Wean Hall 4625
Wean Hall is the huge, award-winning, brutalist, concrete structure that proudly asserts its utopian, proletarian refusal to harmonize with the attractive, Beaux-arts Henry Hornbostel architecture on campus. Deep within its confines, our workshop will be safe from all distractions.
November 5, 20119:30-10:00 Coffee, pastries, fruit.
Jeroen Groenendijk, University of Amsterdam
A First-order Inquisitive Witness Semantics
Abstract: A central notion in inquisitive semantics is that of support. A common way to formulate the semantics is to start with a recursive definition of when a state supports a sentence, and then define the proposition expressed by a sentence as the set of all (maximal) states supporting that sentence. This approach is similar to the one that is usually taken in classical logic. There we start with a recursive definition of truth, and then define the proposition expressed by a sentence as the set of all worlds where the sentence is true. Thus, the role of support in inquisitive semantics is comparable to that of truth in classical logic. However, Ivano Ciardelli has shown that there are certain sentences in the language of first-order logic, the so-called boundedness formulas, which are equivalent in terms of support, even though, intuitively, they invite different types of responses. Ciardelli concludes from this observation that a support- based inquisitive semantics is not fine-grained enough in the first-order setting. In the semantics we will propose in this paper, states do not only contain information, but also a set of witnesses. The main feature of the semantics, then, is that an existentially quantified sentence like Ex:Px is only supported in a state if there is a specific witness in that state which is known to have the property P. As a result, an inquisitive sentence may not only request a response that provides certain information, but also a response that introduces a certain witness. Thus, the notion of inquisitiveness is richer than in the basic first-order system. Because the notion of inquisitiveness is enriched in this way, the semantics is able to make more fine-grained distinctions. In particular, it suitably assigns different semantic values to the boundedness formulas. At the same time, unlike the semantics that Ciardelli proposed to avoid the boundedness problem, the semantics developed here is still support-based.
Craige Roberts, Ohio State University
Mandy Simons, Carnegie Mellon University
Hanti Lin, Carnegie Mellon University
Uncertain Acceptance and Contextual Dependence on Questions
Abstract: A subject may say no to the question ``Will ticket number 1 win the lottery?'' but, when confronted with the refined question ``Which ticket will win the lottery?'', she may be be reluctant to rule out ticket number 1. This paper addresses the extent to which acceptance of uncertain propositions depends on the question in context, by providing two impossibility results formulated in the following. Let uncertainty be modeled by subjective probability. Understand a question as having potential, complete answers that are mutually exclusive and jointly exhaustive; understand answers as disjunctions of complete answers. Assume that accepted answers within each question are closed under entailment. Assume, further, that acceptance is sensible in the sense that contradiction is never accepted, that answers of certainty are always accepted, and that every answer can be accepted without certainty. Then, as our first result, it is impossible that acceptance is independent of questions, namely, that if a proposition is accepted as an answer to a question, then it is accepted in every question to which it is an answer. In light of the preceding result, one might settle on a weaker sense of question-independence. Say that a question is refined by another question if and only if each complete answer to the former question is a disjunction of complete answers to the latter question (e.g., the first question in the above lottery example is refined by the second question). As a weakening of question-independence, refinement-monotonicity requires that when an answer is accepted in a question, that answer is also accepted in every refined question. But refinement-monotonicity is too strong to be plausible, because, due to our second result, it is inconsistent with two intuitive principles for reasoning within each individual question. These two principles are: cautious monotonicity (i.e., do not retract accepted propositions when you learn what you already accept), and case reasoning (i.e., accept a proposition if it would be accepted no matter whether information E or its negation is learned), where information learning is assumed to follow the Bayesian ideal of conditioning.
Kevin T. Kelly, Carnegie Mellon University
Data-mining as Question-mining
Abstract: A perennial debate about scientific method concerns (I) the nature of empirical simplicity and (II) the role of simplicity in scientific justification. In this talk, I present an axiomatic theory of empirical simplicity as an invariant feature of empirical questions. The idea is that simplicity emerges from an apt representation of empirical underdetermination in the scientific question in context. It is shown that for many standard examples, including polynomial laws and linear causal models, the axioms pick out a unique, coarsest, apt representation of the question posed. Scientific justification and Ockham's razor can then be understood as achieving the aim of approximating deductive inference as nearly as the inductive question in context. Thus, it is as appropriate to say that the question in context pulls inquiry forward, as that the data as push it forward.