This article traces the development of the theory and practice of what is known as ‘community of inquiry’ as an ideal of classroom praxis. The concept has ancient and uncertain origins, but was seized upon as a form of pedagogy by the originators of the Philosophy for Children program in the 1970s. Its location at the intersection of the discourses of argumentation theory, communications theory, semiotics, systems theory, dialogue theory, learning theory and group psychodynamics makes of it a rich site (...) for the dialogue between theory and practice in education. This article is an exploration of those intersections, and a prospectus of its possible role in the formation and reformulation of school curriculum. It will be argued here that, when formulated as community of philosophical inquiry in particular, it offers the possibility of ‘philosophising’ the school curriculum in general, by extending the concept-work that doing philosophy entails to all of the disciplines. The article begins with an attempt at an operational definition of the term as, move to an analysis of its dynamics, offers an example of its use in a mathematics classroom, and finishes with a schematic view of its whole-curriculum and whole-school possibilities. (shrink)

In this paper, I propose a solution to Fitch’s paradox that draws on ideas from Edgington (Mind 94:557–568, 1985), Rabinowicz and Segerberg (1994) and Kvanvig (Noûs 29:481–500, 1995). After examining the solution strategies of these authors, I will defend the view, initially proposed by Kvanvig, according to which the derivation of the paradox violates a crucial constraint on quantifier instantiation. The constraint states that non-rigid expressions cannot be substituted into modal positions. We will introduce a slightly modified syntax and semantics (...) that will help underline this point. Furthermore, we will prove results about the consistency of verificationism and the principle of non-omniscience by model-theoretical means. Namely, we prove there exists a model of these principles, and delineate certain constraints they pose on a structure in which they are true. (shrink)

This paper discusses some major similarities and differences between community of philosophical inquiry and community of mathematical inquiry , and offers a few examples of the implementation of CMI in the context of a school mathematics classroom. Three modes of CMI are suggested. The first mode facilitates inquiry into mathematical problems - that is, it provides a medium for “doing and talking mathematics.” In this case, CMI is primarily an avenue for problem solving—defining problems, interpreting them, working with different methods (...) to solve them, reflecting on suggested alternative methods, verifying solutions, and drawing conclusions. The second mode leads us to “talk about mathematics” through collaborative inquiry into mathematical concepts such as axioms, theorems, algorithms, infinity, and the posing of philosophical questions that concern mathematics as a system--particular structures and rules and their relation to human experience. The third mode makes use of CMI for meta-inquiry into our collective experience in “doing and talking mathematics” and “talking about mathematics,” and may be characterized as “talking about doing mathematics.”. (shrink)

One of John Dewey's major contributions to the reconstruction of the educational process was in his understanding that education needed to develop a working relationship between the refined end-products of inquiry that are codified and sedimented in textbooks, and the raw subject matter inquiry that is natural to the young. Such inquiry, he was convinced, should be shaped and fashioned to the well-known model of scientific inquiry which he set forth in How We Think (Dewey, 1933). In that same book, (...) he describes "reflective thinking" as a special kind of ratiocination that is aware of its means and consequences, and thus is a major instrument in discipline-based inquiry. Dewey's "scientific method" became a .. (shrink)

BackgroundSelf-prescribing and prescribing to personal contacts is explicitly discouraged by General Medical Council guidelines.AimsThis study examines how widespread the practice of self-prescribing and prescribing to personal contacts is.MethodsA 16-item questionnaire was distributed via an online forum comprising 4445 young medical doctors, which asked respondents about previous prescribing to themselves, their families, friends and colleagues, including the class of medication prescribed. Demographic details were collected including medical grade and specialty.ResultsA total of 729 responses were obtained, the majority of which were from (...) young non-consultant hospital doctors from a range of specialties. Two-thirds of respondents had self-prescribed, over 70% had prescribed to family, and nearly 60% had prescribed to a friend or colleague. Older doctors were more likely to self-prescribe. Interns being less likely to self-prescribe was not unexpected, while general practitioners and paediatricians were more likely to self-prescribe. GPs, paediatricians and hospital medicine specialties were more likely to prescribe to family and surgeons were more likely to prescribe to friends. Some 3% to 7% who had self-prescribed had prescribed an opiate, benzodiazepine or psychotropic medication. Male doctors, anaesthetists and surgeons were more likely to self-prescribe opioids, while those in hospital medicine were more likely to self-prescribe psychotropic medications.ConclusionPrescribing outside the traditional doctor-patient relationship is widespread despite clear professional guidance advising against it. (shrink)

In this paper, I re-examine Dummett's arguments against realism and, most notably, those against truth conditional semantics. Dummett claims that a (realist) truth conditional meaning theory will invariably encounter limitations when accounting for the meanings of the statements of the so-called "disputed class", and so must be rejected in favour of a theory of meaning couched in terms of proof or verification. The first part of this paper seeks to faithfully reconstruct Dummett's position on meaning. The subsequent parts are critical (...) of this position. In particular, I attempt to expose the shortcomings of an antirealist theory of meaning on the one hand, and then show how truth conditional semantics (be they realist or not) emerge relatively unscathed from Dummett's criticism on the other. (shrink)

In this paper, I discuss the social philosopher Pierre Bourdieu’s concept of habitus, and use it to locate and examine dispositions in a larger constellation of related concepts, exploring their dynamic relationship within the social context, and their construction, manifestation, and function in relation to classroom mathematics practices. I describe the main characteristics of habitus that account for its invisible effects: its embodiment, its deep and pre-reflective internalization as schemata, orientation, and taste that are learned and yet unthought, and are (...) subsumed by our practices, which we understand as something that “goes without saying.” I also propose that, similarly to Bourdieu’s concept of linguistic habitus, a math habitus is made up of a complex intertwining of collective and individual histories that turn into “nature,” which structure all individual and collective action and inform mathematical classroom practice. I suggest that individual math dispositions may be liable to reconstruction through the reconstruction of the collective math habitus, which follows from opening spaces for dialogue, problematization and reconstruction of the unthought categories of the doxa. This requires that students acquire new concrete and symbolic means with which to challenge their current sense of mathematics as a discipline, and mathematical practice tout court. Finally, I argue that community of inquiry, employed as a pedagogical model, provides an avenue for both: for opening those spaces for reflective dialogical inquiry into concepts and questions whose meanings and references have so far been taken for granted, and for acquiring critical thinking and dialogical skills and dispositions that are a necessary means for participating in such reflective inquiry that offers significant promise for reconstructing individual and collective habitus in school settings. (shrink)

This paper is predicated on the idea that some modal operators are better understood as quantificational expressions over worlds that determine not only first-order facts but modal facts also. In what follows, we will present a framework in which these two types of facts are brought closer together. Structural features will be located in the worlds themselves. This result will be achieved by decomposing worlds into parts, where some of these parts will have “modal import” in the sense that they (...) will determine structure on other worldly parts. The main upshot of this will be a clearer grasp of the interaction between modal notions. (shrink)

Kennedy discusses, through dialogue, old concepts in philosophy with children regarding the finite and infinite parts of the Earth and galaxy.

ABSTRACT: In this paper, I revisit arguments for and against various theses concerning higher-order knowledge in order to fully gauge their impact on the principles of positive and negative introspection. I argue that the expression “knowing that one knows” has at least two salient understandings: the more common one, labelled “transparentist”, validates the principle of positive introspection, while the other which is less common, labelled “agrippean”, supports some of the arguments against this principle.

This paper argues that paradox offers an ideal didactic context for open-ended group discussion, for the intensive practice of reasoning, acquiring dispositions critical for mathematical thinking, and higher order learning. In order to characterize the full pedagogical range of paradox, I offer a short overview of the effects of paradox, followed by a discussion of some parallels between the use of paradox in paradoxical psychotherapy and the use of the koan in Zen Buddhist spiritual training. Reasoning with paradoxes in a (...) community of mathematical inquiry is interpreted as a comparative if not isomorphic pedagogical and cognitive phenomenon. Finally, some broad implications are drawn for mathematical inquiry with paradoxes. (shrink)