Abstracta and Possibilia: Modal Foundations of Mathematical Platonism

This paper aims to provide modal foundations for mathematical platonism. I examine Hale and Wright's (2009) objections to the merits and need, in the defense of mathematical platonism and its epistemology, of the thesis of Necessitism. In response to Hale and Wright's objections to the role of epistemic and metaphysical modalities in providing justification for both the truth of abstraction principles and the success of mathematical predicate reference, I examine the Necessitist commitments of the abundant conception of properties endorsed by Hale and Wright and examined in Hale (2013); and demonstrate how a two-dimensional approach to the epistemology of mathematics is consistent with Hale and Wright's notion of there being non-evidential epistemic entitlement rationally to trust that abstraction principles are true. A choice point that I flag is that between availing of intensional or hyperintensional semantics. The hyperintensional semantic approach that I advance is a topic-sensitive epistemic two-dimensional truthmaker semantics. Epistemic and metaphysical states and possibilities may thus be shown to play a constitutive role in vindicating the reality of mathematical objects and truth, and in providing a conceivability-based route to the truth of abstraction principles as well as other axioms and propositions in mathematics

Investigating students’ perspectives of learning and participating in seminars using a Bourdieuian perspective

The purpose of this paper is to examine how Vygotsky's and Bourdieu's theoretical perspectives contributed to the insights I gained about student teachers’ perceptions of seminars and my role as a seminar tutor. The paper is based on the findings from a doctoral study into students’ perspectives of learning and participating in seminars. Using a constructive grounded theory approach, I interviewed five 2nd year teacher education students and consulted relevant institutional documents. From a Vygotskian perspective, the data highlighted the complexity and dynamic nature of seminars where relationships, pedagogical tools and artefacts played an important meditational role. By highlighting the significance of the wider context, however, Bourdieu’s theory of practice and in particular his concept of symbolic violence gave a richer perspective of participants’ perspectives of seminars. In particular, by drawing attention to the impact of dominant discourses on individuals' practices, it provided a more nuanced view about the meanings they attached to their seminar experiences, and enabled a deeper reflection about my own practice and values as a tutor/lecturer in higher education

Fuzzy Spatial Analysis Techniques in a Business GIS Environment

The purpose of the paper is to explore the use of fuzzy logic technology in spatial analysis. Focus is laid on illustrating the value added within the context of Business GIS. We consider the issue of geomarketing for illustrative purposes. Geomarketing may be characterised as address focused marketing. The objective of the case study is to identify spatial customer potentials for a specific product, using real world customer data of an Austrian firm. Fuzzy logic is used to generate customer profiles and to model the spatial customer potential of the product in question. We will illustrate the use of fuzzy logic in comparison to crisp classification techniques and modelling with crisp operators for solving the problem and more generally how the use of fuzzy logic may be to the advantage of businesses. Univ.-Prof. Dr. Manfred M. Fischer (Department of Economic Geography and Geoinformatics, Vienna University of Economics and Business Administration) invited me to attend his special session.