Browsing by Browse by FOR 2008 "010107 Mathematical Logic, Set Theory, Lattices and Universal Algebra"

Despite an extensive literature on the nature and origins of mathematical truth, few if any studies exist of the everyday practices through which the adequacy of mathematical argumentation is cultivated and assessed. The work of a novice prover afforded insight into these practices and, in particular, into the disciplined character of discovering and proving mathematical theorems.

This paper introduces an anthropological approach to the foundations of mathematics. Traditionally, the philosophy of mathematics has focused on the nature and origins of mathematical truth. Mathematicians, however, treat mathematical arguments as determining mathematical truth: if an argument is found to describe a witnessably rigorous proof of a theorem, that theorem is considered—until the need for further examination arises—to be true. The anthropological question is how mathematicians, as a practical matter and as a matter of mathematical practice, make such determinations. This paper looks first at the ways that the logic of mathematical argumentation comes to be realized and substantiated by provers as their own immediate, situated accomplishment. The type of reasoning involved is quite different from deductive logic; once seen, it seems to be endemic to and pervasive throughout the work of human theorem proving. A number of other features of proving are also considered, including the production of notational coherence, the foregrounding of proof-specific proof-relevant detail, and the structuring of mathematical argumentation. Through this material, the paper shows the feasibility and promise of a real-world anthropology of disciplinary mathematical practice.

The number of people suffering from dementia is projected to increase over the coming decades, resulting in enormous pressure on the community and in particular on the family carers of people with dementia. This study aims to explore the broader question of how family carers of people with dementia living in the community successfully manage and sustain informal caring at present, and how they will continue to provide care in the future, by identifying the challenges associated with the continuation of their care. The qualitative study, conducted in the state of Queensland in Australia, focuses on a carer's perspective and was obtained through in-depth interviewing and thematic analysis of family carers' experiences in providing care for their family members with dementia. This research, while providing a greater understanding about the management of caring by family carers, including the impact of caring on them and the interface between informal and formal care, also provides recommendations for increasing the sustainability of informal care of people with dementia at present and in the future.