Bar-On on Self-Knowledge and Expression

I critically discuss the account of self-knowledge presented in Dorit Bar-On’s Speaking My Mind (OUP 2004), focusing on Bar-On’s understanding of what makes our capacity for self-knowledge puzzling and on her ‘neo-expressivist’ solution to the puzzle. I argue that there is an important aspect of the problem of self-knowledge that Bar-On’s account does not sufficiently address. A satisfying account of self-knowledge must explain not merely how we are able to make accurate avowals about our own present mental states, but how we can reasonably regard ourselves as entitled to claim self-knowledge. Addressing this aspect of the problem of self-knowledge requires confronting questions about the metaphysical nature of mental states, questions that Bar-On’s approach seeks to avoid.     

Challenges of maintaining cognitive demand during the limit lessons: understanding one mathematician’s class practices

In this study, we examined five limit lessons using Mathematical Tasks Framework to understand students’ opportunities to learn cognitively challenging tasks and maintain cognitive demand during limit lessons. Our analysis of Dr A’s five lessons shows that students rarely had opportunities to maintain or increase cognitive demand. There are two main factors that shaped her instructional practices, students and time. These two factors greatly influenced how she selects and implements limit tasks in her classes. To serve her students’ needs of knowing more rules, formulas and procedures, she selected and discussed those simple tasks a lot. Although Dr A thinks challenging tasks and asking demanding questions can be potentially good instructional practices, she thinks these instructional practices would not serve her students well. With these factors, we made possible recommendations to have more student-centred teaching.     

Das Kardinalzahlkonzept

This case-study investigates different aspects of the concept of cardinality of an eighteen-year-old student with mental retardation. At the age of six she could not relate number words, finger and objects in counting. These errors still persist in the classroom situation. This investigation shows that nevertheless her concept of cardinality is fairly highly developed. She knows that in counting she must match number words and objects one to one, the number word sequence she uses is stable, and her insight into the irrelevance of order of enumeration when counting, which she finds by trial, is a sign of the robustness of her cardinal concept. She also understands the relationships of equivalence and order of sets, and she solves arithmetical problems by counting on or down, which means that she understands the number words as cardinal and at the same time as sequence numbers. Errors occur in complex situations, where several components have to be considered. But her concept of cardinality is also incomplete: she has special difficulties concerning counting out objects bundled in tens. The same problems occur when she uses multidigit numbers: she does not see a ten-unit as composed of ten single unit items, that is to say, she replaces the hierarchic structure of the number sequence by a concatenated one. These difficulties must be interpreted as a consequence of her special weakness concerning synthetic thinking and simultaneous performing, as similar patterns can be seen in her spatial perception and in her speech. In the syntactic structure of her utterances, too, the combination of simple entities to complicated units is replaced by a mere concatenation. This means that due to brain dysfunction her behavior is determined by a particular pattern which repeatedly appears intrapersonally, and which is characteristic of some mentally retarded persons though not of all of them. Evidently mathematical thinking is also not a determined system, but a variable one. Mentally retarded students may therefore have great difficulties concerning some areas and at the same time make better progress in others. In particular, difficulties in counting objects are no obstacle to knowledge of cardinality.     

Assertibility and Sensitivity

Epistemologists have proposed various norms of assertion to explain when a speaker is in an epistemic position to assert a proposition. In this article I propose a distinct necessary condition on assertibility: that a speaker should assert only what she sensitively believes, where a subject's belief is sensitive just in case the subject would not hold it if it were false. I argue that the Sensitivity Rule underwrites simple explanations for three key features of assertibility that pose explanatory challenges to other prominent proposals: the fact that assertibility is open under known entailment, the general impropriety of assertions that a lottery ticket has lost made purely on the basis of the speaker's knowledge of the odds, and the fact that assertibility varies widely with features of the conversational context. I close by considering three distinct roles the Sensitivity Rule might play in the overall theory of assertibility.     

The Role of the Visual System in Emotion Perception

Looking at a person’s expression is a good way of telling what she feels—what emotions she has. Why is that? Is it because we see her emotion, or is it because we infer her mental state from her expression? My claim is that there is a sense in which we do see the person’s emotion. I first argue that expressions are physical events that carry information about the emotions that produce them. I then examine evidence suggesting that specific brain areas and structures are involved in the process that extracts such information and makes it available in the content of visual experience. I consider only what happens in early stages of visual processing and make no claim about the role of simulation and empathy.     

The Aim of Justification and Epistemic Difference-Making Principles

The idea that truth is the aim of justification is one that is often defended by theorists who uphold different views about the nature of epistemic justification. Despite its prevalence, however, it is not quite clear how one is to cash out the metaphor that justification aims at truth. Some theorists, for example, have objected that the thesis would leave no room for justified false beliefs and unjustified true beliefs. In this paper, I offer an account of what it is for justification to aim at truth using the recently revived idea of difference-making according to which facts often make a difference to other facts. It will be argued that, thus understood, the thesis can illuminate a number of controversial debates in epistemology and that, given its explanatory power, it has a lot to recommend it.     

Risk assessment for infectious disease and its impact on voluntary vaccination behavior in social networks

Achievement of the herd immunity is essential for preventing the periodic spreading of an infectious disease such as the flu. If vaccination is voluntary, as vaccination coverage approaches the critical level required for herd immunity, there is less incentive for individuals to be vaccinated; this results in an increase in the number of so-called “free-riders” who craftily avoid infection via the herd immunity and avoid paying any cost. We use a framework originating in evolutionary game theory to investigate this type of social dilemma with respect to epidemiology and the decision of whether to be vaccinated. For each individual in a population, the decision on vaccination is associated with how one assesses the risk of infection. In this study, we propose a new risk-assessment model in a vaccination game when an individual updates her strategy, she compares her own payoff to a net payoff obtained by averaging a collective payoff over individuals who adopt the same strategy as that of a randomly selected neighbor. In previous studies of vaccination games, when an individual updates her strategy, she typically compares her payoff to the payoff of a randomly selected neighbor, indicating that the risk for changing her strategy is largely based on the behavior of one other individual, i.e., this is an individual-based risk assessment. However, in our proposed model, risk assessment by any individual is based on the collective success of a strategy and not on the behavior of any one other individual. For strategy adaptation, each individual always takes a survey of the degree of success of a certain strategy that one of her neighbors has adopted, i.e., this is a strategy-based risk assessment. Using computer simulations, we determine how these two different risk-assessment methods affect the spread of an infectious disease over a social network. The proposed model is found to benefit the population, depending on the structure of the social network and cost of vaccination. Our results suggest that individuals (or governments) should understand the structure of their social networks at the regional level, and accordingly, they should adopt an appropriate risk-assessment methodology as per the demands of the situation.     

Baker on the Psychological Account of Personal Identity

Lynne Rudder Baker’s Constitution View of human persons has come under much recent scrutiny. Baker argues that each human person is constituted by, but not identical to, a human animal. Much of the critical discussion of Baker’s Constitution View has focused upon this aspect of her account. Less has been said about the positive diachronic account of personal identity offered by Baker. Baker argues that it is sameness of what she labels ‘first-person perspective’ that is essential to understanding personal identity over time. Baker claims that her account avoids the commitment to indeterminacy of personal identity entailed by the psychological account. Further, the psychological account, but not her account, is plagued by what Baker labels the ‘duplication problem’. In the end, I argue that neither of these considerations forces us to renounce the psychological account and adopt Baker’s favored account.

A climbing girl's reflections about angles

The main research question in this paper is whether a climbing discourse can be a resource for a school-geometry discourse. The text is based on a 12-year old girl's story from an exciting climbing trip during her summer holiday. The girl uncovers some of her knowledge that had been invisible to her; she is guided to see some relations between her climbing and her understanding of angles. In the beginning, this girl believes her story does not concern angles at all. The tools for uncovering angles in her story are based on different levels of visibility and objects of the climbing discourse combined with different conceptions of space. The girl develops her consciousness about angles as natural elements in her climbing activity and she is guided to see the angle as an object of her climbing discourse.     

Optimal commutable annuities to minimize the probability of lifetime ruin

We find the minimum probability of lifetime ruin of an investor who can invest in a market with a risky and a riskless asset and who can purchase a commutable life annuity. The surrender charge of a life annuity is a proportion of its value. Ruin occurs when the total of the value of the risky and riskless assets and the surrender value of the life annuity reaches zero. We find the optimal investment strategy and optimal annuity purchase and surrender strategies in two situations: (i) the value of the risky and riskless assets is allowed to be negative, with the imputed surrender value of the life annuity keeping the total positive; (ii) the value of the risky and riskless assets is required to be non-negative. In the first case, although the individual has the flexibility to buy or sell at any time, we find that the individual will not buy a life annuity unless she can cover all her consumption via the annuity and she will never sell her annuity. In the second case, the individual surrenders just enough annuity income to keep her total assets positive. However, in this second case, the individual’s annuity purchasing strategy depends on the size of the proportional surrender charge. When the charge is large enough, the individual will not buy a life annuity unless she can cover all her consumption, the so-called safe level. When the charge is small enough, the individual will buy a life annuity at a wealth lower than this safe level.     

The Social Virtues: Two Accounts

Social (epistemic) virtues are the virtues bound up with those forms of inquiry involved in social routes to knowledge. A thoroughly individualistic account of the social virtues endorses two claims: (1) we can fully characterize the nature of the social virtues independent of the social factors that are typically in play when these virtues are exemplified, and (2) even when a subject’s route to knowledge is social, the only epistemic virtues that are relevant to her acquisition of knowledge are those she herself possesses. A social (or anti-individualistic) account of the social virtues, by contrast, denies one or both of these claims. I will offer some reasons for thinking that the individualistic account is not acceptable, and that one or the other social account provides a better understanding of the social virtues. The argument is not decisive, but it does suggest that the social dimension of social epistemic virtues is not fully characterizable in individualistic terms.     

Natural implementation with semi-responsible agents in pure exchange economies

We study Nash implementation by natural price–quantity mechanisms in pure exchange economies when agents have intrinsic preferences for responsibility. An agent has an intrinsic preference for responsibility if she cares about truth-telling that is in line with the goal of the mechanism designer besides her material well-being. A semi-responsible agent is an agent who, given what her opponents do, acts in an irresponsible manner when a responsible behavior poses obstacles to her material well-being. The class of efficient allocation rules that are Nash implementable is identified provided that there is at least one agent who is semi-responsible. The Walrasian rule is shown to belong to that class.     

Mary Wynne Warner (1932-1998)

Mary Warner, as she was mainly known in the mathematical world,died in April 1998. At a time when few women mathematiciansreached the top in their profession, she succeeded in doingso through her ability and determination. Her research contributionswere commemorated at a recent international conference on fuzzytopology, the field in which she was one of the pioneers andrecognized as one of the leading figures for the past thirtyyears. She was also an outstanding teacher. But to understandher achievements properly it is necessary to know somethingof her life.     

A Preservice Secondary Teacher's Moves to Protect Her View of Herself as a Mathematics Expert

This paper discusses the experience of a preservice secondary mathematics teacher during lesson study. Although the preservice teacher was a strong undergraduate mathematics student, she used compensation “moves” to deflect attention away from her insecurities about her conceptual understanding of secondary mathematics. She feared being labeled as “dumb” and redirected conversations in order to protect her identity as a knower of mathematics. This paper investigates the culture in which preservice teachers develop confidence in their personal mathematics knowledge and how that confidence may influence behavior.     

Demand for longevity securities under relative performance concerns: Stochastic differential games with cointegration

This paper investigates the impact of relative performance concerns on the longevity risk transfer market. When an insurer concerns about the relative performance in a two-insurer economy, she maximizes the expected utility of her terminal wealth benchmarked against her competitor’s. The problem formulation for a general utility, a general interest rate process and cointegrated mortality rates uses a nonzero sum stochastic differential game approach. Explicit solution of the Nash equilibrium is derived for constant relative risk adverse insurers under the Vasicek-type stochastic interest and mortality rates. Existence and uniqueness of the Nash equilibrium are established for the CIR-type models, which rule out negative interest and mortality rates. While previous studies based on the single-agent approaches have shown a high investment demand in longevity bonds, the launch of it was unsuccessful in reality. Ours supplements that the demand is much lower subject to the relative performance concerns.     

Robustness Revised: Frankfurt Cases and the Right Kind of Power to Do Otherwise

Frankfurt’s famous counterexample strategy challenges the traditional association between moral responsibility and alternative possibilities. While this strategy remains controversial, it is now widely agreed that an adequate response to it must preserve an agent’s ability to do otherwise, and not the mere possibility, for only then is her alternative possibility sufficiently robust to ground her responsibility. Here, I defend a more stringent requirement for robustness. To have a robust alternative, I argue, the agent must have the right kind of ability, where the right kind is such that it is up to her whether she does otherwise. I argue that this kind of power attribution is epistemically conditioned. While a few writers have defended an epistemic condition for robustness, seeing this condition as a consequence of the relevant power attributions will provide much-needed support and clarification, while also illuminating the kind of ability in which free will consists.     

Transcendental Kantianism,Naturalized Kantianism,and the Bounds of Psychology

Are there sensory states (“perceptions”) that, unlike mere sensory registrations, require an explanatory framework (“psychology”) that goes beyond biology? Based on a reconstruction of Kant’s a priori, transcendental psychology, contemporary Kantians answer this question in the positive but dramatically limit the scope of psychology. In contrast, naturalistically oriented deflationists answer it in the negative, thereby not giving psychology any explanatory role whatsoever. In his recent monumental book Origins of Objectivity, Burge argues against both of these approaches and seeks to develop an intermediate approach between them. This he does by embedding Kantian transcendental psychology in contemporary science of perception, thereby naturalizing the former and considerably broadening the scope of psychology. In this paper I critically examine Burge’s naturalized Kantianism, thereby defending transcendental Kantianism. To this end, I first outline Kantian transcendental psychology of perception, highlighting the features that distinguish it from biology. I then show how Burge naturalizes this psychology by embedding its most fundamental notions in contemporary science of perception. Based on all this, I conclude the paper by arguing for two closely related claims. First, that transformed into empirical psychology, Kantian transcendental psychology loses the features that distinguish it from biology. Second, that genuine perception starts at the high cognitive level for which transcendental psychology accounts and not at the rather low or elementary level on which Burge focuses.     

The powers and pitfalls of algorithmic knowledge: a case study

This study examines one child's use of computational procedures over a period of 3 years in an urban elementary school where teachers were using a standards-based curriculum. From a sociocultural perspective, the use of standard algorithms to solve mathematical problems is viewed as a cultural tool that both enables and constrains particular practices. As this student appropriated and mastered procedures for addition, subtraction, multiplication and division, she could solve problems that involved fairly straightforward computations or where she could easily model the action to determine an appropriate computation. At the same time, her use of these algorithms, along with other readily available tools, such as her fingers or multiplication tables, constrained her ability to reflect on the tens-structure of the number system, an effect that had serious consequences for her overall mathematical achievement. The results of this study suggest that even when not directly introduced, algorithms have such strong currency that they can mediate more reform-oriented instruction.