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Information Flow in Logics in the Vicinity of BB
Get PDFSituation theory, and channel theory in particular, have been used to provide motivational accounts of the ternary relation semantics of relevant, substructural, and various non-classical logics. Among the constraints imposed by channel-theory, we must posit a certain existence criterion for situations which result from the composites of multiple channels (this is used in modeling information flow). In associative non-classical logics, it is relatively easy to show that a certain such condition is met, but the problem is trickier in non-associative logics. Following Tedder (2017), where it was shown that the conjunction-conditional fragment of the logic B admits the existence of composite channels, I present a generalised version of the previous argument, appropriate to logics with disjunction, in the neighbourhood ternary relation semantic framework. I close by suggesting that the logic BB+(^I), which falls between Lavers' system BB+ and B+ , satisfies the conditions for the general argument to go through (and prove that it satisfies all but one of those conditions)
Ehrenfeucht-Fraïssé games without identity
Get PDFThis note defines Ehrenfeucht-Fraïssé games where identity is not present in the basic language. The formulation is applied to show that there is no elementary theory in the language of one binary relation that exactly characterizes models in which the relation is the identity relation
Translating Metainferences Into Formulae: Satisfaction Operators and Sequent Calculi
Get PDFIn this paper, we present a way to translate the metainferences of a mixed metainferential system into formulae of an extended-language system, called its associated σ-system. To do this, the σ-system will contain new operators (one for each standard), called the σ operators, which represent the notions of "belonging to a (given) standard". We first prove, in a model-theoretic way, that these translations preserve (in)validity. That is, that a metainference is valid in the base system if and only if its translation is a tautology of its corresponding σ-system. We then use these results to obtain other key advantages. Most interestingly, we provide a recipe for building unlabeled sequent calculi for σ-systems. We then exemplify this with a σ-system useful for logics of the ST family, and prove soundness and completeness for it, which indirectly gives us a calculus for the metainferences of all those mixed systems. Finally, we respond to some possible objections and show how our σ-framework can shed light on the “obeying” discussion within mixed metainferential context
Arithmetic Formulated Relevantly
Get PDFThe purpose of this paper is to formulate first-order Peano arithmetic within the resources of relevant logic, and to demonstrate certain properties of the system thus formulated. Striking among these properties are the facts that (1) it is trivial that relevant arithmetic is absolutely consistent, but (2) classical first-order Peano arithmetic is straightforwardly contained in relevant arithmetic. Under (1), I shall show in particular that 0 = 1 is a non-theorem of relevant arithmetic; this, of course, is exactly the formula whose unprovability was sought in the Hilbert program for proving arithmetic consistent. Under (2), I shall exhibit the requisite translation, drawing some Goedelian conclusions therefrom. Left open, however, is the critical problem whether Ackermann’s rule γ is admissible for theories of relevant arithmetic.
The particular system of relevant Peano arithmetic featured in this paper shall be called R♯. Its logical base shall be the system R of relevant implication, taken in its first-order form RQ. Among other Peano arithmetics we shall consider here in particular the systems C♯, J♯, and RM3♯; these are based respectively on the classical logic C, the intuitionistic logic J, and the Sobocinski-Dunn semi-relevant logic RM3. And another feature of the paper will be the presentation of a system of natural deduction for R♯, along lines valid for first-order relevant theories in general. This formulation of R♯ makes it possible to construct relevantly valid arithmetical deductions in an easy and natural way; it is based on, but is in some respects more convenient than, the natural deduction formulations for relevant logics developed by Anderson and Belnap in Entailment
Remark on Relevant Arithmetic
Get PDFThis is a brief note about the history of the analysis of the collection of theories, RM3modn, in Meyer and Mortensen "Inconsistent Models for Relevant Arithmetics" Journal of Symbolic Logic 49 (1984)
Family Stories and Family Secrets
Get PDFFamilies preserve and rewrite history in ways that pass on to the next generation a sense of family history based on what is known and what cannot be told. In this paper, we analyze New Zealand European adolescents’ stories about their parents’ childhood, exploring how these young people tell and do not tell family stories shrouded in secrecy. We identify three major ways in which families express secrets across the generations—through collusion, through confusion, and through whole-family secrets—and discuss the implications of each of these family practices for the preservation of family history
Creating Fictitious Family Memories: The Closed Stranger Adoption of Māori Children into White Families
Get PDFBetween 1955 and 1985 approximately 45,000 closed stranger adoptions took place in Aotearoa New Zealand. Many of these adoptions involved children of Māori ancestry, who were placed into white families, where links to their whakapapa were severed and a space for fictitious narratives (including memories) was created. This article reveals some adoption fictions experienced in the lives of six Māori people who were adopted into Pākehā families. Using a Māori-centred research approach, it found that there were common fictions that Māori adopted people navigated, through counter-narratives and narratives of repair, in their quest to create their own identity
Insanity in a Sea of Islands: Mobility and Mental Health in Aotearoa New Zealand’s Pacific Sphere
Get PDFThis article builds upon the fragmentary historical evidence of mental illness and mental health within South Pacific societies to explore the nexus with migration and mobility. The focus is on the Pacific territories that were under Aotearoa New Zealand’s jurisdiction. The article explores concepts of mental health and mobility within Pacific societies that became entangled with European concepts to designate insanity. The paper then discusses how mental illnesses were exacerbated or induced through migration and travel across the Pacific. The last section explores the transfer of mentally ill patients from some Pacific islands to Aotearoa. This article is based upon the 2018 J. D. Stout Lecture at Victoria University of Wellington
Burdened in Business: Pacific Early Career Academic Experiences with Promoting Pacific Research Methodologies in the Business Academy
Get PDFOngoing calls to indigenise the academy renew debate regarding the value and significance of Pacific and Indigenous philosophies and methodologies. This paper contributes to this conversation by reflecting on our experience as Tongan women and early career academics promoting the utility of Pacific methodologies such as talanoa within business research in Aotearoa. We examine the constraints on and drivers to adopting talanoa in our respective fields to argue that institutional demands and limited Pacific capacity within the business space restrict our ability to work towards legitimising talanoa and drive future-focused directions in research. These factors hinder our ability to actively contribute to the agenda of indigenising the business academy
Disruptions, Decolonial Desire and Diaspora: A Provocation toward a Pacific Queer Worldmaking Scholarly Practice in Aotearoa–New Zealand
Get PDFPacific queer scholarship is underrepresented within Pacific research communities in Aotearoa–New Zealand. What does exist is either hypervisible or centres on narratives of oppression, both of which are archetypes that can deny the complexity of Pacific queer communities. As two queer Samoan scholars raised in the Aotearoa–New Zealand diasporic setting, we offer a provocation that tests the opportunities (and limits) queer theoretics provide for Pacific research. Through a combination of poetry, vignettes, and theory (queer and straight), as well as reflections, we intentionally and generatively transgress heteronormative, exclusionary and static boundaries that still exists within Pacific research in New Zealand
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