A Critique of Armstrong’s Truthmaking Account of Possibility

In this paper I argue against Armstrong’s recent truthmaking account of possibility. I show that the truthmaking account presupposes modality in a number of different ways, and consequently that it is incapable of underwriting a genuine reduction of modality. I also argue that Armstrong’s account faces serious difficulties irrespective of the question of reduction; in particular, I argue that his Entailment and Possibility Principles are both false.

Computational Construction as a Means to Coordinate Representations of Infinity

In this paper, we describe a design experiment aimed at helping students to explore and develop concepts of infinite processes and objects. Our approach is based on the design and development of a computational microworld, which afforded students the means to construct a range of representational models (symbolic, visual and numeric) of infinity-related objects (infinite sequences, in particular). We present episodes based on four students’ activities, seeking to illustrate how the available tools mediated students’ understandings of the infinite in rich ways, allowing them to discriminate subtle process-oriented features of infinite processes. We claim that the microworld supported students in the coordination of hitherto unconnected or conflicting intuitions concerning infinity, based on a constructive articulation of different representational forms we name as ‘representational moderation’.

True Antecedents

In this note I discuss what seems to be a new kind of counterexample to Lewis’s account of counterfactuals. A coin is to be tossed twice. I bet on ‘Two heads’, and I win. Common sense says that (1) is false. But Lewis’s theory says that it is true. (1) If at least one head had come up, I would have won.

Learning axes and bridging tools in a technology-based design for statistics

We introduce a design-based research framework, learning axes and bridging tools, and demonstrate its application in the preparation and study of an implementation of a middle-school experimental computer-based unit on probability and statistics, ProbLab (Probability Laboratory, Abrahamson and Wilensky 2002 [Abrahamson, D., & Wilensky, U. (2002). ProbLab. Northwestern University, Evanston, IL: The Center for Connected Learning and Computer-Based Modeling, Northwestern University. ]). ProbLab is a mixed-media unit, which utilizes traditional tools as well as the NetLogo agent-based modeling-and-simulation environment (Wilensky 1999) [Wilensky, U. (1999). NetLogo. Northwestern University, Evanston, IL: The Center for Connected Learning and Computer-Based Modeling ] and HubNet, its technological extension for facilitating participatory simulation activities in networked classrooms (Wilensky and Stroup 1999a) [Wilensky, U., & Stroup, W. (1999a). HubNet. Evanston, IL: The Center for Connected Learning and Computer-Based Modeling, Northwestern University]. We will focus on the statistics module of the unit, Statistics As Multi-Participant Learning-Environment Resource (S.A.M.P.L.E.R.). The framework shapes the design rationale toward creating and developing learning tools, activities, and facilitation guidelines. The framework then constitutes a data-analysis lens on implementation cases of student insight into the mathematical content. Working with this methodology, a designer begins by focusing on mathematical representations associated with a target concept—the designer problematizes and deconstructs each representation into a pair of historical/cognitive antecedents (idea elements), each lying at the poles of a learning axis. Next, the designer creates bridging tools, ambiguous artifacts bearing interaction properties of each of the idea elements, and develops activities with these learning tools that evoke cognitive conflict along the axis. Students reconcile the conflict by means of articulating strategies that embrace both idea elements, thus integrating them into the target concept. The research reported on this paper was funded by NSF ROLE Grant No. REC-0126227. The opinions expressed here are those of the authors and do not necessarily reflect those of NSF. This paper is based on the authors’ AERA 2004 paper titled S.A.M.P.L.E.R.: Statistics As Multi-Participant Learning-Environment Resource.

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Online Resources in Mathematics, Teachers’ Geneses and Didactical Techniques

The study we present here concerns the consequences of integrating online resources into the teaching of mathematics. We focus on the interaction between teachers and specific online resources they draw on: e-exercise bases. We propose a theoretical approach to study the associated phenomena, combining instrumental and anthropological perspectives. For given didactical tasks, we observe teachers’ instrumental geneses, and the didactical techniques they develop. We exemplify our approach with the analysis of a case study of trigonometry in grade 9.

Using half-baked microworlds to challenge teacher educators’ knowing

This article illustrates how four teacher educators in training were challenged with respect to their epistemology and perceptions of teaching and learning mathematics through their interactions with expressive digital media during a professional development course. The research focused on their experience of communally constructing artifacts and their reflections on the nature of mathematics and mathematics teaching and learning with digital media. I discussed three different ways in which this media was used by the teachers; first, as a means to engage in technical-applied mathematics to engineer mathematical models; second, as a means to construct models for students to engage in experimental-constructivist activity; thirdly, as a means to engage in a discussion of a challenging mathematical problem.

Conversational Implicatures and Cancellability

In this paper I argue against a criticism by Matthew Weiner to Grice’s thesis that cancellability is a necessary condition for conversational implicature. I argue that the purported counterexamples fail because the supposed failed cancellation in the cases Weiner presents is not meant as a cancellation but as a reinforcement of the implicature. I moreover point out that there are special situations in which the supposed cancellation may really work as a cancellation.

Margins for Error and Sensitivity: What Nozick Might Have Said

Timothy Williamson has provided damaging counterexamples to Robert Nozick’s sensitivity principle. The examples are based on Williamson’s anti-luminosity arguments, and they show how knowledge requires a margin for error that appears to be incompatible with sensitivity. I explain how Nozick can rescue sensitivity from Williamson’s counterexamples by appeal to a specific conception of the methods by which an agent forms a belief. I also defend the proposed conception of methods against Williamson’s criticisms.

Conceptualism and the Problem of Illusory Experience

According to the conceptualist view in the philosophy of perception, we possess concepts for all the objects, properties, and relations which feature in our experiences. Richard Heck has recently argued that the phenomenon of illusory experience provides us with conclusive reasons to reject this view. In this paper, I examine Heck’s argument, I explain why I think that Bill Brewer’s conceptualist response to it is ineffective, and I then outline an alternative conceptualist response which I myself endorse. My argument turns on the fact that both Heck, in constructing his objection to conceptualism, and Brewer, in responding to it, miss a crucial distinction between perceptual demonstrative concepts of objects, on the one hand, and perceptual demonstrative concepts of properties, on the other.

Transglobal Evidentialism-Reliabilism

We propose an approach to epistemic justification that incorporates elements of both reliabilism and evidentialism, while also transforming these elements in significant ways. After briefly describing and motivating the non-standard version of reliabilism that Henderson and Horgan call “transglobal” reliabilism, we harness some of Henderson and Horgan’s conceptual machinery to provide a non-reliabilist account of propositional justification (i.e., evidential support). We then invoke this account, together with the notion of a transglobally reliable belief-forming process, to give an account of doxastic justification.

Measuring in dynamic geometry environments as a tool for conjecturing and proving

This paper sits within the research on the affordances of new technologies in the mathematics classroom and focuses on a specific feature that is available in dynamic geometry environments, i.e. measuring tools, within the context of conjecturing and proving in open geometry problems. We develop a classification of different modalities of measuring, based on our previous work on dragging. The modalities are illustrated through the analysis of 15–16 year-old students’ proving processes, which focuses on how these modalities relate to the moves between the spatio-graphical field and the theoretical field and may either support or hinder the proving process. The classification of the modalities of measuring enables researchers to access students’ cognitive processes and teachers to be aware of the different possible uses and interpretation of measuring, giving them tools to support students when difficulties arise.

Sperm, Eggs and Hunks: Biological Origins and Identity

In several publications Graeme Forbes has developed and defended one of the strongest arguments for essentialism about biological origins. I attempt to show that there are deep, as yet unrecognized, problems with this argument. The problems with Forbes’s argument suggest that a range of other arguments for various forms of origin essentialism are also likely to be flawed, and that we should abandon the seemingly plausible general metaphysical thesis that concrete entities that share all intrinsic properties are identical.

Understanding Equivalence of Symbolic Expressions in a Spreadsheet-Based Environment

Use of spreadsheets in a beginning algebra course was investigated mainly with regard to their potential to promote generalization of patterns. Less is known about their use in promoting understanding and learning of transformational activities. The overall purpose of this paper is to consider the conceptual aspects of learning a transformational skill (use of the distributive law to produce equivalent algebraic expressions) in a learning sequence composed of both spreadsheets and paper-and-pencil activities. We conducted a sequence of classroom activities in several classes, and analyzed the students’ work on a spreadsheet activity and on an assessment activity by both qualitative and quantitative methods. The findings indicate both encouraging benefits and some potential sources of difficulties caused by the use of spreadsheets at initial stages of learning symbolic transformations.

Shape up or ship out: social networks,turnover, and organizational culture

This paper considers a formal model of cultural transmission in organizations, examining the interplay of structured social influence and organizational demography. A set of focused and fine-grained computational experiments elucidates this model’s assumptions, facilitates deeper explanations for some of its behavior, and explores the robustness and scope conditions of previously published conclusions. In doing so, this investigation highlights several important issues in the design and evaluation of computational experiments.

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.

Models as lab equipment: science from computational experiments

Computer models are artifacts that facilitate conducting computational experiments. In that sense they are laboratory equipment. The utility of a piece of laboratory equipment comes from the range of useful experiments it supports. However, general purpose models are in general much more costly to create and maintain. Consequently, issues regarding the design of computer models are best understood as pragmatic questions regarding the costs and utility of alternative designs.

Qualia and the Argument from Illusion: A Defence of Figment

This paper resurrects two discredited ideas in the philosophy of mind. The first: the idea that perceptual illusion might have something metaphysically significant to tell us about the nature of phenomenal consciousness. The second: that the colours and other qualities that ‘fill’ our sensory fields are occurrent properties (rather than representations of properties) that are, nevertheless, to be distinguished from the ‘objective’ properties of things in the external world. Theories of consciousness must recognize the existence of what Daniel Dennett mockingly labels ‘figment,’ but this result—though metaphysically and epistemologically significant—is not incompatible with either physicalism or naturalized semantics.

Reference and Incommensurability: What Rigid Designation Won’t Get You

Causal theories of reference in the philosophy of language and philosophy of science have suggested that it could resolve lingering worries about incommensurability between theoretical claims in different paradigms, to borrow Kuhn’s terms. If we co-refer throughout different paradigms, then the problems of incommensurability are greatly diminished, according to causal theorists. I argue that assuring ourselves of that sort of constancy of reference will require comparable sorts of cross-paradigm affinities, and thus provides us with no special relief on this problem. Suggestions on how to think about rigid designation across paradigms are included.

Playing with Representations: How Do Kids Make Use of Quantitative Representations in Video Games?

This paper describes the use of quantities in video games by young people as part of a broader effort to understand thinking and learning across naturally occurring contexts of activity. Our approach to investigating the use of quantities in game play is ethnographic; we have followed eight children over a six-month period as they play their own games at home. The data set is composed of video recordings and artifact-based interviews. The concept of disciplined perception is used to understand how quantities are coordinated during game play. The current study shows young people using quantities in games to make predictions and organize their actions based on those predictions. Some ideas based on the study’s findings for using video games in school are discussed.

Anomaly detection in a mobile communication network

Mobile communication networks produce massive amounts of data which may be useful in identifying the location of an emergency situation and the area it affects. We propose a one pass clustering algorithm for quickly identifying anomalous data points. We evaluate this algorithm’s ability to detect outliers in a data set and describe how such an algorithm may be used as a component of an emergency response management system.