elaborate the latter concept and the distinction between absolute chance and relative randomness, where the latter, but not the former, is governed by the theory of probability. I argue that in the twentieth century virtually nobody believes seriously (...) in the possiblity of absolute chance, whereas the concept of chance in the Scientific World Picture is only ‘chancy’ relative to a limited belief in chance grounded in the Manifest World Picture of an orderly world. (shrink)

Between Calculability and Non-Calculability. Issues of Calculability and Predictability in the Physics of Complex Systems. The ability to predict has been a very important qualifier of what constitutes scientific knowledge, ever since the successes of Babylonian and Greek astronomy. More recent is the general appreciation of the fact that in the presence of deterministic chaos, predictability is severely limited (the so-called ‘butterfly effect’): Nearby trajectories diverge during time evolution; small errors typically grow exponentially with time. The system obeys deterministic laws (...) and still is unpredictable, seemingly a paradox for the traditional viewpoint of Laplacian determinisms. With the concept of deterministic chaos the epistemological issue about an adequate understanding of predictability is no longer just a mere philosophical topic. Physicists on the one hand recognize the limits of (long term) predictability, computability and even of scientific knowledge, on the other hand they work on concepts for extending the horizon of predictability. It is shown in this paper that physics of complex systems is useful to clarify the jungle of different meanings of the terms ‘predictability’ and ‘computability’ — also with philosophical implications for understanding science and nature. Today, from the physical point of view, the relevance of the concepts of predictability seems to be underestimated by philosophers as a mere methodological topic. In the paper I analyse the importance of predictability and computability in physics of complex systems. I show a way how to cope with problems of unpredictability and noncomputability. Nine different concepts of predictability and computability (i.e. open solution, sensitivity/chaos, redundancy/chance) are presented, compared and evaluated. (shrink)

Laplacean determinism remains a popular theory among philosophers and scientists alike, in spite of the fact that the Copenhagen Interpretation of quantum mechanics, with which it is inconsistent, has been around for more than fifty years. There are a number of reasons for its continuing popularity. One, recently articulated by Honderich, is that there are too many possible interpretations of quantum mechanics, and the subject is too controversial even among physicists to be an adequate basis for overturning determinism. Nevertheless, quantum (...) mechanics is an enormously successful theory, considering the quantity and variety of its predictions which have been verified under conditions never dreamt of by its originators; and the Copenhagen Interpretation is the only widely accepted interpretation of it. Although a hidden variable theory consistent with the results of quantum mechanics is not impossible, one of its major advocates admits that it is highly speculative, and far from adequately developed. Yet such a theory would be needed to reconcile Laplacean determinism with quantum mechanics; most of the controversies alluded to by Honderich are irrelevant. (shrink)

Some have argued that chaos, with its characteristic feature of sensitive dependence on initial conditions, should be sensitive to quantum events (Hobbs 1991; Kellert 1993). The upshot of these arguments is that classical chaos would then be indeterministic, but such a conclusion is dependent on which versions of quantum theory and solutions to the measurement problem are adopted (Bishop and Kronz 1999). In this essay, the relationship between quantum mechanics and sensitive dependence is placed in the general context of nonlinear (...) dynamics and is investigated in detail, revealing further limitations and quali…cations on these sensitive dependence arguments. (shrink)

In a paper fifteen years ago about the meaning and the possibility of the beginning and end of time, our redoubtable session chair, John Earman, ended up like this:…[T]he answers to the questions posed at the outset lie somewhere in a thicket of problems growing out of the intersection of mathematics, physics, and metaphysics. This paper has only located the thicket and engaged in a little initial bush beating. This is not much progress, but knowing which bushes to beat is (...) a necessary first step.Some philosophers will be disappointed that the thicket is populated by so many problems of a technical and scientific nature. On the contrary, I am encouraged by this result because it shows that a long-standing philosophical problem has a nontrivial and, indeed, a surprisingly large content. Moreover, this result is a good illustration of the artificiality and danger of trying to separate philosophy from science. (Earman 1977, p. 131-2)These remarks are a kind of manifesto of an approach to philosophical questions about space and time dating from the late 1960’s. (shrink)

Laws of nature have been traditionally thought to express regularities in the systems which they describe, and, via their expression of regularities, to allow us to explain and predict the behavior of these systems. Using the driven simple pendulum as a paradigm, we identify three senses that regularity might have in connection with nonlinear dynamical systems: periodicity, uniqueness, and perturbative stability. Such systems are always regular only in the second of these senses, and that sense is not robust enough to (...) support predictions. We thus illustrate precisely how physical laws in the classical regime of dynamical systems fail to exhibit predictive power. *R. G. Holt gratefully acknowledges the support of the National Center for Physical Acoustics at Oxford, Mississippi, and the Office of Naval Research. (shrink)

The discovery of sensitive dependence on initial conditions (SDIC) in nonlinear models runs counter to the textbook vision of CM, a vision guided by an almost exclusive focus on linear systems. Therefore, it is important to clearly distinguish between linear and nonlinear systems along with establishing some basic terminology (§I). The notions of SDIC and chaos also need clarification, since they play crucial roles in sensitive dependence (SD) arguments. This will require some discussion of Lyapunov exponents as well as the (...) relationship between nonlinear dynamics and chaos (§II and Appendix). For the sake of concreteness, it will also be useful to focus on the Laplacean vision for classical particle mechanics (e.g., Bishop 2002b, 2003 and 2005a), particularly the crucial notion of unique evolution (§III). The SD argument can then be stated in a clear form and its defenses, criticisms and limitations assessed in the more general context of nonlinear dynamics (§IV). Concluding remarks follow (§V). (shrink)

Determinism is usually understood as a commonly clear and obvious thesis. In the most of the actual literature a character of determinism is rarely enough explicitly underlined and we believe that it is the reason why common uses of the term often leads to inconsistencies and present a source of misunderstandings of different sorts. Here we will try to show that that there are many forms of determinism; that the concept of determinism has a composite character; and that conceptions of (...) determinism can be mutually discriminated and organized according to particular elements they are consisting of by applying the procedure of classification. (shrink)

This article focuses on three recent discussions on determinism in the philosophy of science. First, determinism and predictability will be discussed. Then, second, the paper turns to the topic of determinism, indeterminism, observational equivalence and randomness. Finally, third, there will be a discussion about deterministic probabilities. The paper will end with a conclusion.

Determinism is a rich and varied concept. At an abstract level of analysis, Jordan Howard Sobel (1998) identifies at least ninety varieties of what determinism could be like. When it comes to thinking about what deterministic laws and theories in physical sciences might be like, the situation is much clearer. There is a criterion by which to judge whether a law–expressed as some form of equation–is deterministic. A theory would then be deterministic just in case all its laws taken as (...) a whole were deterministic. In contrast, if a law fails this criterion, then it is indeterministic and any theory whose laws taken as a whole fail this criterion must also be indeterministic. Although it is widely believed that classical physics is deterministic and quantum mechanics is indeterministic, application of this criterion yields some surprises for these standard judgments. (shrink)

In this thesis I will examine the philosophy of the physicist Max Born. As well as his scientific work, Born wrote on a number of philosophical topics: causation, realism, determinism, and probability. They appear as an interest throughout his career, but he particularly concentrates on them from the 1940s onwards. Born is a significant figure in the development of quantum mechanics whose philosophical work has been left largely unexamined. It is the aim of this thesis to elucidate and to critically (...) examine that work. I will give a defence of presentist historiography in the history and philosophy of science and a brief biography of Born. With regards to causation, the thesis will argue that he holds that there exist principles regarding causal relations that have guided the development of physics and have, in the modern formulation of the subject, been confirmed as having an empirical status. I will argue that he is a selective realist, initially with regards to invariant properties and, later on, a structural realist. With regards to determinism, I will argue that Born has produced an argument, compatible with modern philosophical definitions of determinism, that we were never entitled to conclude from the success of classical mechanics that the world was deterministic. Finally, I will argue that Born holds an objective interpretation of probabilities in quantum mechanics which, due to his strong belief in the physical reality of quantum-mechanical probabilities and his apparent disbelief in the superposition of the wave-function, is most likely a long-run propensity theory. (shrink)

There is a persistent confusion about determinism and predictability. In spite of the opinions of some eminent philosophers, it is possible to understand that the two concepts are completely unrelated. In few words we can say that determinism is ontic and has to do with how Nature behaves, while predictability is epistemic and is related to what the human beings are able to compute. An analysis of the Lyapunov exponents and the Kolmogorov-Sinai entropy shows how deterministic chaos, although with an (...) epistemic character, is non subjective at all. This should clarify the role and content of stochastic models in the description of the physical world. (shrink)