Well, this is interesting!
ABSTRACT: In this short paper I describe the research project I am currently work-ing on. I also look at recent research regarding the role of logical implica-tion in mathematical thought and suggest that Sperber & Wilson’s (1986) relevance theory may shed light on the cognitive processes involved in un-derstanding and interpreting conditional statements. For my Ph.D. research I am looking at how mathematicians, both successful and unsuccessful, use and understand logical implication. Logic has always been considered an important part of mathematics but, perhaps strangely, there has been little research into how mathematicians use formal logic in their reason-ing. Currently I am planning a research project that looks at the relationship between the formal concept definition of logical implication as it is taught at university (the material conditional) and the (syntactic) concept image that mathematicians use on a day to day basis. Initial investigations using the Wason selection task seem to indicate that there is a significant difference between these two constructs (Inglis & Simpson, 2004). If this is the case it raises questions about the value of teaching the material implication in first year university courses. The Maze Task. Whilst investigating students’ understanding of logical implication, several au-thors (e.g. Rogalski & Rogalski, 2001; Durand-Guerrier, 2003) have used what has become known as the Durand-Guerrier maze task (see figure 1). Participants in this task are told that a person (named X) passes through the maze without using the same door twice. They are then asked to evaluate the truth/falsity of a series of statements about the situation. For each statement participants are given three options: true, false or can’t tell. For example, ‘X crossed P ‘ is a false statement, whereas the correct answer to ‘X crossed M ‘ is can’t tell. 1 The ideas expressed in the paper were developed jointly with my supervisor, Adrian Simpson.
This does seem to be the same Matthew Inglis who has worked with Lara Alcock, because he mentions Adrian Simpson, but that means this paper must be pretty old.