This thesis focuses on expressively rich languages that can formalise talk about probability. These languages have sentences that say something about probabilities of probabilities, but also sentences that say something about the probability of themselves. For example: (π): “The probability of the sentence labelled π is not greater than 1/2.” Such sentences lead to philosophical and technical challenges; but can be useful. For example they bear a close connection to situations where ones confidence in something can affect whether it is (...) the case or not. The motivating interpretation of probability as an agent's degrees of belief will be focused on throughout the thesis. -/- This thesis aims to answer two questions relevant to such frameworks, which correspond to the two parts of the thesis: “How can one develop a formal semantics for this framework?” and “What rational constraints are there on an agent once such expressive frameworks are considered?”. (shrink)

Moss (2018) argues that rational agents are best thought of not as having degrees of belief in various propositions but as having beliefs in probabilistic contents, or probabilistic beliefs. Probabilistic contents are sets of probability functions. Probabilistic belief states, in turn, are modeled by sets of probabilistic contents, or sets of sets of probability functions. We argue that this Mossean framework is of considerable interest quite independently of its role in Moss’ account of probabilistic knowledge or her semantics for epistemic (...) modals and probability operators. It is an extremely general model of uncertainty. Indeed, it is at least as general and expressively powerful as every other current imprecise probability framework, including lower probabilities, lower previsions, sets of probabilities, sets of desirable gambles, and choice functions. In addition, we partially answer an important question that Moss leaves open, viz., why should rational agents have consistent probabilistic beliefs? We show that an important subclass of Mossean believers avoid Dutch bookability iff they have consistent probabilistic beliefs. (shrink)

Simulation models of the Reiterated Prisoner's Dilemma have been popular for studying the evolution of cooperation since more than 30 years now. However, there have been practically no successful instances of empirical application of any of these models. At the same time this lack of empirical testing and confirmation has almost entirely been ignored by the modelers community. In this paper, I examine some of the typical narratives and standard arguments with which these models are justified by their authors despite (...) the lack of empirical validation. I find that most of the narratives and arguments are not at all compelling. None the less they seem to serve an important function in keeping the simulation business running despite its empirical shortcomings. (shrink)

This is an introduction to the English translation of Hogo Dingler's (1881-1954) grounsbreaking paper "Methodik statt Erkenntnistheorie und Wissenschaftslehre". Dingler is the founder of operationalism in physics and relatively little know in the Anglophone world.