This article focuses on three themes concerning determinism and indeterminism. The first is observational equivalence between deterministic and indeterministic models. The article discusses several results about observational equivalence and presents an argument on how to choose between deterministic and indeterministic models involving indirect evidence. The second is whether Newtonian physics is indeterministic. The article argues that the answer depends on what one takes Newtonian mechanics to be and highlights how contemporary debates on this issue differ from those in the nineteenth century. The third theme is how the method of arbitrary functions can be used to make sense of deterministic probabilities. The article discusses various ways of interpreting the initial probability distributions and argues that they are best understood as physical, biological, and other quantities characterizing the particular situation. The fact that the method of arbitrary functions deserves more attention than it has received so far is also emphasized.
This article focuses on three themes concerning determinism and indeterminism. The first is observational equivalence between deterministic and indeterministic models. The article discusses several results about observational equivalence and presents an argument on how to choose between deterministic and indeterministic models involving indirect evidence. The second is whether Newtonian physics is indeterministic. The article argues that the answer depends on what one takes Newtonian mechanics to be and highlights how contemporary debates on this issue differ from those in the nineteenth century. The third theme is how the method of arbitrary functions can be used to make sense of deterministic probabilities. The article discusses various ways of interpreting the initial probability distributions and argues that they are best understood as physical, biological, and other quantities characterizing the particular situation. The fact that the method of arbitrary functions deserves more attention than it has received so far is also emphasized.
This article is about deterministic models, what they are, why they are useful, and what their limitations are. First, the article emphasizes that determinism is a property of models, not of physical systems. Whether a model is deterministic or not depends on how one defines the inputs and behavior of the model. To define behavior, one has to define an observer. The article compares and contrasts two classes of ways to define an observer, one based on the notion of “state” and another that more flexibly defines the observables. The notion of “state” is shown to be problematic and lead to nondeterminism that is avoided when the observables are defined differently. The article examines determinism in models of the physical world. In what may surprise many readers, it shows that Newtonian physics admits nondeterminism and that quantum physics may be interpreted as a deterministic model. Moreover, it shows that both relativity and quantum physics undermine the notion of “state” and therefore require more flexible ways of defining observables. Finally, the article reviews results showing that sufficiently rich sets of deterministic models are incomplete. Specifically, nondeterminism is inescapable in any system of models rich enough to encompass Newton’s laws.
Abstract Is the world deterministic and can we ever know whether it is or is not so? This chapter critically evaluates recent results that bear on these issues, and points out the relation to probabilities. While results from classical physics are neither fully relevant nor conclusive, quantum mechanics is often assumed to establish indeterminism beyond doubt. However, whether the quantum world is indeterministic crucially depends on how the measurement problem is solved. There are both deterministic and indeterministic contenders in this field, some of them empirically equivalent to another one. This is shown using the deterministic Bohm theory and Nelsonsion mechanics, which is indeterministic. Two arguments that purport to establish indeterminism and that rely on Gleason's theorem and on Conway and Kochen's recent Free Will Theorem are shown to be wanting.
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.
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.
In a deterministic theory, one can deduce the state of the universe at any one time from the dynamical laws that govern its evolution and its state at any other time.In particular, one can deduce from the conditions that obtained at some early boundary condition for the universe, its state at all subsequent times.It is a piece of well-received philosophical common sense that there is no room in a deterministic theory for objective probabilities.Arguments will be given below that this piece of philosophical common sense is mistaken, and that a probability measure over the space of physically possible trajectories is an indispensable component of any theory -deterministic or otherwise -that can be used as a basis for prediction or receive confirmation from the evidence.Phase space is the central representational space in physics.It is the space within which all of the states pertaining to a system are represented, and it encodes all of the general information that we have about those states.To take an obvious example (less obvious examples will be given below) the fact that a pair of quantities are represented by different dimensions in phase space encodes the fact that they represent separate degrees of freedom.Physically possible histories are represented by trajectories through phase space and in a deterministic theory, when dealing with a closed system, there is (no more than) one trajectory through each point.Since the universe as a whole is the only truly closed system, this means there is one trajectory through each point in the phase space of the universe.Probabilities may be invoked in applications of theory, when the state of a system or the values of external variables are not known with full precision, but they are eliminable given complete knowledge.And they don't appear in the statement of the laws.The laws serve simply to identify the physically allowable trajectories.About Newtonian dynamics, Laplace famously said "given for one instant an intelligence which could comprehend all the forces by which nature is animated and the respective situation of the beings who compose it -an intelligence sufficiently vast to submit these data to analysis -it would embrace in the same formula the movements of the greatest bodies of the universe and those of the lightest atom; for it, nothing would be uncertain and the future, and the past, would be present to its eyes."ii It is a short step from this to the idea that probabilities invoked in classical contexts are subjective rather than objective.If they represent anything, it is facts about our epistemic states, not facts about the world.iii Popper, and Lewis, and other influential figures have endorsed this view, categorically rejecting any role for objective probabilities indeterministic contexts.In Popper's words: