This tutorial will illustrate how, theories are developed in sociology about the relation between social networks and trust using game-theoretic tools. In addition, it will be discussed how testable hypotheses can be derived from these theories. Finally, a number of complementary strategies to test these hypotheses will be described. These include laboratory experiments in which subjects are involved in abstract trust situations as well as surveys on transactions in which buyers and sellers are involved in actual trust problems.
The tutorial will introduce the main qualitative research methods in the social sciences, such as qualitative interviews, ethnography and conversation analysis. For each method, aims and scope are discussed as well as common problems. One central idea of qualitative research is to offer insights into the life-worlds of actors, into their concepts and understanding of social life. Thus qualitative research aims at re-establishing the actors' point of view.
Mathematical objects and operations can be viewed as abstract entities or as mental constructs with measurable properties. Cognitive science typically focuses on simple mathematical skills (like subitizing, counting, and addition) and interprets their behavioral manifestations (response times, accuracy and preferences for certain operands or operations) as clues to mental representations.
The tutorial will sketch basic findings from the empirical literature and introduce techniques and methodologies (eye-tracking, computational cognitive modeling, fMRI) used to investigate mathematical skills. Recent research (e.g., effects of spatial layout, notations, and means of physical interaction) highlights the importance of an embodied and embedded perspective on numeric skills.
In the first part of my paper I discuss several objections that have been made to certain "new creations" in mathematics, as there are, e.g., infinite or uncountable sets or distributions. The second part is dealing with the connection between creation and assumption.
In this paper I challenge what appears to be the current paradigm in the study of analogies, namely that they fare best characterized in terms of structure-preserving mappings between two domains (Gentner 1983). Gentner's "structural theory of analogies" or variants thereof, have become generally accepted in cognitive science, and they seem to have become standard also in the philosophy of science literature (see, e.g., Magnani and Nersessian 2002, and Shelley 2003). Moreover, the techniques for finding and expressing analogies are often assumed to be universally applicable to all domains alike.
To point out certain theoretical limitations of this approach I introduce a distinction between "relation-rich" and "object-rich" domains. On the one hand, domains with few objects and a rich relational structure occur frequently in scientific expositions and they are often used as examples for the application of the structural theory of analogies. On the other hand, domains with many elements but with only few relevant relations between them are very common in mathematics (e.g., number systems, algebraic structures, geometries), but for certain of these domains the standard account of analogies based on structure-preserving mappings fails. This important difference between relation-rich and object-rich domains has been overlooked so far in the quest for an adequate explication of analogies, since the numerous investigations regarding the nature of analogies and the use of analogies in science (beginning with Hesse 1966) have focused exclusively on relation-rich domains, while the process of drawing analogies in mathematics has received only scant attention (Polya 1954).
In search for an alternative, or better, complementary account of analogies I revisit a construal of analogies that is based on a common linguistic description of the analogous domains. As I show, not only does this approach overcome the difficulties of the structure-mapping account for object-rich domains, but it also has various advantages with regard to mathematical and scientific practice. Some examples from the history of mathematics will reveal that axiomatizations (understood as characterizing commonalities between analogous domains) did in fact play a role in finding and describing analogies between object-rich domains and thereby also in the discovery of new mathematics. In addition, I argue that such an understanding of analogies is also better suited for illuminating certain aspects of scientific methodology in general. For example, the formulation of laws can be understood as the explication of conditions that are satisfied by different structures or systems, i.e., as the characterization of the analogies between these systems.
References
This tutorial will have two halves: the first will introduce some claims in the literature about irrational deductive reasoning and decision performances, and raise issues about their interpretation. The second will look at differences between sentential and diagrammatic reasoning, both logical differences in reasoning systems and in individuals' reasoning performance with them. I will connect the latter to sociological claims about the justification of knowledge.
The talk will be a three component report on work in progress :