Inexact Knowledge with Introspection

Standard Kripke models are inadequate to model situations of inexact knowledge with introspection, since positive and negative introspection force the relation of epistemic indiscernibility to be transitive and euclidean. Correlatively, Williamson’s margin for error semantics for inexact knowledge invalidates axioms 4 and 5. We present a new semantics for modal logic which is shown to be complete for K45, without constraining the accessibility relation to be transitive or euclidean. The semantics corresponds to a system of modular knowledge, in which iterated modalities and simple modalities are not on a par. We show how the semantics helps to solve Williamson’s luminosity paradox, and argue that it corresponds to an integrated model of perceptual and introspective knowledge that is psychologically more plausible than the one defended by Williamson. We formulate a generalized version of the semantics, called token semantics, in which modalities are iteration-sensitive up to degree n and insensitive beyond n. The multi-agent version of the semantics yields a resource-sensitive logic with implications for the representation of common knowledge in situations of bounded rationality.     

Cut-free common knowledge

Starting off from the infinitary system for common knowledge over multi-modal epistemic logic presented in [L. Alberucci, G. Jäger, About cut elimination for logics of common knowledge, Annals of Pure and Applied Logic 133 (2005) 73–99], we apply the finite model property to “finitize” this deductive system. The result is a cut-free, sound and complete sequent calculus for common knowledge.     

Williamson on justification

Timothy Williamson has a marvelously precise account of epistemic justification in terms of knowledge and probability. I argue that the account runs aground on certain cases involving the probability values 0 and 1.     

Valuing Knowledge: A Deontological Approach

The fact that we ought to prefer what is comparatively more likely to be good, I argue, does, contrary to consequentialism, not rest on any evaluative facts. It is, in this sense, a deontological requirement. As such it is the basis of our valuing those things which are in accordance with it. We value acting (and believing) well, i.e. we value acting (and believing) as we ought to act (and to believe). In this way, despite the fact that our interest in justification depends on our interest in truth, we value believing with justification on non-instrumental grounds. A deontological understanding of justification, thus, solves the Value of Knowledge Problem.

Epistemic luck and the generality problem

Epistemic luck has been the focus of much discussion recently. Perhaps the most general knowledge-precluding type is veritic luck, where a belief is true but might easily have been false. Veritic luck has two sources, and so eliminating it requires two distinct conditions for a theory of knowledge. I argue that, when one sets out those conditions properly, a solution to the generality problem for reliabilism emerges.

Common knowledge of payoff uncertainty in games

Using epistemic logic, we provide a non-probabilistic way to formalise payoff uncertainty, that is, statements such as ‘player i has approximate knowledge about the utility functions of player j.’ We show that on the basis of this formalisation common knowledge of payoff uncertainty and rationality (in the sense of excluding weakly dominated strategies, due to Dekel and Fudenberg (1990)) characterises a new solution concept we have called ‘mixed iterated strict weak dominance.’     

First Order Common Knowledge Logics

In this paper we investigate first order common knowledge logics; i.e., modal epistemic logics based on first order logic with common knowledge operators. It is shown that even rather weak fragments of first order common knowledge logics are not recursively axiomatizable. This applies, for example, to fragments which allow to reason about names only; that is to say, fragments the first order part of which is based on constant symbols and the equality symbol only. Then formal properties of "quantifying into" epistemic contexts are investigated. The results are illustrated by means of epistemic representations of Nash Equilibria for finite games with mixed strategies.     

Propositional knowledge and know-how

This paper is roughly in two parts. The first deals with whether know-how is constituted by propositional knowledge, as discussed primarily by Gilbert Ryle (1949) The concept of mind. London: Hutchinson, Jason Stanley and Timothy Williamson (2001). Knowing how. Journal of Philosophy, 98, pp. 411–444 as well as Stephen Hetherington (2006). How to know that knowledge-that is knowledge-how. In S. Hetherington (Ed.) Epistemology futures. Oxford: Oxford University Press. The conclusion of this first part is that know-how sometimes does and sometimes does not consist in propositional knowledge. The second part defends an analysis of know-how inspired by Katherine Hawley’ (2003). Success and knowledge-how. American Philosophical Quarterly, 40, pp. 19–31, insightful proposal that know-how requires counterfactual success. I conclude by showing how this analysis helps to explain why know-how sometimes does and sometimes does not consist of propositional knowledge.     

Three decades of lay epistemics: The why,how, and who of knowledge formation

A conceptual integration and review are presented of three separate research programmes informed by the theory of lay epistemics (Kruglanski, 1989 Kruglanski, A. W. 1989. Lay epistemics and human knowledge: Cognitive and motivational bases, New York: Plenum. [Crossref] , [Google Scholar]). They respectively address the “why”, “how”, and “who” questions about human knowledge formation. The “why” question is treated in work on the need for cognitive closure that propels epistemic behaviour and affects individual, interpersonal, and group phenomena. The “how” question is addressed in work on the unimodel (Kruglanski, Pierro, Mannetti, Erb, & Chun, 2007 Kruglanski, A. W., Pierro, A., Mannetti, L., Erb, H. P. and Chun, W. Y. 2007. “On the parameters of social judgement”. In Advances in experimental social psychology, Edited by: Zanna, M. P. Vol. 39, 255–296. New York: Academic Press.  [Google Scholar]) depicting the process of drawing conclusions from the “information given”. The “who” question is addressed in work on “epistemic authority” highlighting the centrality of source effects (including oneself as a source) in human epistemic behaviour. These separate research paradigms explore facets of epistemic behaviour that jointly produce human knowledge, of essential significance to people's’ individual and social functioning.     

Empirical indistinguishability: From the knowledge structure to the skills

Recent literature has pointed out that the basic local independence model (BLIM) when applied to some specific instances of knowledge structures presents identifiability issues. Furthermore, it has been shown that for such instances the model presents a stronger form of unidentifiability named empirical indistinguishability, which leads to the fact that the existence of certain knowledge states in such structures cannot be empirically tested. In this article the notion of indistinguishability is extended to skill maps and, more generally, to the competence-based knowledge space theory. Theoretical results are provided showing that skill maps can be empirically indistinguishable from one another. The most relevant consequence of this is that for some skills there is no empirical evidence to establish their existence. This result is strictly related to the type of probabilistic model investigated, which is essentially the BLIM. Alternative models may exist or can be developed in knowledge space theory for which this indistinguishability problem disappears.     

A metaphysics for practical knowledge

Is Anscombean practical knowledge independent of what the agent actually does on an occasion? Failure to understand Anscombe’s answer to this question is a major obstacle to appreciating the subtlety and plausibility of her view. I argue that Anscombe’s answer is negative, and turns on the nature of mistakes in performance, and reveals a distinctive implicit metaphysics of mind and knowledge, structured by related capacities and exercises of capacities. If my interpretation is correct, then practical knowledge shares features with knowledge-how and knowledge-that, but deserves its own epistemic category.     

On the empirical indistinguishability of knowledge structures

In recent years a number of articles have focused on the identifiability of the basic local independence model. The identifiability issue usually concerns two model parameter sets predicting an identical probability distribution on the response patterns. Both parameter sets are applied to the same knowledge structure. However, nothing is known about cases where different knowledge structures predict the same probability distribution. This situation is referred to as ʻempirical indistinguishabilityʼ between two structures and is the main subject of the present paper. Empirical indistinguishability is a stronger form of unidentifiability, which involves not only the parameters, but also the structural and combinatorial properties of the model. In particular, as far as knowledge structures are concerned, a consequence of empirical indistinguishability is that the existence of certain knowledge states cannot be empirically established. Most importantly, it is shown that model identifiability cannot guarantee that a certain knowledge structure is empirically distinguishable from others. The theoretical findings are exemplified in a number of different empirical scenarios.     

Being perceived as a knowledge sender or knowledge receiver: A multistudy investigation of the effect of age on knowledge transfer

As a result of demographic changes, workforces are becoming older and more age diverse. While interactions between workers from different age groups can provide opportunities for mutual learning through bidirectional knowledge transfer, research has yet to investigate how age influences knowledge transfer between age‐diverse colleagues. Building on the organizational theory of age effects, we conducted two studies to examine how age influenced the roles assigned to individuals in knowledge transfer processes, that is, whether they were perceived as knowledge senders or knowledge recipients. In Study 1, we used an experimental vignette design with 450 employees to assess how age affected perceived ability and motivation to share and receive knowledge. Further, we tested the extent to which trustworthiness moderated these relationships. In Study 2, we extended these findings using a dyadic research design with data from 53 age‐diverse knowledge transfer dyads. We examined through which mechanisms the age of one's colleague affected one's knowledge transfer behaviour. We found that the age of one's colleague had a positive effect on one's knowledge receiving behaviour and a negative effect on one's knowledge sharing behaviour. Further, perceived ability to receive knowledge and perceived motivation to share knowledge mediated these effects.     

Older (but not younger) preschoolers understand that knowledge differs between people and across time

We examined 3‐ to 5‐year‐olds' understanding of general knowledge (e.g., knowing that clocks tell time) by investigating whether (1) they recognize that their own general knowledge has changed over time (i.e., they knew less as babies than they know now), and (2) such intraindividual knowledge differences are easier/harder to understand than interindividual differences (i.e., Do preschoolers understand that a baby knows less than they do?). Forty‐eight 3‐ to 5‐year‐olds answered questions about their current general knowledge (‘self‐now’), the general knowledge of a 6‐month‐old (‘baby‐now’), and their own general knowledge at 6 months (‘self‐past’). All age groups were significantly above chance on the self‐now questions, but only 5‐year‐olds were significantly above chance on the self‐past and baby‐now questions. Moreover, children's performance on the baby‐now and self‐past questions did not differ. Our findings suggest that younger preschoolers do not fully appreciate that their past knowledge differs from their current knowledge, and that others may have less knowledge than they do. We situate these findings within the research on knowledge understanding, more specifically, and cognitive development, more broadly.     

Approximately counting and sampling knowledge states

Approximately counting and sampling knowledge states from a knowledge space is a problem that is of interest for both applied and theoretical reasons. However, many knowledge spaces used in practice are far too large for standard statistical counting and estimation techniques to be useful. Thus, in this work we use an alternative technique for counting and sampling knowledge states from a knowledge space. This technique is based on a procedure variously known as subset simulation, the Holmes–Diaconis–Ross method, or multilevel splitting. We make extensive use of Markov chain Monte Carlo methods and, in particular, Gibbs sampling, and we analyse and test the accuracy of our results in numerical experiments.     

Effects of domain-specific knowledge on memory for serial order

Knowledge concerning domain-specific regularities in sequential structure has long been known to affect recall for serial order. However, very little work has been done toward specifying the exact role such knowledge plays. The present article proposes a theory of serial recall in structured domains, based on Bayesian decision theory and a set of representational assumptions proceeding from recent computational and neurophysiologic research. The theory suggests that the accuracy with which a target sequence will be recalled is influenced by two interacting factors: (1) the 'goodness' of the sequence, i.e. its fit with the sequencing constraints that characterize its source domain, and (2) the sequence's neighborhood relations, i.e. the degree to which it resembles other sequences in the source domain. A specific prediction of the theory is that recall will be relatively poor for target lists with high-goodness near neighbors (the good neighbor effect). This prediction was tested and confirmed in an experiment evaluating recall for sequences based on an artificial grammar.     

Environmental knowledge and conservation behavior: exploring prevalence and structure in a representative sample

Knowledge is commonly seen as a necessary precondition for a person’s behavior. Consistent with this, most educational interventions rely on knowledge transfer. However, for the most efficient informational strategies for education, it is essential that we identify the types of knowledge that promote behavior effectively and investigate their structure. A questionnaire consisting of three environmental knowledge scales and a conservation behavior measure was sent to 5000 randomly selected Swiss adults. A completed questionnaire was returned by 55% of them (N=2736). A series of structural equation analyses indicates that the three knowledge forms exert different influences on conservation behavior: Action-related knowledge and effectiveness knowledge have a direct effect on performance. In contrast, system knowledge is more remote from behavior, exerting only a mediated influence on it by way of affecting the other two knowledge types.