Charlotte Sophie Werndl

References to Popper’s concept of three worlds occupy a central position in ontological and human ecological questions in the recent literature on theoretical geography. This article demonstrates that Popper’s ideas and concepts have not been fully understood, causing problems for integrative research. Firstly, we critically review the discussion of Popper’s concept of three worlds in geography. We criticize its popular ontological interpretation, and furthermore we point out that Popper’s evolutionary basis has been consistently neglected. Subsequently we present an interpretation of Popper’s concept of three worlds which seems most plausible. We thereby identify his intentions and emphasize the evolutionary foundation of our interpretation of his theory. Finally, perspectives for human ecological research in geography on the basis of theories of evolution and emergence will be outlined.

The relation between the Boltzmannian and the Gibbsian formulations of statistical mechanics is one of the major conceptual issues in the foundations of the discipline. In their celebrated review of statistical mechanics, Paul Ehrenfest and Tatiana Ehrenfest-Afanassjewa discuss this issue and offer an argument for the conclusion that Boltzmannian equilibrium values agree with Gibbsian phase averages. In this paper, we analyse their argument, which is still important today, and point out that its scope is limited to dilute gases.

This paper argues that common intuitions regarding a) the specialness of 'use-novel' data for confirmation, and b) that this specialness implies the 'no-double-counting rule', which says that data used in 'constructing' (calibrating) a model cannot also play a role in confirming the model's predictions, are too crude. The intuitions in question are pertinent in all the sciences, but we appeal to a climate science case study to illustrate what is at stake. Our strategy is to analyse the intuitive claims in light of prominent accounts of confirmation of model predictions. We show that, on the Bayesian account of confirmation, and also on the standard Classical hypothesis-testing account, claims a) and b) are not generally true, but for some select cases, it is possible to distinguish data used for calibration from use-novel data, where only the latter confirm. The more specialised Classical model-selection methods, on the other hand, uphold a nuanced version of claim a), but this comes apart from b), which must be rejected in favour of a more refined account of the relationship between calibration and confirmation. Thus, depending on the framework of confirmation, either the scope or the simplicity of the intuitive position must be revised.

The relation between the Boltzmannian and the Gibbsian formulations of statistical mechanics is one of the major conceptual issues in the foundations of the discipline. In their celebrated review of statistical mechanics, Paul Ehrenfest and Tatiana Ehrenfest-Afanassjewa discuss this issue and offer an argument for the conclusion that Boltzmannian equilibrium values agree with Gibbsian phase averages. In this paper, we analyse their argument, which is still important today, and point out that its scope is limited to dilute gases.

It is customary to classify approaches in statistical mechanics (SM) as belonging either to Boltzmanninan SM (BSM) or Gibbsian SM (GSM). It is, however, unclear how the Boltzmann equation (BE) fits into either of these approaches. To discuss the relation between BE and BSM, we first present a version of BSM that differs from standard presentation in that it uses local field variables to individuate macro-states, and we then show that BE is a special case of BSM thus understood. To discuss the relation between BE and GSM, we focus on the BBGKY hierarchy and note the version of the BE that follows from the hierarchy is “Gibbsian” only in the minimal sense that it operates with an invariant measure on the state space of the full system.

Climate science is an umbrella term referring to scientific disciplines studying aspects of the Earth’s climate. It includes, among others, parts of atmospheric science, oceanography, and glaciology. In the wake of public discussions about an appropriate reaction to climate change, parts of decision theory and economics have also been brought to bear on issues of climate. The philosophy of climate science is a new sub-discipline of the philosophy of science that began to crystalise at the turn of the twenty-first century when philosophers started having a closer look at climate science. It comprises a reflection on almost all aspects of climate science, including observation and data, methods of detection and attribution, kinds of uncertainties, model ensembles, and decision-making under uncertainty. The philosophy of climate science operates in close contact with science itself and pays careful attention to the scientific details.

There are two theoretical approaches in statistical mechanics, one associated with Boltzmann and the other with Gibbs. The theoretical apparatus of the two approaches offer distinct descriptions of the same physical system with no obvious way to translate the concepts of one formalism into those of the other. This raises the question of the status of one approach vis-à-vis the other. We answer this question by arguing that the Boltzmannian approach is a fundamental theory while Gibbsian statistical mechanics (GSM) is an effective theory, and we describe circumstances under which Gibbsian calculations coincide with the Boltzmannian results. We then point out that regarding GSM as an effective theory has important repercussions for a number of projects, in particular attempts to turn GSM into a nonequilibrium theory.

Gibbsian statistical mechanics (GSM) is the most widely used version of statistical mechanics among working physicists. Yet a closer look at GSM reveals that it is unclear what the theory actually says and how it bears on experimental practice. The root cause of the difficulties is the status of the Averaging Principle, the proposition that what we observe in an experiment is the ensemble average of a phase function. We review different stances toward this principle, and eventually present a coherent interpretation of GSM that provides an account of the status and scope of the principle.

The aim of the paper 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, is 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.

A popular view in contemporary Boltzmannian statistical mechanics is to interpret the measures as typicality measures. In measure-theoretic dynamical systems theory measures can similarly be interpreted as typicality measures. However, a justification why these measures are a good choice of typicality measures is missing, and the paper attempts to fill this gap. The paper first argues that Pitowsky's (2012) justification of typicality measures does not fit the bill. Then a first proposal of how to justify typicality measures is presented. The main premises are that typicality measures are invariant and are related to the initial probability distribution of interest (which are translation-continuous or translation-close). The conclusions are two theorems which show that the standard measures of statistical mechanics and dynamical systems are typicality measures. There may be other typicality measures, but they agree about judgements of typicality. Finally, it is proven that if systems are ergodic or epsilon-ergodic, there are uniqueness results about typicality measures.

This is a highly welcome book that offers a fresh perspective on the philosophy of biology.1 It is of interest to both philosophers and biologists and to experienced readers as well as novices. The book is structured into four sections ‘Science’, ‘Biology’, ‘Microbes’ and ‘Humans’ and consists of a collection of articles written by John Dupré over the past few years. A very wide range of topics are discussed. Among other things, Dupré defends a pluralism that emphasizes that while there is only physical stuff, the kind of things composed of this stuff are fundamentally diverse, a modest form of social constructivism, the inseparability of science and values, the thesis of promiscuous individualism that there are various ways of dividing living systems into organisms and an anti-reductionist position about biology stating that complex objects possess properties that are autonomous from properties of their constituent parts. Dupré also argues that the success in understanding the chemical basis of genetics has undermined a simplistic view of inheritance, that the New Synthesis is flawed and instead evolutionary theory is a theory in flux, that biological individuals are typically symbiotic wholes involving many organisms of radically different kinds and genomes, that cooperation is a characteristic of life, that medicine has to take seriously the microbial symbiotic relationships, that contrary to evolutionary psychology human beings are in fact pretty well adapted to modern life, that in no sense of the word ‘gene’ can biological legitimacy be given to the concept of human race, that human nature as something fixed and constant throughout the human species is an illusion and that a denial of genetic determinism gives way to a robust sense of human autonomy.

A gas prepared in a nonequilibrium state will approach equilibrium and stay there. An influential contemporary approach to statistical mechanics explains this behavior in terms of typicality. However, this explanation has been criticized as mysterious as long as no connection with the dynamics of the system is established. We take this criticism as our point of departure. Our central claim is that Hamiltonians of gases that are epsilon-ergodic are typical with respect to the Whitney topology. Because equilibrium states are typical, it follows that typical initial conditions approach equilibrium and stay there.

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.

We argue that concerns about double-counting -- using the same evidence both to calibrate or tune climate models and also to confirm or verify that the models are adequate --deserve more careful scrutiny in climate modelling circles. It is widely held that double-counting is bad and that separate data must be used for calibration and confirmation. We show that this is far from obviously true, and that climate scientists may be confusing their targets. Our analysis turns on a Bayesian/relative-likelihood approach to incremental confirmation. According to this approach, double-counting is entirely proper. We go on to discuss plausible difficulties with calibrating climate models, and we distinguish more and less ambitious notions of confirmation. Strong claims of confirmation may not, in many cases, be warranted, but it would be a mistake to regard double-counting as the culprit.

This chapter explains the most important notions of entropy and clarifies their interrelations. It furthermore explores what notions of probabilities are at work when entropy is defined in terms of probability. Entropies from thermodynamics, information theory, statistical mechanics, dynamical systems theory, and fractal geometry are surveyed. Notions of entropy from statistical mechanics such as varieties of the Boltzmann and Gibbs entropies can be traced back to information-theoretic entropy. As the chapter points out, an analytic connection between fine-grained Boltzmann entropy and thermodynamic entropy can be established for ideal gases. No easy results about probabilities follow, since several interpretations are compatible with each definition of entropy.

In this contribution I will start in Sect. 2 by introducing epistemic competence. I will stress that like Bussmann, I regard it as fundamental that people in a democratic society possess epistemic competence and that it would be important to teach epistemic competence at school. In Sect. 3 I show that even for countries where the epidemiological situation is roughly the same or very similar such as Austria, Germany and Switzerland, there are often very different recommendations concerning vaccinations. In Sect. 4 I will identify and discuss five rational reasons that can alone or in combination lead to different vaccine recommendations. Finally, Sect. 5 will reflect on epistemic competence and vaccine recommendations. In particular, I will point out that different vaccine recommendations are an example where students can develop epistemic competence. Further, I will stress that different vaccine recommendations are an example where epistemic competence among the general population is desirable; if it is not present, this can lead to science scepticism and mistrust about science.

Dieser Open Access-Band präsentiert die aktuellen Debatten über das Selbstverständnis der Philosophiedidaktik, ihre Beziehung zur Fachphilosophie und den Stellenwert bzw. das Wesen der Interdisziplinarität. Dies betrifft zum einen die Innenperspektive der Fachdidaktik selbst. Neben den klassischen Arbeitsfeldern auf der theoretisch-konzeptionellen, der methodisch-praktischen und der empirisch-kritischen Ebene entstehen immer neue Teilbereiche der Philosophiedidaktik. Gleichzeitig wachsen von Seiten der Fachphilosophie sowohl Wertschätzung als auch Erwartungshaltung bezüglich der Fachdidaktik. Die hieraus resultierenden Aushandlungsprozesse sind immer auch mit der Frage nach Interdisziplinarität und dem thematischen und methodischen Proprium der Philosophie bzw. der Philosophiedidaktik verbunden. War Philosophie schon immer inter- bzw. metadisziplinär? Sollte philosophische Bildung immer nach Interdisziplinarität streben, oder geraten methodische und thematische Spezifika auf diese Weise in Gefahr?

The guiding question of this paper is: how similar are deterministic descriptions and indeterministic descriptions from a predictive viewpoint? The deterministic and indeterministic descriptions of concern in this paper are measure-theoretic deterministic systems and stochastic processes, respectively. I will explain intuitively some mathematical results which show that measure-theoretic deterministic systems and stochastic processes give more often the same predictions than one might perhaps have expected, and hence that from a predictive viewpoint these descriptions are quite similar.

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.

The general theme of this article is the actual practice of how definitions are justified and formulated in mathematics. The theoretical insights of this article are based on a case study of topological definitions of chaos. After introducing this case study, I identify the three kinds of justification which are important for topological definitions of chaos: natural-world-justification, condition-justification and redundancy-justification. To my knowledge, the latter two have not been identified before. I argue that these three kinds of justification are widespread in mathematics. After that, I first discuss the state of the art in the literature about the justification of definitions in the light of actual mathematical practice. I then go on to criticize Lakatos’s account of proof-generated definitions—the main account in the literature on this issue—as being limited and also misguided: as for topological definitions of chaos, in nearly all mathematical fields various kinds of justification are found and are also reasonable.

This article focuses on three themes concerning determinism and indeterminism. The first theme is observational equivalence between deterministic and indeterministic models. Here I discuss several results about observational equivalence and present an argument on how to choose between deterministic and indeterministic models involving indirect evidence. The second theme is whether Newtonian physics is indeterministic. I argue that the answer depends on what one takes Newtonian mechanics to be, and I highlight how contemporary debates on this issue differ from those in the nineteenth century. The third major theme is how the method of arbitrary functions can be used to make sense of deterministic probabilities. I discuss various ways of interpreting the initial probability distributions and argue that they are best understood as physical, biological etc. quantities characterising the particular situation at hand. Also, I emphasise that the method of arbitrary functions deserves more attention than it has received so far.