Contextualist theories of knowledge

Contextualist theories of knowledge offer a semantic hypothesis to explain the observed contextual variation in what people say they know, and the difficulty people have resolving skeptical paradoxes. Subject or speaker relative versions make the truth conditions of “S knows that p” depend on the standards of either the knower’s context (Hawthorne and Stanley) or those of the speaker’s context (Cohen and DeRose). Speaker contextualism avoids objections to subject contextualism, but is implausible in light of evidence that “know” does not behave like an indexical. I deepen and extend these criticisms in light of recent defenses by contextualists (including Ludlow). Another difficulty is that whether certain standards are salient or intended does not entail that they are the proper standards. A normative form of contextualism on which the truth of a knowledge claim depends on the proper standards for the context is more promising, but still unsatisfactory whether the view is speaker or subject relative. I defend alternative explanations for the observed linguistic and psychological data: a pragmatic account for some cases and a cognitive account for others.¹ I presented this paper at the 2004 Bled Conference on Contextualism, sponsored by Mirabor and Northern Illinois Universities.     

Why contextualists cannot know they are right: Self-refuting implications of contextualism

Conversational contextualism in epistemology is characterized by four main theses: 1. the indexicality of knowledge claims thesis; 2. the attributor contextualism thesis; 3. the conversational contextualism thesis, and 4. the main thesis of contextualism according to which a knowledge claim can be true in one context and false in another context in which more stringent standards for knowledge are operant. It is argued that these theses taken together generate problems for contextualism. In particular, it is shown that there is no context in which the contextualist can truthfully claim to know her theory is true. Since these results were obtained only with principles the contextualist cannot give up—like the principle of epistemic closure and the principle that knowledge implies truth—it seems that contextualism is in need of a thoroughgoing revision if it is to become a successful epistemic theory.     

A noncontextualist account of contextualist linguistic data

The paper takes as its starting point the observation that people can be led to retract knowledge claims when presented with previously ignored error possibilities, but offers a noncontextualist explanation of the data. Fallibilist epistemologies are committed to the existence of two kinds of Kp-falsifying contingencies: (i) Non-Ignorable contingencies [NI-contingencies] and (ii) Properly-Ignorable contingencies [PI-contingencies]. For S to know that p, S must be in an epistemic position to rule out all NI-contingencies, but she need not be able to rule out the PI-contingencies. What is required vis-à-vis PI-contingencies is that they all be false. In mentioning PI-contingencies, an interlocutor can lead S mistakenly to think that these contingencies are NI-contingencies, when in fact they are not. Since S cannot rule out these newly mentioned contingencies and since she mistakenly takes them to be NI-contingencies, it is quite natural that she retract her earlier knowledge claim. In short, mentioning NI-contingencies creates a distortion effect. It makes S think that the standards for knowledge are higher than they actually are, which in turn explains why she mistakenly thinks she lacks knowledge. Conclusion: The primary linguistic data offered in support of contextualism can be explained without resorting to contextualism.     

Contextualism on a pragmatic,not a skeptical,footing

Contextualism is supposed to explain why the following argument for skepticism seems plausible: (1) I don’t know that I am not a bodiless brain-in-a-vat (BIV); (2) If I know I have hands, then I know I am not a bodiless BIV; (3) Therefore, I do not know I have hands. Keith DeRose claims that (1) and (2) are “initially plausible.” I claim that (1) is initially plausible only because of an implicit argument that stands behind it; it is not intuitively plausible. The argument DeRose offers is based on the requirement of sensitivity, that is, on the idea that if you know something then you would not believe it if it were false. I criticize the sensitivity requirement thereby undercutting its support for (1) and the skeptical data that contextualism is meant to explain. While skepticism is not a plausible ground for contextualism, I argue that certain pragmatic considerations are. It’s plausible to think that to know something more evidence is required when more is at stake. The best way to handle skepticism is to criticize the arguments for it. We should not adopt contextualism as a means of accommodating skepticism even if there are other pragmatic reasons for being a contextualist about knowledge.     

Mathematics education: Procedures, rituals and man's search for meaning

An attempt is made to analyze mathematical behavior from more general psychological perspectives. The mathematical language is a special case of the human language, which is a form of expression. Many people use common language in a meaningless way. The same is true about the mathematical language. Rituals are other forms of expression. Many people identify rituals in many mathematical contexts (procedures, argumentation). Thus, quite often, they behave in a meaningless way as required by many rituals. On the other hand, the community of mathematics education struggles for meaningful learning. This can be regarded as a special case of man's search for meaning. The general claims will be illustrated by some examples from various mathematical contexts.     

Modal Fictionalism, Possible Worlds, and Artificiality

Accounts of modality in terms of fictional possible worlds face an objection based on the idea that when modal claims are analysed in terms of fictions, the connection between analysans and analysandum seems artificial. Strong modal fictionalism, the theory according to which modal claims are analysed in terms of a fiction, has been defended by, among others, Seahwa Kim, who has recently claimed that the philosophical objection that the connection between modality and fictions is artificial can be met. I propose a new way of spelling out the intuition of artificiality and show that strong modal fictionalism should be rejected.     

An epistemic model of an agent who does not reflect on reasoning processes

This paper introduces an epistemic model of a boundedly rational agent under the two assumptions that (i) the agent’s reasoning process is in accordance with the model but (ii) the agent does not reflect on these reasoning processes. For such a concept of bounded rationality a semantic interpretation by the possible world semantics of the Kripke (1963) type is no longer available because the definition of knowledge in these possible world semantics implies that the agent knows all valid statements of the model. The key to my alternative semantic approach is the extension of the method of truth tables, first introduced for the propositional logic by Wittgenstein (1922), to an epistemic logic so that I can determine the truth value of epistemic statements for all relevant truth conditions. In my syntactic approach I define an epistemic logic–consisting of the classical calculus of propositional logic plus two knowledge axioms–that does not include the inference rule of necessitation, which claims that an agent knows all theorems of the logic. As my main formal result I derive a determination theorem linking my semantic with my syntactic approach. The difference between my approach and existing knowledge models is illustrated in a game-theoretic application concerning the epistemic justification of iterative solution concepts.     

Particularist semantic normativity

We sketch the view we call contextual semantics. It asserts that truth is semantically correct affirmability under contextually variable semantic standards, that truth is frequently an indirect form of correspondence between thought/language and the world, and that many Quinean commitments are not genuine ontological commitments. We argue that contextualist semantics fits very naturally with the view that the pertinent semantic standards are particularist rather than being systematizable as exceptionless general principles.     

An epistemic model of an agent who does not reflect on reasoning processes

This paper introduces an epistemic model of a boundedly rational agent under the two assumptions that (i) the agent’s reasoning process is in accordance with the model but (ii) the agent does not reflect on these reasoning processes. For such a concept of bounded rationality a semantic interpretation by the possible world semantics of the Kripke (1963) type is no longer available because the definition of knowledge in these possible world semantics implies that the agent knows all valid statements of the model. The key to my alternative semantic approach is the extension of the method of truth tables, first introduced for the propositional logic by Wittgenstein (1922), to an epistemic logic so that I can determine the truth value of epistemic statements for all relevant truth conditions. In my syntactic approach I define an epistemic logic–consisting of the classical calculus of propositional logic plus two knowledge axioms–that does not include the inference rule of necessitation, which claims that an agent knows all theorems of the logic. As my main formal result I derive a determination theorem linking my semantic with my syntactic approach. The difference between my approach and existing knowledge models is illustrated in a game-theoretic application concerning the epistemic justification of iterative solution concepts.     

A Note on Belief Reports and Context Dependence

The aim of this paper is to pose a problem for theories that claim that belief reports are context dependent. Firstly, I argue that the claim (interpreted in the spirit of moderate contextualism) is committed to verbalism, a theory that derives the context sensitivity of belief reports from the context sensitivity of the psychological verbs used in such reports. Secondly, I argue that verbalism is not an attractive theoretical option because it is in conflict with the non-proto-rigidity of verbs like ‘believe’. Finally, I describe various consequences that the argument has for invariantism and moderate contextualism.     

A particularist epistemology: ‘Affectual intuitionism’

Jonathan Dancy has developed a very refined theory called ethical particularism. He has argued extensively for the metaphysical part of his position. However, the accompanying epistemology is not yet clear. In this paper I will sketch a particularist epistemology that is consistent with Dancy’s particularist metaphysics, although my approach differs in certain respects from epistemological claims Dancy has made. I will defend an epistemology that states: 1. that moral knowledge is based on intuitions and 2. that we need emotions in order to have moral knowledge. I will call this approach ‘affectual intuitionism’. Dancy rejects both claims, but I will argue that his arguments against these claims are not convincing.     

Memetic algorithms, domain knowledge, and financial investing

How might domain knowledge constrain a genetic algorithm and systematically impact the algorithm’s traversal of the search space? In particular, in this paper the hypothesis is advanced that a semantic tree of financial knowledge can be used to influence the results of a genetic algorithm for financial investing problems. An algorithm is described, called the “Memetic Algorithm for Domain Knowledge”, and is instantiated in a software system. In mutation experiments, this system chooses financial ratios to use as inputs to a neural logic network which classifies stocks as likely to increase or decrease in value. The mutation is guided by a semantic tree of financial ratios. In crossover experiments, this system solves a portfolio optimization problem in which components of an individual represent weights on stocks; knowledge in the form of a semantic tree of industries determines the order in which components are sorted in individuals. Both synthetic data and real-world data are used. The experimental results show that knowledge can be used to reach higher fitness individuals more quickly. More interestingly, the results show how conceptual distance in the human knowledge can correspond to distance between evolutionary individuals and their fitness. In other words, knowledge might be dynamically used to at times increase the step size in a search algorithm or at times to decrease the step size. These results shed light on the role of knowledge in evolutionary computation and are part of the larger body of work to delineate how domain knowledge might usefully constrain the genetic algorithm.     

Semantic contamination and mathematical proof: Can a non-proof prove?

The way words are used in natural language can influence how the same words are understood by students in formal educational contexts. Here we argue that this so-called semantic contamination effect plays a role in determining how students engage with mathematical proof, a fundamental aspect of learning mathematics. Analyses of responses to argument evaluation tasks suggest that students may hold two different and contradictory conceptions of proof: one related to conviction, and one to validity. We demonstrate that these two conceptions can be preferentially elicited by making apparently irrelevant linguistic changes to task instructions. After analyzing the occurrence of “proof” and “prove” in natural language, we report two experiments that suggest that the noun form privileges evaluations related to validity, and that the verb form privileges evaluations related to conviction. In short, we show that (what is judged to be) a non-proof can sometimes (be judged to) prove.     

Cynefin: uncertainty,small worlds and scenarios

Uncertainty, its modelling and analysis have been discussed across many literatures including statistics and operational research, knowledge management and philosophy: (i) adherents to Bayesian approaches have usually argued that uncertainty should either be modelled by probabilities or resolved by discussion that clarifies meaning; (ii) some have followed Knight in distinguishing between contexts of risk and of uncertainty: the former admitting modelling and analysis through probability; the latter not; (iii) there are also host of approaches in the literatures stemming from Zadeh’s concept of a fuzzy set; (iv) theories of sense-making in the philosophy and management literatures see knowledge and uncertainty as opposite extremes of human understanding and discuss the resolution of uncertainty accordingly. Here I provide a personal perspective, taking a Bayesian stance. However, I adopt a softer position than conventional and recognise the concerns in other approaches. In particular, I use the Cynefin framework of decision contexts to reflect on processes of modelling and analysis in statistical, risk and decision analysis. The approach builds on several recent strands of discussion that argue for a convergence of qualitative scenario planning ideas and more quantitative approaches to analysis. I discuss how these suggestions and discussions relate to some earlier thinking on the methodology of modelling and, in particular, the concept of a ‘small world’ articulated by Savage.     

Event risk, contingent claims and the temporal resolution of uncertainty

We study the pricing and hedging of contingent claims that are subject to Event Risk which we define as rare and unpredictable events whose occurrence may be correlated to, but cannot be hedged perfectly with standard marketed instruments. The super-replication costs of such event sensitive contingent claims (ESCC), in general, provide little guidance for the pricing of these claims. Instead, we study utility based prices under two scenarios of resolution of uncertainty for event risk: when the event is continuously monitored, or when it is revealed only at the payment date. In both cases, we transform the incomplete market optimal portfolio choice problem of an agent endowed with an ESCC into a complete market problem with a state and possibly path-dependent utility function. For negative exponential utility, we obtain an explicit representation of the utility based prices under both information resolution scenarios and this in turn leads us to a simple characterization of the early resolution premium. For constant relative risk aversion utility functions we propose a simple numerical scheme and study the impact of size of the position, wealth and expected return on these prices.     

Global approximation to arbitrary cost functions: A Bayesian approach with application to US banking

This paper proposes and estimates a globally flexible functional form for the cost function, which we call Neural Cost Function (NCF). The proposed specification imposes a priori and satisfies globally all the properties that economic theory dictates. The functional form can be estimated easily using Markov Chain Monte Carlo (MCMC) techniques or standard iterative SURE. We use a large panel of U.S. banks to illustrate our approach. The results are consistent with previous knowledge about the sector and in accordance with mathematical production theory.     

Critical systems thinking and practice

Critical systems thinking and the methodologies associated with it were developed precisely to allow analysis of complex societal problems and intervention to resolve such problems. Early approaches employing systems ideas, such as operational research, systems analysis and systems engineering, were suitable for tackling certain well-defined problems, but were found to have limitations when faced with complex problems involving people with a variety of viewpoints and frequently at odds with one another. Systems thinkers responded with approaches such as system dynamics and organisational cybernetics to tackle complexity; soft systems methodology (SSM) and interactive planning to handle subjectivity; and critical systems heuristics to help the disadvantaged in situations involving conflict. There was a corresponding enlargement of the range of problem contexts in which they felt competent to intervene. It has been critical systems thinking, however, which has supplied the bigger picture, has allowed systems thinking to mature as a discipline and has set out how the variety of methodologies now available can be used together in a coherent manner to promote successful intervention in complex societal problem situations. This paper outlines, at the request of the editor of this special issue, my involvement in developing critical systems thinking and practice, describes its origins, nature and use, and sets out a programme for future research in the area.     

Where do preferences come from?

Rational choice theory analyzes how an agent can rationally act, given his or her preferences, but says little about where those preferences come from. Preferences are usually assumed to be fixed and exogenously given. Building on related work on reasons and rational choice (Dietrich and List, Nous, forthcoming), we describe a framework for conceptualizing preference formation and preference change. In our model, an agent’s preferences are based on certain ‘motivationally salient’ properties of the alternatives over which the preferences are held. Preferences may change as new properties of the alternatives become salient or previously salient properties cease to be salient. Our approach captures endogenous preferences in various contexts and helps to illuminate the distinction between formal and substantive concepts of rationality, as well as the role of perception in rational choice.     

Elementary preservice teachers’ reasoning about statistical modeling in a civic statistics context

Elements of statistical modeling can be implemented already in primary school. A prerequisite for this approach is that teachers are well-educated in this domain. Content knowledge, pedagogical content knowledge and (pedagogical) content related technological knowledge are core components of teacher education. We designed a course for elementary preservice teachers with regard to developing statistical thinking including the mentioned knowledge facets. The course includes exploring data and modeling and simulating chance experiments with TinkerPlots. We use the ‘data factory metaphor’ in fictive contexts and in contexts stemming from civic statistics for supporting the idea of modeling. We interviewed four participants of the course to assess and analyze their reasoning. We analyze how they model a given civic statistics contextual problem using the TinkerPlots sampler and how they evaluate their model with regard to a civic statistics context (the situation of hospitals in Germany).     

A knowledge-based approach to scheduling in an F.M.S.

This paper reports the development of a computer-based system for production scheduling in a dedicated FMS. The system is based on the state-operator framework commonly used in artificial intelligence. Such a system consists of three components: (i) a knowledge base of states, which describes both the current task domain situation and the goal to be achieved; (ii) a set of operators that are used to manipulate the knowledge base; and (iii) a control strategy to decide which operators to apply next and to resolve conflicts. Some of the interesting features of the scheduling system include: (i) the ability to detect resource conflicts; (ii) the ability to determine alternate routes for a given part in the event of a resource conflict; and (iii) the ability to amend plans if an alternate route is found. These features allow the system to take advantage of the flexible routing for parts that an FMS allows. The system has been implemented using the XLISP programming language. Implementation considerations are discussed. A small but comprehensive example is presented. Further research directions are suggested.