Groningen-Oldenburg Formal Epistemology Workshop
25-26 May 2012, University of Oldenburg, A6 1-111
Friday, 25 May 2012
14:30-15:30 Jan-Willem Romeijn (Groningen): "All Agreed: Aumann Meets DeGroot"
15:45-16:45 Michael Schippers (Oldenburg): "Coherence: Explicating Conceptual Distinctions"
17:00-18:00 Peter Brössel (Mainz): "An Argument for Pluralism in Bayesian Confirmation Theory"
18:15-19:00 Mark Siebel (Oldenburg): "Inconsistent Testimonies as a Touchstone of Coherence Measures"
Saturday, 26 May 2012
09:30-10:30 David Atkinson & Jeanne Peijnenburg (Groningen): "Possible Worlds and Probable Worlds"
10:45-11:45 Allard Tamminga (Groningen & Oldenburg): "Katz's Revisability Paradox Dissolved"
12:00-13:00 Barteld Kooi (Groningen): "Correspondence Theory for Many-Valued Logic"
Jan-Willem Romeijn: "All Agreed: Aumann Meets DeGroot"
This paper shows that a consensus formation process following the rules laid down by Morris DeGroot, and later by Lehrer and Wagner, can be represented in the context of Aumann's famous agreement theorem: for any such process there is a common prior so that the approach to agreement, as described by Genneakoplos and Polymarchakis, coincides with the consensus formation process. Conversely, any common prior is associated with some process of consensus formation. A number of connections are considered between classes of priors and restrictions on the approach to consensus.
Michael Schippers: "Coherence: Explicating Conceptual Distinctions"
In this paper I comment on two prominent counterexamples purporting to establish the untenability of probabilistic measures of coherence: the problem of belief individuation (Moretti & Akiba 2007) on the one hand and the child's play objection on the other (Siebel 2005). Referring to Bonjour's coherence theory as well as to considerations in the context of belief revision theory, I argue for the existence of two levels on which to apply coherence measures: the representational and the content level. Then I display a notion of content by means of elementary mathematical logic. Finally I show in how far the distinction of different levels allows us to do justice to basic intuitions concerning coherence as well as the formal results put forward by Moretti & Akiba and Siebel.
Peter Brössel: "An Argument for Pluralism in Bayesian Confirmation Theory"
According to one standard assumption in Bayesian confirmation theory there is just "one true" measure of confirmation. In this presentation I present one simple argument to the effect that no Bayesian measure of confirmation can serve all the originally intended purposes of confirmation theory. More specifically, it is argued that there are two intuitively appealing and originally intended purposes of confirmation theory which cannot be satisfied by a single Bayesian confirmation measure. Those two intuitively appealing and originally intended purposes of confirmation are: measuring the degree of acceptability of hypotheses in the light of the evidence; and measuring the degree of evidential support provided by the evidence for that hypothesis. Thus, if an adequate confirmation theory is supposed to serve both purposes, then it requires a plurality of confirmation measures.
Mark Siebel: "Inconsistent Testimonies as a Touchstone of Coherence Measures"
Sets of inconsistent testimonies may differ in their incoherence. For example, if two of three witnesses incriminate the same subject whereas the third one disagrees, the incoherence is smaller than in cases of total, i.e. pairwise, disagreement. I will show which probabilistic measures of coherence conform to requirements of this kind and which do not.
David Atkinson & Jeanne Peijnenburg: "Possible Worlds and Probable Worlds"
If a proposition p is true, how probable is it that we know it to be true? According to Timothy Williamson, the probability is as small as you like. He defends this surprising claim by applying possible worlds semantics to a model of a clock with no markings on its dial and only the one hour hand. We constructively criticize Williamson's claim by offering a more thoroughgoing probabilistic version of his clock model, using what we call probable worlds. On the basis of these probable worlds we show that, if p is true, the probability that we know it to be true has a value that is not so small.
Allard Tamminga: "Katz's Revisability Paradox Dissolved"
W.V. Quine's holistic empiricist account of scientific inquiry can be characterized by three constitutive principles: noncontradiction, universal revisability and pragmatic ordering. Jerrold Katz (1998; 2002) argues that holistic empiricism suffers from what he calls the Revisability Paradox: because the three constitutive principles of holistic empiricism cannot themselves be rationally revised, holistic empiricism is incoherent. In this paper, we show that Katz's argument fails. Using Gärdenfors and Makinson's logic of belief revision based on epistemic entrenchment, we argue that Katz wrongly assumes that the three constitutive principles are statements within a holistic empiricist's scientific theory of the world. Instead, we show that constitutive principles are best seen as properties of a holistic empiricist's theory of scientific inquiry and argue that without Katz's mistaken assumption the paradox cannot be formulated. Finally, we argue that our perspective on the status of constitutive principles is perfectly in line with Quinean orthodoxy.
Barteld Kooi: "Correspondence Theory for Many-Valued Logics"
Taking our inspiration from modal correspondence theory, we present the idea of correspondence theory for many-valued logics. As a benchmark case, we study truth-functional extensions of the Logic of Paradox ($LP$). First, we characterize each of the possible truth-table entries for unary and binary operators that could be added to $LP$ by an inference scheme. Second, we define a class of natural deduction systems on the basis of these characterizing inference schemes and a natural deduction system for $LP$. Third, we show that each of the resulting natural deduction systems is sound and complete with respect to its particular semantics.