This paper supersedes an ealier version, entitled "A Non-Standard Semantics for Inexact Knowledge with Introspection", which appeared in the Proceedings of "Rationality and Knowledge". The definition of token semantics, in particular, has been modified, both for the single- and the multi-agent case.

I develop a non-representationalist account of mathematical thought, on which the point of mathematical theorizing is to provide us with the conceptual capacity to structure and articulate information about the physical world in an epistemically useful way. On my view, accepting a mathematical theory is not a matter of having a belief about some subject matter; it is rather a matter of structuring logical space, in a sense to be made precise. This provides an elegant account of the cognitive utility (...) of mathematics. Further, it makes explicit how the brand of non-representationalism I develop is compatible with there being substantive rationality constraints on our mathematical theorizing. (shrink)

Williamson (2000a) has argued that posi- tive introspection is incompatible with in- exact knowledge. His argument relies on a margin-for-error requirement for inexact knowledge based on a intuitive safety prin- ciple for knowledge, but leads to the counter- intuitive conclusion that no possible creature could have both inexact knowledge and posi- tive introspection. Following Halpern (2004) I put forward an alternative margin-for-error requirement that preserves the safety require- ment while blocking Williamson’s argument. I argue that the infallibilist conception of knowledge (...) that underlies the new require- ment provides a better account of inexact knowledge and higher-order knowledge than both Williamson’s and Halpern’s. (shrink)

Many philosophers believe that there is a fundamental distinction between knowing that something is the case and knowing how to do something. According to Gilbert Ryle, to whom the insight is credited, knowledge-how is an ability, which is in turn a complex of dispositions. Knowledge-that, on the other hand, is not an ability, or anything similar. Rather, knowledge-that is a relation between a thinker and a true proposition.

How should one understand knowledge-wh ascriptions? That is, how should one understand claims such as ‘‘I know where the car is parked,’’ which feature an interrogative complement? The received view is that knowledge-wh reduces to knowledge that p, where p happens to be the answer to the question Q denoted by the wh-clause. I will argue that knowledge-wh includes the question—to know-wh is to know that p, as the answer to Q. I will then argue that knowledge-that includes a contextually (...) implicit question. I will conclude that knowledge is a question-relative state. Knowing is knowing the answer, and whether one knows the answer depends (in part) on the question. (shrink)

Metacognition is often defined as thinking about thinking. It is exemplified in all the activities through which one tries to predict and evaluate one’s own mental dispositions, states and properties for their cognitive adequacy. This article discusses the view that metacognition has metarepresentational structure. Properties such as causal contiguity, epistemic transparency and procedural reflexivity are present in metacognition but missing in metarepresentation, while open-ended recursivity and inferential promiscuity only occur in metarepresentation. It is concluded that, although metarepresentations can redescribe metacognitive (...) contents, metacognition and metarepresentation are functionally distinct. (shrink)

Dynamic Epistemic Logic This article tells the story of the rise of dynamic epistemic logic, which began with epistemic logic, the logic of knowledge, in the 1960s. Then, in the late 1980s, came dynamic epistemic logic, the logic of change of knowledge. Much of it was motivated by puzzles and paradoxes. The number … Continue reading Dynamic Epistemic Logic →.

A joint modelling of objective worlds and subjective perceptions within two-dimensional semantics eliminates the margin for error principle and solves the epistemic sorites paradox. Two objective knowledge modalities can be defined in two-dimensional frames accounting for subjective perceptions: “necessary knowledge” (NK) and “possible knowledge” (PK), the latter being better suited to the interpretation of knowledge utterances. Two-dimensional semantics can in some cases be reduced to one-dimensional ones, by defining accessibility relations between objective worlds that reflect subjective perceptions: NK and PK (...) are respectively equivalent to ${\square \square }$ and ${\lozenge \square }$ in some one-dimensional frame, and to ${\square }$ and another modality in some other. (shrink)

Role of the entrepreneur in a distinct role of profit.

Reasoning About Knowledge is the first book to provide a general discussion of approaches to reasoning about knowledge and its applications to distributed ...

Researchers have begun to explore animals' capacities for uncertainty monitoring and metacognition. This exploration could extend the study of animal self-awareness and establish the relationship of self-awareness to other-awareness. It could sharpen descriptions of metacognition in the human literature and suggest the earliest roots of metacognition in human development. We summarize research on uncertainty monitoring by humans, monkeys, and a dolphin within perceptual and metamemory tasks. We extend phylogenetically the search for metacognitive capacities by considering studies that have tested less (...) cognitively sophisticated species. By using the same uncertainty-monitoring paradigms across species, it should be possible to map the phylogenetic distribution of metacognition and illuminate the emergence of mind. We provide a unifying formal description of animals' performances and examine the optimality of their decisional strategies. Finally, we interpret animals' and humans' nearly identical performances psychologically. Low-level, stimulus-based accounts cannot explain the phenomena. The results suggest granting animals a higher-level decision-making process that involves criterion setting using controlled cognitive processes. This conclusion raises the difficult question of animal consciousness. The results show that animals have functional features of or parallels to human conscious cognition. Remaining questions are whether animals also have the phenomenal features that are the feeling/knowing states of human conscious cognition, and whether the present paradigms can be extended to demonstrate that they do. Thus, the comparative study of metacognition potentially grounds the systematic study of animal consciousness. Key Words: cognition; comparative cognition; consciousness; memory monitoring; metacognition; metamemory; self-awareness; uncertainty; uncertainty monitoring. (shrink)

In this paper we compare different models of vagueness viewed as a specific form of subjective uncertainty in situations of imperfect discrimination. Our focus is on the logic of the operator “clearly” and on the problem of higher-order vagueness. We first examine the consequences of the notion of intransitivity of indiscriminability for higher-order vagueness, and compare several accounts of vagueness as inexact or imprecise knowledge, namely Williamson’s margin for error semantics, Halpern’s two-dimensional semantics, and the system we call Centered semantics. (...) We then propose a semantics of degrees of clarity, inspired from the signal detection theory model, and outline a view of higher-order vagueness in which the notions of subjective clarity and unclarity are handled asymmetrically at higher orders, namely such that the clarity of clarity is compatible with the unclarity of unclarity. (shrink)

We discuss the 'problem of convergent knowledge', an argument presented by J. Schaffer in favour of contextualism about knowledge attributions, and against the idea that knowledge- wh can be simply reduced to knowledge of the proposition answering the question. Schaffer's argument centrally involves alternative questions of the form 'whether A or B'. We propose an analysis of these on which the problem of convergent knowledge does not arise. While alternative questions can contextually restrict the possibilities relevant for knowledge attributions, what (...) Schaffer's puzzle reveals is a pragmatic ambiguity in what 'knowing the answer' means: in his problematic cases, the subject knows only a partial answer to the question. This partial knowledge can be counted as adequate only on externalist grounds. (shrink)

The paper examines the logic and semantics of knowledge attributions of the form “s knows whether A or B”. We analyze these constructions in an epistemic logic with alternative questions, and propose an account of the context-sensitivity of the corresponding sentences and of their presuppositions.

A knowledge-how attributing sentence of the form ' S knows how to F ' may yield an 'ability-entailing' reading as well as an 'ability-neutral' reading. The present paper offers an epistemological account of the availability of both readings, based on two conceptual distinctions: first, a distinction between a 'practical' and a 'theoretical' kind of knowledge of how to do something; second, a distinction between an 'intrinsic' and an 'extrinsic' kind of ability to do something. The first part of the paper (...) presents the double distinction that constitutes the proposed account; the second part presents a number of theoretical, mainly epistemological motivations for accepting the account. (shrink)

In recent years, much work has been dedicated by logicians, computer scientists and economists to understanding awareness, as its importance for human behaviour becomes evident. Although several logics of awareness have been proposed, little attention has been explicitly dedicated to change in awareness. However, one of the most crucial aspects of awareness is the changes it undergoes, which have countless important consequences for knowledge and action. The aim of this paper is to propose a formal model of awareness change, and (...) to derive from it logics of awareness change. In the first part of the paper, the model of epistemic states of bounded agents proposed in Hill (Stud Log 89(1):81–109, 2008a ) is extended with operations modelling awareness change. In the second part of the paper, it is shown how this model naturally extends the “standard” logic of awareness to yield a logic of awareness change. (shrink)

Forthcoming in D.H. Pritchard & V. Hendricks, New Waves in Epistemology,.

This note argues that, under some circumstances, it is more rational not to behave in accordance with a Bayesian prior than to do so. The starting point is that in the absence of information, choosing a prior is arbitrary. If the prior is to have meaningful implications, it is more rational to admit that one does not have sufficient information to generate a prior than to pretend that one does. This suggests a view of rationality that requires a compromise between (...) internal coherence and justification, similarly to compromises that appear in moral dilemmas. Finally, it is argued that Savage's axioms are more compelling when applied to a naturally given state space than to an analytically constructed one; in the latter case, it may be more rational to violate the axioms than to be Bayesian. (shrink)