Claus Beisbart

How can probabilistic models from physics represent a target, and how can one understand the probabilities that figure in such models? The aim of this chapter is to answer these questions by analyzing random models of Brownian motion and point process models of the galaxy distribution as examples. This chapter defends the view that such models represent because we may learn from them by setting our degrees of belief following the probabilities suggested by the model. This account is not incompatible with an objectivist view of the pertinent probabilities, but stock objectivist interpretations, e.g., frequentism or Lewis’ Humean account of probabilities have problems to provide a suitable objectivist methodology for statistical inference from data. This point is made by contrasting Bayesian statistics with error statistics.

Statistical physicists assume a probability distribution over micro-states to explain thermodynamic behavior. The question of this paper is whether these probabilities are part of a best system and can thus be interpreted as Humean chances. I consider two Boltzmannian accounts of the Second Law, viz. a globalist and a localist one. In both cases, the probabilities fail to be chances because they have rivals that are roughly equally good. I conclude with the diagnosis that well-defined micro-probabilities under-estimate the robust character of explanations in statistical physics.

What is it to judge something to be a natural end? And what objects may properly be judged natural ends? These questions pose a challenge, because the predicates “natural” and “end” seemingly can not be instantiated at the same time – at least given some Kantian assumptions. My paper defends the thesis that Kant’s “Critique of Teleological Judgment”, nevertheless, provides a sensible account of judging something a natural end. On the account, a person judges an object O a natural end, if she thinks that the parts of O cause O and if she is committed to approach O in a top-down manner, as if the parts were produced in view of the whole. The account is non-realist, because it involves a commitment. With the account comes a characterization that provides necessary and sufficient conditions on objects that may properly be judged natural ends. My paper reconstructs the argument in CTJ, §§64-65 where the account and the characterization are derived.

If cosmology is to obtain knowledge about the whole universe, it faces an underdetermination problem: Alternative space-time models are compatible with our evidence. The problem can be avoided though, if there are good reasons to adopt the Cosmological Principle (CP), because, assuming the principle, one can confine oneself to the small class of homogeneous and isotropic space-time models. The aim of this paper is to ask whether there are good reasons to adopt the Cosmological Principle in order to avoid underdetermination in cosmology. Various strategies to justify the CP are examined. For instance, arguments to the effect that the truth of the CP follows generically from a large set of initial conditions; an inference to the best explanation; and an inductive strategy are assessed. I conclude that a convincing justification of the CP has not yet been established, but this claim is contingent on a number of results that may have to be revised in the future.

Monte Carlo simulations arrive at their results by introducing randomness, sometimes derived from a physical randomizing device. Nonetheless, we argue, they open no new epistemic channels beyond that already employed by traditional simulations: the inference by ordinary argumentation of conclusions from assumptions built into the simulations. We show that Monte Carlo simulations cannot produce knowledge other than by inference, and that they resemble other computer simulations in the manner in which they derive their conclusions. Simple examples of Monte Carlo simulations are analysed to identify the underlying inferences.

If we are to constrain our place in the world, two principles are often appealed to in science. According to the Copernican Principle, we do not occupy a privileged position within the Universe. The Cosmological Principle, on the other hand, says that our observations would roughly be the same, if we were located at any other place in the Universe. In our paper we analyze these principles from a logical and philosophical point of view. We show how they are related, how they can be supported and what use is made of them. Our main results are: 1. There is a logical gap between both principles insofar as the Cosmological Principle is significantly stronger than the Copernican Principle. 2. A step that is often taken for establishing the Cosmological Principle on the base of the Copernican Principle and observations is not incontestable as it stands, but can be supplemented with a different argument. 3. The Cosmological Principle might be crucial for cosmology to the extent it is not supported by empirical evidence.

It is often claimed that scientists can obtain new knowledge about nature by running computer simulations. How is this possible? I answer this question by arguing that computer simulations are arguments. This view parallels Norton’s argument view about thought experiments. I show that computer simulations can be reconstructed as arguments that fully capture the epistemic power of the simulations. Assuming the extended mind hypothesis, I furthermore argue that running the computer simulation is to execute the reconstructing argument. I discuss some objections and reject the view that computer simulations produce knowledge because they are experiments. I conclude by comparing thought experiments and computer simulations, assuming that both are arguments.

Kant famously thought that mathematics contains synthetic a priori truths. In his book, Wille defends a version of the Kantian thesis on not-so-Kantian grounds. Wille calls his account neo-Kantian, because it makes sense of Kantian tenets by using a methodology that takes the linguistic and pragmatic turns seriously.Wille's work forms part of a larger project in which the statuses of mathematics and proof theory are investigated. The official purpose of the present book is to answer the question: what is mathematics. Wille sets himself the task of finding a definition that enables him to distinguish between mathematics and proof theory. His solution reads roughly as follows. Mathematics is about how to generate synthetic a priori knowledge by acting within some calculus. This definition does not seem to be a promising starting point, because in this way a very controversial claim becomes true by definition. However, Wille's strategy is to make sense of his definition during the course of his argument and to show that the definition is appropriate regarding research that is commonly taken to be mathematics.The second part of the book explains what ‘acting within some calculus’ amounts to. In Wille's view, mathematics should be characterized in …