Dwelling With Wildflowers: Qualitative Inquiry as Life-Living and Life-Giving

In this short piece, I reconsider qualitative inquiry based on my chance encounter with a buttonhole flower. This encounter offered me an opportunity to explore not only my relationship with vegetal life, but also how dwelling with wildflowers allows one to reconceptualize qualitative inquiry as a practice of life-living and live-giving that emerges from a logic of conviviality. Practicing qualitative inquiry as life-living and life-giving serves as a means to unmoor our practices of inquiry from the abstraction of re-presentation and the predicative logic on which this is based, and to offer instead a conceptualization of inquiry as a process of dwelling with/in the world, and in this togetherness, experience (the potential of) life.

Neo-Fregeanism and the Burali-Forti Paradox

This chapter considers what form a neo-Fregean account of ordinal numbers might take. It begins by discussing how the natural abstraction principle for ordinals yields a contradiction (the Burali-Forti Paradox) when combined with impredicative second-order logic. It continues by arguing that the fault lies in the use of impredicative logic rather than in the abstraction principle per se. As the focus is on a form of predicative logic which reflects a philosophical diagnosis of the source of the paradox, the chapter considers how far Hale and Wright’s neo-logicist programme in cardinal arithmetic can be carried out in that logic.

Deductive systems for BigData integration

The globalization is associated with an increased data to be processed from E-commerce transactions. The specialists are looking for different solutions, such as BigData, Hadoop, Datawarehoues, but it seems that the future is the predicative logic implemented through deductive database technology. It has to be done the swift from imperative languages, to not declaratively languages used for the application development. The deductive databases are very useful in the student teaching programs, too. Thus, the article makes a consistent literature review in the field and shows practical examples of using predicative logic in deductive systems, in order to integrate different kind of data types.

Formalising Overlap Algebras in Matita

We describe some formal topological results, formalised in Matita 1/2, presented in predicative intuitionistic logic and in terms of Overlap Algebras.Overlap Algebras are new algebraic structures designed to ease reasoning about subsets in an algebraic way within intuitionistic logic. We find that they also ease the formalisation of formal topological results in an interactive theorem prover.Our main result is the existence of a functor between two categories of ‘generalised topological spaces’, one with points (Basic Pairs) and the other point-free (Basic Topologies). This formalisation is part of a wider scientific collaboration with the inventor of the theory, Giovanni Sambin. His goal is to verify in what sense his theory is ‘implementable’, and to discover what problems may arise in the process. We check that all intermediate constructions respect the stringent size requirements imposed by predicative logic. The formalisation is quite unusual, since it has to make explicit size information that is often hidden.We found that the version of Matita used for the formalisation was largely inappropriate. The formalisation drove several major improvements of Matita that will be integrated in the next major release (Matita 1.0). We show some motivating examples, taken directly from the formalisation, for these improvements. We also describe a possibly sub-optimal solution in Matita 1/2, which is exploitable in other similar systems. We briefly discuss a better solution available in Matita 1.0.