Typicality is routinely invoked in everyday contexts: bobcats are typically short-tailed; people are typically less than seven feet tall. Typicality is invoked in scientific contexts as well: typical gases expand; typical quantum systems exhibit probabilistic behaviour. And typicality facts like these support many explanations, both quotidian and scientific. But what is it for something to be typical? And how do typicality facts explain? In this paper, I propose a general theory of typicality. I analyse the notion of a typical property. (...) I provide a formalism for typicality explanations, and I give an account of why typicality explanations are explanatory. Along the way, I show how typicality facts explain a variety of phenomena, from everyday phenomena to the statistical mechanical behaviour of gases. Finally, I argue that typicality is not the same thing as probability. (shrink)

The aim of the article is to provide a clear and thorough conceptual analysis of the main candidates for a definition of climate and climate change. Five desiderata on a definition of climate are presented: it should be empirically applicable; it should correctly classify different climates; it should not depend on our knowledge; it should be applicable to the past, present, and future; and it should be mathematically well-defined. Then five definitions are discussed: climate as distribution over time for constant (...) external conditions; climate as distribution over time when the external conditions vary as in reality; climate as distribution over time relative to regimes of varying external conditions; climate as the ensemble distribution for constant external conditions; and climate as the ensemble distribution when the external conditions vary as in reality. The third definition is novel and is introduced as a response to problems with existing definitions. The conclusion is that most definitions encounter serious problems and that the third definition is most promising. 1 Introduction2 Climate Variables and a Simple Climate Model3 Desiderata on a Definition of Climate4 Climate as Distribution over Time4.1 Definition 1: Distribution over time for constant external conditions4.2 Definition 2: Distribution over time when the external conditions vary as in reality4.3 Definition 3: Distribution over time for regimes of varying external conditions4.4 Infinite versions5 Climate as Ensemble Distribution5.1 Definition 4: Ensemble distribution for constant external conditions5.2 Definition 5: Ensemble distribution when the external conditions vary as in reality5.3 Infinite versions6 ConclusionAppendix. (shrink)

En este escrito se analizan ciertos conceptos del estructuralismo empirista de Bas van Fraassen, en particular, el de representación, para intentar una crítica a su posición con respecto al vínculo entre los modelos de las teorías y, en última instancia, el mundo físico por medio de los modelos de datos, a los cuales van Fraassen les adjudica el papel de representantes de los fenómenos. Al final se delinea, a muy grandes rasgos, una alternativa conceptualista.

This paper reviews some major episodes in the history of the spatial isomorphism problem of dynamical systems theory. In particular, by analysing, both systematically and in historical context, a hitherto unpublished letter written in 1941 by John von Neumann to Stanislaw Ulam, this paper clarifies von Neumann's contribution to discovering the relationship between spatial isomorphism and spectral isomorphism. The main message of the paper is that von Neumann's argument described in his letter to Ulam is the very first proof that (...) spatial isomorphism and spectral isomorphism are not equivalent because spectral isomorphism is weaker than spatial isomorphism: von Neumann shows that spectrally isomorphic ergodic dynamical systems with mixed spectra need not be spatially isomorphic. (shrink)

Van Fraassen argues that data provide the target-end structures required by structuralist accounts of scientific representation. But models represent phenomena not data. Van Fraassen agrees but argues that there is no pragmatic difference between taking a scientific model to accurately represent a physical system and accurately represent data extracted from it. In this article I reconstruct his argument and show that it turns on the false premise that the pragmatic content of acts of representation include doxastic commitments.

The distribution of matter in our universe is strikingly time asymmetric. Most famously, the Second Law of Thermodynamics says that entropy tends to increase toward the future but not toward the past. But what explains this time-asymmetric distribution of matter? In this paper, I explore the idea that time itself has a direction by drawing from recent work on grounding and metaphysical fundamentality. I will argue that positing such a direction of time, in addition to time-asymmetric boundary conditions, enables a (...) better explanation of the thermodynamic asymmetry than is available otherwise. (shrink)

Je défends ici la nécessité, et ébauche une première version, d’une théorie iconique des propositions. Selon celle-ci, les propositions sont comme les objets de représentation, ou similaires à eux. Les propositions, suivant cette approche, sont des propriétés que l’esprit instancie lorsqu’il modélise le monde. Je connecte cette théorie aux récents développements de la littérature académique sur les propositions, ainsi qu’à une branche de recherches en sciences cognitives, qui explique certains types de représentations mentales en termes d’iconicité. I motivate the need (...) for, and then sketch, an iconic theory of propositions according to which propositions are like or similar to their objects of representation. Propositions on this theory are properties that the mind instantiates when it models the world. I connect the theory to recent developments in the propositions literature as well as to a strain of cognitive science that explains some kinds of mental representation in terms of iconicity. (shrink)

The sensitive dependence on initial conditions (SDIC) associated with nonlinear models imposes limitations on the models’ predictive power. We draw attention to an additional limitation than has been underappreciated, namely, structural model error (SME). A model has SME if the model dynamics differ from the dynamics in the target system. If a nonlinear model has only the slightest SME, then its ability to generate decision-relevant predictions is compromised. Given a perfect model, we can take the effects of SDIC into account (...) by substituting probabilistic predictions for point predictions. This route is foreclosed in the case of SME, which puts us in a worse epistemic situation than SDIC. (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)

I develop an account of productive surprise as an epistemic virtue of scientific investigations which does not turn on psychology alone. On my account, a scientific investigation is potentially productively surprising when results can conflict with epistemic expectations, those expectations pertain to a wide set of subjects. I argue that there are two sources of such surprise in science. One source, often identified with experiments, involves bringing our theoretical ideas in contact with new empirical observations. Another, often identified with simulations, (...) involves articulating and bringing together different parts of our knowledge. Both experiments and simulations, then, can surprise. (shrink)

This is a companion to another paper. Together they rebut two widespread philosophical doctrines about emergence. The first, and main, doctrine is that emergence is incompatible with reduction. The second is that emergence is supervenience; or more exactly, supervenience without reduction.In the other paper, I develop these rebuttals in general terms, emphasising the second rebuttal. Here I discuss the situation in physics, emphasising the first rebuttal. I focus on limiting relations between theories and illustrate my claims with four examples, each (...) of them a model or a framework for modelling, from well-established mathematics or physics.I take emergence as behaviour that is novel and robust relative to some comparison class. I take reduction as, essentially, deduction. The main idea of my first rebuttal will be to perform the deduction after taking a limit of some parameter. Thus my first main claim will be that in my four examples (and many others), we can deduce a novel and robust behaviour, by taking the limit N→∞ of a parameter N.But on the other hand, this does not show that the N=∞ limit is “physically real”, as some authors have alleged. For my second main claim is that in these same examples, there is a weaker, yet still vivid, novel and robust behaviour that occurs before we get to the limit, i.e. for finite N. And it is this weaker behaviour which is physically real.My examples are: the method of arbitrary functions (in probability theory); fractals (in geometry); superselection for infinite systems (in quantum theory); and phase transitions for infinite systems (in statistical mechanics). (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.

The received wisdom in statistical mechanics is that isolated systems, when left to themselves, approach equilibrium. But under what circumstances does an equilibrium state exist and an approach to equilibrium take place? In this paper we address these questions from the vantage point of the long-run fraction of time definition of Boltzmannian equilibrium that we developed in two recent papers. After a short summary of Boltzmannian statistical mechanics and our definition of equilibrium, we state an existence theorem which provides general (...) criteria for the existence of an equilibrium state. We first illustrate how the theorem works with a toy example, which allows us to illustrate the various elements of the theorem in a simple setting. After a look at the ergodic programme, we discuss equilibria in a number of different gas systems: the ideal gas, the dilute gas, the Kac gas, the stadium gas, the mushroom gas and the multi-mushroom gas. In the conclusion we briefly summarise the main points and highlight open questions. (shrink)