On the Observational Equivalence of Continuous-Time Deterministic and Indeterministic Descriptions

This paper presents and philosophically assesses three types of results on the observational equivalence of continuous-time measure-theoretic deterministic and indeterministic descriptions. The first results establish observational equivalence to abstract mathematical descriptions. The second results are stronger because they show observational equivalence between deterministic and indeterministic descriptions found in science. Here I also discuss Kolmogorov's contribution. For the third results I introduce two new meanings of 'observational equivalence at every observation level'. Then I show the even stronger result of observational equivalence at every (and not just some) observation level between deterministic and indeterministic descriptions found in science. These results imply the following. Suppose one wants to find out whether a phenomenon is best modeled as deterministic or indeterministic. Then one cannot appeal to differences in the probability distributions of deterministic and indeterministic descriptions found in science to argue that one of the descriptions is preferable because there is no such difference. Finally, I criticise the extant claims of philosophers and mathematicians on observational equivalence

Explaining Thermodynamic-Like Behaviour In Terms of Epsilon-Ergodicity

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

Initial conditions dependence and initial conditions uncertainty in climate science

This paper examines initial conditions dependence and initial conditions uncertainty for climate projections and predictions. The first contribution is to provide a clear conceptual characterisation of predictions and projections. Concerning initial conditions dependence, projections are often described as experiments that do not depend on initial conditions. Although prominent, this claim has not been scrutinized much and can be interpreted differently. If interpreted as the claim that projections are not based on estimates of the actual initial conditions of the world or that what makes projections true are conditions in the world, this claim is true. However, what is often meant is that the simulations used to obtain projections are independent of initial conditions. This paper argues that evidence does not support this claim. Concerning initial conditions uncertainty, three kinds of initial conditions uncertainty are identified (two have received little attention from philosophers so far). The first (the one usually discussed) is the uncertainty associated with the spread of the ensemble simulations. The second arises because the theoretical initial ensemble cannot be used in calculations and has to be approximated by finitely many initial states. The third uncertainty arises because it is unclear how long the model should be run to obtain potential initial conditions at pre-industrial times. Overall, the discussion shows that initial conditions dependence and uncertainty in climate science are more complex and important issues than usually acknowledged

Initial conditions dependence and initial conditions uncertainty in climate science

This paper examines initial conditions dependence and initial conditions uncertainty for climate projections and predictions. The first contribution is to provide a clear conceptual characterisation of predictions and projections. Concerning initial conditions dependence, projections are often described as experiments that do not depend on initial conditions. Although prominent, this claim has not been scrutinized much and can be interpreted differently. If interpreted as the claim that projections are not based on estimates of the actual initial conditions of the world or that what makes projections true are conditions in the world, this claim is true. However, what is often meant is that the simulations used to obtain projections are independent of initial conditions. This paper argues that evidence does not support this claim. Concerning initial conditions uncertainty, three kinds of initial conditions uncertainty are identified (two have received little attention from philosophers so far). The first (the one usually discussed) is the uncertainty associated with the spread of the ensemble simulations. The second arises because the theoretical initial ensemble cannot be used in calculations and has to be approximated by finitely many initial states. The third uncertainty arises because it is unclear how long the model should be run to obtain potential initial conditions at pre-industrial times. Overall, the discussion shows that initial conditions dependence and uncertainty in climate science are more complex and important issues than usually acknowledged

Determinism

This article focuses on three recent discussions on determinism in the philosophy of science. First, determinism and predictability will be discussed (Section 2). Then, second, the paper turns to the topic of determinism, indeterminism, observational equivalence and randomness (Section 3). Finally, third, there will be a discussion about deterministic probabilities (Section 4). The paper will end with a conclusion (Section 5)