This is an extensive review of recent work on the foundations of statistical mechanics.

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)

I examine the argument that scientific theories are typically 'underdetermined' by the data, an argument which has often been used to combat scientific realism. I deal with two objections to the underdetermination argument: (i) that the argument conflicts with the holistic nature of confirmation, and (ii) that the argument rests on an untenable theory/data dualism. I discuss possible responses to both objections, and argue that in both cases the proponent of underdetermination can respond in ways which are individually plausible, but (...) that the best response to the first objection conflicts with the best response to the second. Consequently underdetermination poses less of a problem for scientific realism than has often been thought. (shrink)

On the observational equivalence of continuous-time deterministic and indeterministic descriptions Content Type Journal Article Pages 193-225 DOI 10.1007/s13194-010-0011-5 Authors Charlotte Werndl, Department of Philosophy, Logic and Scientific Method, London School of Economics, Houghton Street, London, WC2A 2AE UK Journal European Journal for Philosophy of Science Online ISSN 1879-4920 Print ISSN 1879-4912 Journal Volume Volume 1 Journal Issue Volume 1, Number 2.

The central question of this paper is: are deterministic and indeterministic descriptions observationally equivalent in the sense that they give the same predictions? I tackle this question for measure-theoretic deterministic systems and stochastic processes, both of which are ubiquitous in science. I first show that for many measure-theoretic deterministic systems there is a stochastic process which is observationally equivalent to the deterministic system. Conversely, I show that for all stochastic processes there is a measure-theoretic deterministic system which is observationally equivalent (...) to the stochastic process. Still, one might guess that the measure-theoretic deterministic systems which are observationally equivalent to stochastic processes used in science do not include any deterministic systems used in science. I argue that this is not so because deterministic systems used in science even give rise to Bernoulli processes. Despite this, one might guess that measure-theoretic deterministic systems used in science cannot give the same predictions at every observation level as stochastic processes used in science. By proving results in ergodic theory, I show that also this guess is misguided: there are several deterministic systems used in science which give the same predictions at every observation level as Markov processes. All these results show that measure-theoretic deterministic systems and stochastic processes are observationally equivalent more often than one might perhaps expect. Furthermore, I criticise the claims of the previous philosophy papers Suppes (1993, 1999), Suppes and de Barros (1996) and Winnie (1998) on observational equivalence. (shrink)

Various processes are often classified as both deterministic and random or chaotic. The main difficulty in analysing the randomness of such processes is the apparent tension between the notions of randomness and determinism: what type of randomness could exist in a deterministic process? Ergodic theory seems to offer a particularly promising theoretical tool for tackling this problem by positing a hierarchy, the so-called ‘ergodic hierarchy’, which is commonly assumed to provide a hierarchy of increasing degrees of randomness. However, that notion (...) of randomness requires clarification. The mathematical definition of EH does not make explicit appeal to randomness; nor does the usual way of presenting EH involve a specification of the notion of randomness that is supposed to underlie the hierarchy. In this paper we argue that EH is best understood as a hierarchy of random behaviour if randomness is explicated in terms of unpredictability. We then show that, contrary to common wisdom, EH is useful in characterising the behaviour of Hamiltonian dynamical systems. (shrink)

In this paper, I explore Larry Laudan's and Jarrett Leplin's recent claim that empirically equivalent theories may be differentially confirmed. I show that their attempt to prise apart empirical equivalence and epistemic parity commits them to two principles of confirmation that Hempel demonstrated to be incompatible.

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)