Williamson on Gettier Cases and Epistemic Logic

Abstract

Timothy Williamson has fruitfully exploited formal resources to shed considerable light on the nature of knowledge. In the paper under examination, Williamson turns his attention to Gettier cases, showing how they can be motivated formally. At the same time, he disparages the kind of justification he thinks gives rise to these cases. He favors instead his own notion of justification for which Gettier cases cannot arise. We take issue both with his disparagement of the kind of justification that figures in Gettier cases and the specifics of the formal motivation.     

Epistemic Instrumentalism and Reasons for Belief: A Reply to Tom Kelly's "Epistemic Rationality as Instrumental Rationality: A Critique"

Tom Kelly argues that instrumentalist accounts of epistemic rationality fail because what a person has reason to believe does not depend upon the content of his or her goals. However, his argument fails to distinguish questions about what the evidence supports from questions about what a person ought to believe . Once these are distinguished, the instrumentalist can avoid Kelly's objections. The paper concludes by sketching what I take to be the most defensible version of the instrumentalist view.     

Epistemic Friction: Reflections on Knowledge, Truth, and Logic

Knowledge requires both freedom and friction. Freedom to set up our epistemic goals, choose the subject matter of our investigations, espouse cognitive norms, design research programs, etc., and friction (constraint) coming from two directions: the object or target of our investigation, i.e., the world in a broad sense, and our mind as the sum total of constraints involving the knower. My goal is to investigate the problem of epistemic friction, the relation between epistemic friction and freedom, the viability of foundationalism as a solution to the problem of friction, an alternative solution in the form of a neo-Quinean model, and the possibility of solving the problem of friction as it applies to logic and the philosophy of logic within that model.     

Understanding and Semantic Strucure: Reply to Timothy Williamson

In his essay '"Conceptual Truth"', Timothy Williamson (2006) argues that there are no truths or entailments that are constitutive of understanding the sentences involved. In this reply I provide several examples of entailment patterns that are intuitively constitutive of understanding in just the way that Williamson rejects, and I argue that Williamson's argument does nothing to show otherwise. Williamson bolsters his conclusion by appeal to a certain theory about the nature of understanding. I argue that his theory fails to consider the role that the structure of a sentence plays in determining its meaning. The cases I present suggest that this role imposes greater cognitive requirements on understanding than Williamson can acknowledge.     

A Non-alethic Multi-agent Doxastic Logic as a Solution to Epistemic Conflicts

Axiomathes - The non-alethic systems N1 of da Costa and A of Grana are both paraconsistent and paracomplete. Based on them, a multi-agent doxastic logic NADK can be obtained by logical expansion....     

The Epistemic Status of Auxiliary Hypotheses: A Reply to Douven

I have previously argued that anti-realism cannot use the claim that theories have empirically equivalent rivals (EE) to establish that theories are underdetermined by evidence (UD). Douven objects that the auxiliary hypotheses needed to generate observational equivalence need not as I claimed be themselves underdetermined if (EE) is true, because they may be either compatible with observation or acceptable in the constructive-empiricist sense. I reply that these conditions are not strong enough to establish (EE): the auxiliaries have to be epistemically warranted if they are to fix a theory's observational commitments unambiguously. The support they require need not presuppose their respective observational consequences, because there are more holistic sources of warrant.     

Cooperation,Knowledge, and Time: Alternating-time Temporal Epistemic Logic and its Applications

Branching-time temporal logics have proved to be an extraordinarily successful tool in the formal specification and verification of distributed systems. Much of their success stems from the tractability of the model checking problem for the branching time logic CTL, which has made it possible to implement tools that allow designers to automatically verify that systems satisfy requirements expressed in CTL. Recently, CTL was generalised by Alur, Henzinger, and Kupferman in a logic known as Alternating-time Temporal Logic (ATL). The key insight in ATL is that the path quantifiers of CTL could be replaced by cooperation modalities, of the form , where is a set of agents. The intended interpretation of an ATL formula is that the agents can cooperate to ensure that holds (equivalently, that have a winning strategy for ). In this paper, we extend ATL with knowledge modalities, of the kind made popular in the work of Fagin, Halpern, Moses, Vardi and colleagues. Combining these knowledge modalities with ATL, it becomes possible to express such properties as group can cooperate to bring about iff it is common knowledge in that . The resulting logic — Alternating-time Temporal Epistemic Logic (ATEL) — shares the tractability of model checking with its ATL parent, and is a succinct and expressive language for reasoning about game-like multiagent systems.     

Knowledge as a thick concept: explaining why the Gettier problem arises

The Gettier problem has stymied epistemologists. But, whether or not this problem is resolvable, we still must face an important question: Why does the Gettier problem arise in the first place? So far, philosophers have seen it as either a problem peculiar to the concept of knowledge, or else an instance of a general problem about conceptual analysis. But I would like to steer a middle course. I argue that the Gettier problem arises because knowledge is a thick concept, and a Gettier-like problem is just what we should expect from attempts at analyzing a thick concept. Section 2 is devoted to establishing the controversial claim that knowledge is thick, and, in Sect. 3, I show that there is a general problem for analyzing thick concepts of which the Gettier problem is a special instance. I do not take a stand on whether the Gettier problem, or its general counterpart, is resolvable. My primary aim is to bring these problems into better focus.     

Children's Understanding of Behavioral Consequences of Epistemic States: A Comparison of Knowledge,Ignorance, and False Belief

The author addressed the issue of the simultaneity of false belief and knowledge understanding by investigating children's ability to predict the behavioral consequences of knowledge, ignorance, and false belief. The second aim of the study was to explore the role of counterfactuals in knowledge understanding. Ninety-nine (99) children, age 3–7 years old, completed the unexpected transfer task and a newly designed task in which a protagonist experienced 1 of the following 4 situations: knowing a fact, not knowing a fact, knowing a procedure, and not knowing a procedure. The results showed that factual ignorance was as difficult as false belief for the children, whereas the other conditions were all easier than false belief, suggesting that the well-known lag between ignorance and false belief may be partly methodologically based. The results provide support for a common underlying conceptual system for both knowing and believing, and evidence of the role of counterfactual reasoning in the development of epistemic state understanding. Methodological variations of the new task are proposed for future research.     

A Compatibilist Account of the Epistemic Conditions on Rational Deliberation

A traditional concern for determinists is that the epistemic conditions an agent must satisfy to deliberate about which of a number of distinct actions to perform threaten to conflict with a belief in determinism and its evident consequences. I develop an account of the sort that specifies two epistemic requirements, an epistemic openness condition and a belief in the efficacy of deliberation, whose upshot is that someone who believes in determinism and its evident consequences can deliberate without inconsistent beliefs. I argue that conditions of both types are indispensable, and that they can be formulated so as to withstand the relevant objections.     

A Sat-Based Approach to Unbounded Model Checking for Alternating-Time Temporal Epistemic Logic

This paper deals with the problem of verification of game-like structures by means of symbolic model checking. Alternating-time Temporal Epistemic Logic (ATEL) is used for expressing properties of multi-agent systems represented by alternating epistemic temporal systems as well as concurrent epistemic game structures. Unbounded model checking (a SAT based technique) is applied for the first time to verification of ATEL. An example is given to show an application of the technique.