Abstract: A composite Skyrms-Lewis signaling game can be used to provide a simple model for how a probability predicate and successful prediction might coevolve with descriptive expressions in a base language. We will briefly consider such a model and how inductive behavior may lead to a language that allows for explicit inductive inference.
Abstract: According to an argument by Colin Howson, the no-miracles argument is contingent on committing the base-rate fallacy and is therefore bound to fail. In this note, we demonstrate that Howson’s argument only applies to one of two versions of the no-miracles argument. The other, more considerate version is not adequately reconstructed in Howson’s approach and thus remains unaffected by his line of reasoning. We provide a Bayesian reconstruction of this version of the no-miracles argument and show that it is sound.
Abstract: Bayesian treatments of inductive inference and decision making presuppose that the structure of the situation under consideration is fully known. Such situations are called ‘small worlds’ by Savage. However, as Savage already pointed out himself, we are often faced with ‘large worlds’ (‘grand worlds’ in Savage’s terminology). In a large world one might only have very fragmentary information about the basic structure of an epistemic situation. This makes planning ahead difficult, if not impossible. Since planning is at the heart of Bayesian inductive inference and decision making, it is not easy to see how a Bayesian can navigate a large world.In this talk I will outline a general approach to these problems and consider some concrete examples of learning rules for large worlds.
Abstract: I will deal with the role that theoretical terms might play for scientific inductive reasoning. I will argue that (i) Carnap’s account of theoretical terms is not affected by Hempelian worries about inductive systematization, and (ii) that “logical“ uniform probability measures for scientific languages with theoretical terms might well allow for inductive learning (contra Carnap).
Abstract: Goodman showed with his new riddle that induction is inconsistent without a restriction on the occurring predicates. Davidson observed that the restriction must be applied to the whole set of predicates occurring in an induction: The inductive inference that all emeralds are green and all lapis lazulis are blue is perfectly consistent with the inductive inference that all emerzulis are grue, where unobserved emerzulis are lapis lazulis. In my talk I show that Davidson’s observation is a special case of a slight generalization of Newman’s objection to structuralism and use this result to evaluate the possibility of blocking Goodman’s new riddle with the help of analogue models.
Abstract: Elia Zardini (2013) and Hartry Field (2014) have recently argued that a key semantic ingredient of the v-Curry Paradox, a validity-involving version of Curry’s Paradox, is in tension with Goedel’s Second Incompleteness Theorem. Moreover, Zardini points to some paradoxes of consistency and incompatibility which, in his view, ‘cannot be adequately solved by simply changing the logic’ of one’s theory, but rather call for a radical weakening of the logic of one’s metatheory—in particular, of the metatheoretical counterpart of the rule of structural contraction (Zardini, 2014). I show that Goedelian reservations, if sound, equally apply to the paradoxes of naive logical properties. But I also argue that they are not sound, and that, insofar as restrictions of structural contraction are to be motivated by the existence of unstable sentences, sentences whose truth is incompatible with that of some of their consequences (Zardini, 2011; Zardini, 2014), the paradoxes of naive logical properties may not be solved by weakening such a rule.
Abstract: Carnap, in his nachlass, calls attention to 3 open problems in philosophy. I suggest that answers to each of these problems already exist in the Bayesian canon.
Abstract: To evaluate climate models, it is essential that the best available methods for confirmation are used. A hotly debated issue on confirmation in climate science (as well as in philosophy) is the requirement of use-novelty (i.e. that data can only confirm models if they have not already been used before, e.g. for calibrating parameters). This paper investigates the issue of use-novelty in the context of the mathematical methods provided by model selection theory. We will show that the picture model selection theory presents us with about use-novelty is more subtle and nuanced than the commonly endorsed positions by climate scientists and philosophers. More specifically, we will argue that there are two main cases in model selection theory. On the one hand, there are the methods such as cross-validation where the data are required to be use-novel. On the other hand, there are the methods such as the Akaike Information Criterion (AIC) for which the data cannot be use-novel. Still, for some of these methods (like AIC) certain intuitions behind the use-novelty approach are preserved: there is a penalty term in the expression for the degree of confirmation by the data because the data have already been used for calibration. The common positions argued for in climate science and philosophy are either that data should always be use-novel or that the use-novelty criterion is irrelevant. According to model selection theory these positions are too simple: whether or not data should be use-novel depends on the specific method used. For certain methods data should be use-novel, but for others they cannot and thus need not be use-novel.
Abstract: I take a closer look at Poincare’s (1905) heated-disk world Gedankenexperiment by analysing how a conventionalist and an a priori Euclidean mathematician would make sense of space in this world. Such an unpacking of the scenario both helps to clarify the relationships between experience and geometry underlying each viewpoints as well as demonstrates that the conventionalist mathematician can derive epistemological advantages from his approach. In particular, conventionalism about geometry appears to capture Poincare’s later (1914) thoughts on the ways good mathematicians think.