Opening Celebration Conference

June 26-27, 2010

To celebrate its founding, the Center hosted a gala Opening Celebration Conference on June 26-27 in the Adamson Wing in Baker Hall, on the Carnegie Mellon campus in Pittsburgh, PA. Speakers were encouraged to present the work that interests them most.  The result was a stellar sampling  of the best work in formal epistemolgy.  The celebration ended with a lively round table on formal epistemology.  Thanks to all who attended to make it such a great success.

Talk Abstracts

Revised schedule

Paul Egre

Vagueness: Tolerant, Classical, Strict

Joint work with Pablo Cobreros (U. of Navarra), David Ripley (IJN) and Robert van Rooij (ILLC, Amsterdam)

In this paper, we investigate a semantic framework originally defined by van Rooij (2010) to account for the idea that vague predicates are tolerant, namely for the principle that if x is P, then y should be P whenever y is similar enough to x. The semantics, which makes use of indifference relations in order tocapture the notion of similarity relevant for the application of vague predicates, rests on the interaction of three notions of truth: the classical notion, and two dual notions simultaneously defined in terms of it, which we call tolerant truth and strict truth. Basically, a vague predicate P is said to hold tolerantly of an object x provided
there is an object y similar enough to x in the relevant respects that satisfies P classically. Dually, a vague predicate is said to hold strictly of an object provided it holds classically of all objects that are similar enough in the relevant respects.

In the first part of the paper, we explain how the semantics allows us to validate the tolerance principle and to solve the sorites paradox. We characterize, in particular, the space of consequence relations definable on the basis of the notions of classical, strict and tolerant truth at hand. We present and discuss some correspondences and differences between our approach and other approaches used to deal with vagueness (in particular supervaluationism, subvaluationism, and three-valued logics).

A specificity of the notion of tolerant truth we get is that it is paraconsistent: in particular, it implies that borderline cases are tolerantly P and not P (while they are neither strictly P nor strictly not P). We argue for the plausibility of this conception. In particular, we discuss how the framework can be used to accommodate the recent experimental data by Ripley (2009) and Alxatib and Pelletier (2010) regarding the way subjects respond to classical contradictions and tautologies for borderline cases.

Branden Fitelson, Rutgers

The Problem of Irrelevant Conjunction --- Revisited

Joint work with James Hawthorne

The problem of irrelevant conjunction (aka, the "tacking problem") was originally one which plagued Hypothetico-Deductive accounts of confirmation.  More recently, Bayesians have offered various sorts of analyses of the problem.  I will survey the (early) Bayesian analyses, and explain how they are deficient in several crucial ways.  Then, I will present what I take to be a more probative Bayesian analysis (due to myself and Jim Hawthorne).  Finally, I will address some recent criticisms of our approach (due to Maher, and Crupi & Tentori).

Stephan Hartmann, Tilburg

Confirmation and Reduction: A Bayesian Account

Various scientific theories stand in a reductive relation to each other. In a recent article (F. Dizadji-Bahmani, R. Frigg and S. Hartmann: Who is Afraid of Nagelian Reduction? To appear in Erkenntnis), we have argued that a generalized version of the Nagel-Schaffner model (GNS) is the right account of this relation. In this talk, we present a Bayesian analysis of how GNS impacts on confirmation. We formalize the relation between the reducing and the reduced theory before and after the reduction using Bayesian networks, and thereby show that, post-reduction, the two theories are confirmatory of each other. We then ask when a purported reduction should be accepted on epistemic grounds. To do so, we compare the prior and posterior probabilities of the conjunction of both theories before and after the reduction and ask how well each is confirmed by the available evidence. (This talk is based on a joint paper, forthcoming in Synthese, with Foad Dizadji-Bahmani and Roman Frigg.)

James Joyce, Michigan

A Defense of Imprecise Credences in Inference and Decision Making

Many people – including Issac Levi, Peter Walley, Teddy Seidenfeld, Richard Jeffrey and Mark Kaplan – have suggested that uncertain beliefs that are based on ambiguous or incomplete evidence are best represented using sets of probability functions.  I will defend the use of such “imprecise credal states” against some recent objections, raised by Roger White and Adam Elga, which concern the phenomenon of dilation.  Dilation occurs when learning some definite fact forces a person’s beliefs about an event to shift from a sharp, point-valued subjective probability to an imprecise spread of probabilities. Some commentators have found dilation disturbing, both from the epistemic and decision-theoretic perspectives, and have placed the blame on the use of sets of probabilities to represent beliefs.  I will argue that these reactions are based on an overly narrow conception of imprecise credal states which assumes that we know everything there is to know about a person’s doxastic attitude toward an event once we know the spread of values of her subjective probability for that event.  Once we recognize that the theory of imprecise credences has the resources to characterize a much richer family of doxastic attitudes than this, we will see that the charges of incoherence brought by White and Elga are unfounded. Dilation is not disturbing when properly understood, and it does not lead to any incoherence in either inference of decision making.

Hans Kamp, Stuttgart

Back and Forth between Language and Thought

What can we learn about the structure of thought from studying the structure of language and the ways in which it is used? The question is ancient and it has given rise to a long défilé of speculations, hypotheses and claims. I will begin by looking at one aspect of this question: What can we learn about the structure of mental representations from close attention to the ways in which linguistic form maps onto utterance meaning and the meaning of extended discourse and text?  After rehearsing some earlier conclusions about plausible conclusions that can be drawn from such considerations about the structure of the mental representations which result from language interpretation, I will argue for the hypothesis that similar representations also serve as inputs to language production.  These assumptions lead to a picture of verbal communication according to which communicative success consists in the similarity between the representation constructed by the interpreter of an utterance and the representation that led the speaker/author to choose the words contained in the utterance she produced.   In order that such similarity (and thus communicative success) can be achieved on a regular basis, discourse participants must share their understanding of the relations between words and thoughts. (Which entails that they must share the syntactic, semantic and pragmatic rules of the language they use to communicate.)  But more often than not, just sharing the rules of the language isn’t enough.  Most speech acts presuppose that, in addition, speaker and interpreter share certain bits of background information - about particular entities and facts as well as general principles to which the world conforms (with few exceptions if any).   What has been argued earlier about the input to language production and output from language interpretation also applies to such background information: the form in which the information is represented is as important as its propositional content. The final part of the talk will focus on this particular aspect of what renders verbal communication possible and effective.

Hannes Leitgeb, Ludwig-Maximiliens University

Reducing Belief Simpliciter to Degrees of Belief

We prove that given quite reasonable assumptions, it is possible to give an explicit definition of belief simpliciter in terms of subjective probability, such that it is neither the case that belief is stripped of any of its usual logical properties, nor is it the case that believed propositions are bound to have probability 1. Belief simpliciter is not to be eliminated in favour of degrees of belief, rather, by reducing it to assignments of consistently high degrees of belief, both quantitative and qualitative belief turn out to be governed by one unified theory. Turning to possible applications and extensions of the theory, we suggest that this will allow us to see: how the Bayesian approach in general philosophy of science can be reconciled with the deductive or semantic conception of scientific theories and theory change; how the assertability of conditionals can become an all-or-nothing affair in the face of non-trivial subjective conditional probabilities; how knowledge entails a high degree of belief but not necessarly certainty; how primitive conditional probability functions (Popper functions) arise from conditionalizing absolute probability measures on maximally strong believed propositions with respect to different cautiousness thresholds; and how conditional chances may become the truthmakers of counterfactuals.

Rohit Parikh, CUNY

Behavior and Belief

 One common interpretation of states of belief is that they are sets of propositions, that these propositions are sets of worlds, represented by sentences, and that  communication changes one’s belief state by replacing one such set by another.  The assumption of logical closure is also common, and appealed to, as early as Plato’s dialogue Meno.  Such a representation does allow various formal theories to come into play. The AGM theory uses this representation of belief and so does the KD45 representation by means of Kripke structures. However, there are severe difficulties in the way of accepting such an account of belief (and hence of knowledge which typically presupposes belief). We want to present a “propositionless” account of belief and change in belief relying more on some automata theoretic models. Beliefs can change not only by hearing sentences but also by witnessing events and via purely internal process, like deduction. Moreover, beliefs come in two flavors. Beliefs inferred from action, our usual method with infants and animals, and beliefs expressed in words. With Ramsey and Savage, beliefs are revealed by the actions one takes and the choices one makes between various options. These beliefs which we call e-beliefs are a little like Gendler’s “aliefs.” The other variety of beliefs, which are our usual “vanilla” beliefs, are expressed in words. These are vulnerable to “morning star, evening star” and “Pierre” examples. We explain the two notions and how they relate to each other.

Selected References:

Carlos Alchourron, Peter Gardenfors and David Makinson, “On the logic of theory change: partial meet contraction and revision functions”,  J. Symbolic Logic 50, (1985) 510–530.

Tamar Gendler (2009). Alief in Action (and Reaction). Mind & Language 23 (5):552-585.

[Pa94] R. Parikh, "Vagueness and Utility: the Semantics of Common Nouns" in Linguistics and Philosophy 17, 1994, 521-35.

[Pa09]  R. Parikh, "From language games to social software", in Reduction, Asbstraction, Analysis, proceedings of the 31st International Ludwig Wittgenstein Symposium in Kirchberg, edited by Alexander Hieke and Hannes Leitgeb, Ontos Verlag 2009, pp. 365-376.

[Pa08] R. Parikh "Sentences, belief and logical omniscience, or what does deduction tell us? ", Review of Symbolic Logic, 1 (2008) 459-476.

[Plato]  Meno

[Ramsey] F. P. Ramsey,  "Truth and Probability", in The Foundations of Mathematics, Routledge 1931.

[Savage]   Leonard Savage, The Foundations of Statistics, Wiley 1954

Oliver Schulte, Simon Fraser

Causal Models for Relational Data

The traditional paradigm cases of causal modelling concern individuals  and their properties (e.g., patients and their symptoms).  Relational data provide information about individuals, their properties and links among the individuals. Examples of relational causal patterns
are “smoking by co-workers causes cancer” and “my enemy’s enemy is my friend”. The availability of relational data has increased over the last few decades, for instance in social networks and relational databases, and there is therefore much practical interest in applying statistical learning to such data. As relational databases make use of formal logic to
describe complex multi-level, multi-population relationships, statistical-relational learning raises conceptual questions about probability and logic that relate to philosophical investigations, such as the relationship between frequencies and single-case probabilities. A surprising development is that directed graphical models have posed so far unresolved conceptual problems that have been more successfully addressed with undirected models (Markov networks). This has led researchers to conclude that “the applicability of directed models to relational data is severely constrained” (Jensen and Neville 2007). Philosophically, this
means that predictive relational models that represent symmetric correlations but not asymmetric causation have been more successful. I will review the main difficulties in applying causal graphs to relational data, with an emphasis on the conceptual issues, and discuss possible new solutions. I also present an efficient new algorithm for learning causal graphs (Bayes nets) from relational data, based on a new theoretical approach.

Teddy Seidenfeld, Carnegie Mellon

Getting to Know your Probabilities: Three ways to frame personal probabilities for decision making.

An old, wise, and widely held attitude in Statistics is that modest intervention in the design of an experiment followed by simple statistical analysis may yield much more of value than using very sophisticated statistical analysis on a poorly designed existing data set.  In this sense, good inductive learning is active and forward looking, not passive and focused exclusively on analyzing what is already known.  In this talk I review three different approaches for how a decision maker might actively frame her/his probability space rather than being passive in that phase of decision making.

Method-1:  Assess precise/determinate probabilities only for the set of random variables that define the decision problem at hand.  Do not include other "nuisance" variables in the space of possibilities.   In this sense, over-refining the space of possibilities may make assessing probabilities infeasible for good decision making.

Method-2:  With respect to a particular decision problem, choose wisely a set of events E that you can assess with precise/determinate probabilities. Coherence (as in de Finetti's theory) requires that you extend these probabilities to the linear span generated by E, which may be a smaller and simpler set than the Boolean algebra generated by E.  If E is wisely chosen, the decision problem at hand may be solved by the assessments over the smaller space.

Method-3: Your probabilistic assessments may be incoherent so that you may be exposed to a sure-loss in your decision making about some specific quantities.  Nonetheless, you may be able to use familiar algorithms (e.g., Bayes' theorem) to update your views with new data and to improve your incoherent assessments about these quantities.  That is, you may be able to reduce your degree of incoherence about these quantities by active, Bayesian-styled learning.  Specifically, by framing your probability space so that incoherence is concentrated in your "prior," you may use Bayesian algorithms to update to a less-incoherent "posterior."

I illustrate these three methods with several problems, including how to sidestep what others have claimed to be some computational limitations of Bayesian inference.

Wilfried Sieg, Carnegie Mellon

Structural Proof Theory: Uncovering Aspects of the Mathematical Mind

Abstract. What shapes mathematical arguments into intelligible proofs (that can be found efficiently)?  This is the informal question I address by investigating, on the one hand, the abstract ways of the axiomatic method in modern mathematics and, on the other hand, the concrete ways of proof construction suggested by modern proof theory.

The theoretical investigations are complemented by experiments with the proof search algorithm AProS.  Its strategically guided search has been extended beyond pure logic to elementary parts of set theory. Here, the subtle interaction between understanding and reasoning, i.e., between introducing concepts and proving theorems, is crucial and suggests principles for structuring proofs conceptually.

These strands are part of a fascinating intellectual fabric and connect classical themes with contemporary problems - reaching from proof theory and the foundations of mathematics through computer science to cognitive science and back.

Brian Skyrms, UC Irvine

The Concepts of Information and Deception in Signalling Games

I discuss the concepts of information in signals - both quantity of information and informational content - in the context of signaling games. The analysis is meant to apply at all levels of biological organization.

Wolfgang Spohn, Konstanz

A Guided Tour through the Cosmos of Ranking Theory

Ranking theory is a dynamic theory of belief and as such of comparable fundamentality and generality to Bayesianism. Ranks also are degrees of belief ranging from - to + infinity, behaving in many ways similar and in characteristic ways unlike probabilities; in particular, positive ranks adequately represent belief and distinguish more or less firm beliefs (negative ranks correspondingly express disbelief). Moreover, in contrast to other theories of belief it can fully account for the dynamics of belief, a task equivalent to answering the problem of induction. The talk will explain some basic features and some surprising applications of ranking theory.

James Woodward, Pittsburgh

Causal Learning and Judgment: Covariation and Contact Mechanics

Contemporary philosophical and psychological accounts of causation may be grouped into two broad categories, which may seem to draw on fundamentally different ideas about causation. Difference-making theories (including “interventionist” accounts and accounts of casual learning and representation in terms of Bayes nets) rely on the guiding idea that causes make a difference to their effects. Such theories emphasize the role of information about the role of contingencies or covariation in causal learning. Such theories contrast with a second family of contact mechanical theories thatfocus on the role of connecting processes mechanical relationships in causal learning and the characterization of casual relationships. Within psychology, such approaches stress the role of causal representations in terms of “forces” and “generative mechanisms” and often assign a central role to the so-called perception of causation. This talk will explore the relationship between these two ways of thinking about causation (and the capacities for learning and understanding associated with them). One issue: adult humans apparently seamlessly integrate information from about causal relationships derived from causal perception and contact mechanics with contingency information, including  information resulting from interventions. In contrast, although there is some dispute about this, infants are often claimed to show sensitivity to contact mechanical relationships, as revealed in looking time studies, before they are able to exploit such information in action. This raises the question of when (and how) these two sources of information and two ways of thinking about causal relationships are integrated in human development. I will discuss some conceptual and empirical considerations bearing on this question.


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Kevin T. Kelly, Director Horacio Arlo-Costa, Associate Director Mauren Antkowski, Administrator