In this article I examine two mathematical definitions of observational equivalence, one proposed by Charlotte Werndl and based on manifest isomorphism, and the other based on Ornstein and Weiss’s ε-congruence. I argue, for two related reasons, that neither can function as a purely mathematical definition of observational equivalence. First, each definition permits of counterexamples; second, overcoming these counterexamples will introduce non-mathematical premises about the systems in question. Accordingly, the prospects for a broadly applicable and purely mathematical definition of observational equivalence (...) are unpromising. Despite this critique, I suggest that Werndl’s proposals are valuable because they clarify the distinction between provable and unprovable elements in arguments for observational equivalence. (shrink)

Philosophers of science have often favoured reductive approaches to how-possibly explanation. This article identifies three alternative conceptions making how-possibly explanation an interesting phenomenon in its own right. The first variety approaches “how possibly X?” by showing that X is not epistemically impossible. This can sometimes be achieved by removing misunderstandings concerning the implications of one’s current belief system but involves characteristically a modification of this belief system so that acceptance of X does not result in contradiction. The second variety offers (...) a potential how-explanation of X. It is usually followed by a range of further potential how-explanations of the same phenomenon. In recent literature the factual claims implied by the second variety have been downplayed whereas the heuristic role of mapping the space of conceptual possibilities has been emphasized. I will focus especially on this truth-bracketing sense of potentiality when looking closer at the second variety in the paper. The third variety has attracted less interest. It presents a partial how-explanation of X. Typically it aims to establish the existence of a mechanism by which X could be and was generated. The third conception stands out as the natural alternative for the advocate of ontic how-possibly explanations. This article transfers Salmon’s view that explanation-concepts can be broadly divided into epistemic, modal, and ontic to the context of how-possibly explanations. Moreover, it is argued that each of the three above-mentioned varieties of how-possibly explanation occurs in science. To recognize this may be especially relevant for philosophers. We are often misled by the promises of various why-explanation accounts, and seem to have forgotten nearly everything about the diversity of how-possibly explanations. (shrink)

The conspicuous similarities between interpretive strategies in classical statistical mechanics and in quantum mechanics may be grounded on their employment of common implementations of probability. The objective probabilities which represent the underlying stochasticity of these theories can be naturally associated with three of their common formal features: initial conditions, dynamics, and observables. Various well-known interpretations of the two theories line up with particular choices among these three ways of implementing probability. This perspective has significant application to debates on primitive ontology (...) and to the quantum measurement problem. (shrink)

It can be shown that certain kinds of classical deterministic and indeterministic descriptions are observationally equivalent. Then the question arises: which description is preferable relative to evidence? This paper looks at the main argument in the literature for the deterministic description by Winnie (The cosmos of science—essays of exploration. Pittsburgh University Press, Pittsburgh, pp 299–324, 1998). It is shown that this argument yields the desired conclusion relative to in principle possible observations where there are no limits, in principle, on observational (...) accuracy. Yet relative to the currently possible observations (of relevance in practice), relative to the actual observations, or relative to in principle observations where there are limits, in principle, on observational accuracy the argument fails. Then Winnie’s analogy between his argument for the deterministic description and his argument against the prevalence of Bernoulli randomness in deterministic descriptions is considered. It is argued that while the arguments are indeed analogous, it is also important to see they are disanalogous in another sense. (shrink)

Gases reach equilibrium when left to themselves. Why do they behave in this way? The canonical answer to this question, originally proffered by Boltzmann, is that the systems have to be ergodic. This answer has been criticised on different grounds and is now widely regarded as flawed. In this paper we argue that some of the main arguments against Boltzmann's answer, in particular, arguments based on the KAM-theorem and the Markus-Meyer theorem, are beside the point. We then argue that something (...) close to Boltzmann's original proposal is true for gases: gases behave thermodynamic-like if they are epsilon-ergodic, i.e., ergodic on the entire accessible phase space except for a small region of measure epsilon. This answer is promising because there are good reasons to believe that relevant systems in statistical mechanics are epsilon-ergodic. (shrink)

We review the question of whether objective chances are compatible with determinism. We first outline what we mean by chance and what we mean by determinism. We then look at the alleged incompatibility between those concepts. Finally, we look at some ways that one might attempt to overcome the incompatibility.

The aim of this paper is to establish that free agency, which is a capacity of many animals including human beings, is compatible with indeterminism: an indeterministic world allows for the existence of free agency. The question of the compatibility of free agency and indeterminism is less discussed than its mirror image, the question of the compatibility of free agency and determinism. It is, however, of great importance for our self-conception as free agents in our (arguably) indeterministic world. We begin (...) by explicating the notions of indeterminism and free agency and by clarifying the interrelation of free agency and the human-specific notion of free will. We then situate our claim of the compatibility of free agency and indeterminism precisely in the landscape of the current debate on freedom and determinism, exposing an unhappy asymmetry in that debate. Then we proceed to make our case by describing the mathematically precise, physically motivated model of projective simulation, which employs indeterminism as a central resource for agency modeling. We argue that an indeterministic process of deliberation modeled by the dynamics of projective simulation can exemplify free agency under indeterminism, thereby establishing our compatibility claim: Free agency can develop and thrive in an indeterministic world. (shrink)

Equilibrium is a central concept of statistical mechanics. In previous work we introduced the notions of a Boltzmannian alpha-epsilon-equilibrium and a Boltzmannian gamma-epsilon-equilibrium. This was done in a deterministic context. We now consider systems with a stochastic micro-dynamics and transfer these notions from the deterministic to the stochastic context. We then prove stochastic equivalents of the Dominance Theorem and the Prevalence Theorem. This establishes that also in stochastic systems equilibrium macro-regions are large in requisite sense.

I show explicitly how concerns about wave function collapse and ontology can be decoupled from the bulk of technical analysis necessary to recover localized, approximately Newtonian trajectories from quantum theory. In doing so, I demonstrate that the account of classical behavior provided by decoherence theory can be straightforwardly tailored to give accounts of classical behavior on multiple interpretations of quantum theory, including the Everett, de Broglie-Bohm and GRW interpretations. I further show that this interpretation-neutral, decoherence-based account conforms to a general (...) view of inter-theoretic reduction in physics that I have elaborated elsewhere, which differs from the oversimplified and often ambiguous picture that treats reduction simply as a matter of taking limits. This interpretation-neutral account rests on a general three-pronged strategy for reduction between quantum and classical theories that combines decoherence, an appropriate form of Ehrenfest's Theorem, and a decoherence-compatible mechanism for collapse. It also incorporates a novel argument as to why branch-relative trajectories should be approximately Newtonian, which is based on a little-discussed extension of Ehrenfest's Theorem to open systems, rather than on the more commonly cited but less germane closed-systems version. In the Conclusion, I briefly suggest how the strategy for quantum-classical reduction described here might be extended to reduction between other classical and quantum theories, including classical and quantum field theory and classical and quantum gravity. (shrink)

Recently some results have been presented which show that certain kinds of deterministic descriptions and indeterministic descriptions are observationally equivalent (Werndl 2009a, 2010). This paper focuses on some philosophical questions prompted by these results. More specifically, first, I will discuss the philosophical comments made by mathematicians about observational equivalence, in particular Ornstein and Weiss (1991). Their comments are vague, and I will argue that, according to a reasonable interpretation, they are misguided. Second, the results on observational equivalence raise the question (...) of whether the deterministic or indeterministic description is preferable relative to all evidence. If none of them is preferable, there is underdetermination. I will criticize Winnie's (1998) argument that, by appealing to different observations, one finds that the deterministic description is preferable. In particular, I will clarify a confusion in this argument. Furthermore, I will argue that if the concern is a strong kind of underdetermination, the argument delivers the desired conclusion but this conclusion is trivial; and for other kinds of underdetermination of interest the argument fails. (shrink)

Does the brain behave indeterministically? I argue that accounting for ion channels, key functional units in the brain, requires indeterministic models. These models are probabilistic, so the brain does behave indeterministically in a weak sense. I explore the implications of this point for a stronger sense of indeterminism. Ultimately I argue that it is not possible, either empirically or through philosophical argument, to show that the brain is indeterministic in that stronger sense.

In this paper I examine two mathematical definitions of observational equivalence, one proposed by Charlotte Werndl and based on manifest isomorphism, and the other based on Ornstein and Weiss's ε-congruenceε-congruence. I argue, for two related reasons, that neither can function as a purely mathematical definition of observational equivalence. First, each definition permits of counterexamples; second, overcoming these counterexamples will introduce non-mathematical premises about the systems in question. Accordingly, the prospects for a broadly applicable and purely mathematical definition of observational equivalence (...) are unpromising. Despite this critique, I suggest that Werndl's proposals are valuable because they clarify the distinction between provable and unprovable elements in arguments for observational equivalence. (shrink)

This paper gives an overview of logico-philosophical issues of time and determinism. After a brief review of historical roots and 20th century developments, three current research areas are discussed: the definition of determinism, space-time indeterminism, and the temporality of individual things and their possibilities.