Traditional philosophy of mathematics has been concerned with the nature of mathematical objects rather than events. This traditional focus on reified objects is reflected in dominant theories of learning mathematics whereby the learner is meant to acquire familiarity with ideal mathematical objects, such as number, polygon, or tangent. I argue that the concept of event—rather than object—better captures the vitality of mathematics, and offers new ways of thinking about mathematics education. In this paper I draw on two different but related (...) theories of event articulated in the philosophies of Alain Badiou and Gilles Deleuze to argue that the central activity of ‘problem solving’ in mathematics education should be recast in terms of a problematic of events. (shrink)

This study creates and develops a concept called the untimely-image including two sub-concepts called contours of the new and the untimely-site. The untimely-image concerns the clearing for and the expression of figures of “potential” in thought in the form of moving-images. The aim of these concepts is to form a critical framework for evaluating and conceptualizing political film as expressive, not of the new itself but of its “untimely” contours. The untimely-image, and its many implications, is developed over the course (...) of six chapters. Chapter 1 extensively defines “contours” and “new” as operative in this study, and also introduces a theme that runs through all the chapters: how to think the contours of the new in relation to the cult of the new in consumer culture and in relation to the larger mechanisms of advanced capitalism. Chapter 2 defines the parameters of the untimely-image as specifically regarding moving images, and continues the development of this concept. In Chapters 3 to 6, The Wire serves the double function of complicating and giving specification to the elaboration of the untimely-image as well as a case in which the untimely-image is used as a critical framework. The Wire and the untimely-image relate in processes of juxtaposition, wherein they meet, cross over, separate, and reproblematize each other. An untimely-image is fully defined in relation to concrete political issues. The untimely-image is therefore advanced by articulating the components and characteristics that, independently of the concrete issue, remain in every case, as well as by putting the concept to work regarding two specific problems in The Wire: its expression of blackness and its mapping of advanced capitalism. (shrink)

This paper makes two claims. Firstly, it shows that thinking the truth of any particular concept (such as politics) is founded upon an instrumental logic that betrays the truth of a situation. Truth cannot be thought ‘of something’, for this would fall back into a theory of correspondence. Instead, truth is a function of thought. In order to make this move to a functional concept of truth, I outline Dewey’s criticism, and two important repercussions, of dogmatically instrumental philosophy. I then (...) show how Badiou’s philosophy is indeed guilty of instrumentalisation, but emphasise that his prioritisation of truth is nevertheless important to maintain. The second claim this paper makes is that the criticism of Deleuze’s conception of truth as circular is misplaced, as it is founded on the assumption that Deleuze conceptualises the truth of objects. Instead, I show that, for Deleuze, truth is not a property of an object but of its production. To reach this conclusion, I develop what I call Dewey’s account of pragmatic instrumentalisation (as opposed to the dogmatic instrumentalisation he criticises) into Deleuze’s conceptualisation of truth as the process of making sense of our precarious world. I conclude by making some provisional remarks that Deleuze’s pragmatic account of truth paves the way for an ethics that is not founded on truths it cannot explain (i.e. God or mathematics), but as an ongoing, subversive practice. (shrink)