Michael H. G. Hoffmann

Different situations — like school and workplace — demand different forms of knowledge. Even more important, in particular for lifelong learning, are forms of knowledge we need for managing movements between those situations. To develop a better understanding of how to ‘navigate’ knowledge boundaries, this paper analyzes, firstly, interviews with scientists interpreting familiar and unfamiliar graphs. Our goal is to identify those forms of knowledge that should receive special attention in education. Secondly, the article elaborates — based on Peirce’s semiotics — an epistemologically reflected semiotic model to describe the role and conditions of knowledge necessary for crossing knowledge boundaries.

Abductive reasoning takes place in forming``hypotheses'''' in order to explain ``facts.'''' Thus, theconcept of abduction promises an understanding ofcreativity in science and learning. It raises,however, also a lot of problems. Some of them will bediscussed in this paper. After analyzing thedifference between induction and abduction (1), Ishall discuss Peirce''s claim that there is a ``logic''''of abduction (2). The thesis is that this claim can beunderstood, if we make a clear distinction between inferential elements and perceptive elements of abductive reasoning. For Peirce, the creative act offorming explanatory hypotheses and the emergence of``new ideas'''' belongs exclusively to the perceptive side of abduction. Thus, it is necessary to study the roleof perception in abductive reasoning (3). A furtherproblem is the question whether there is arelationship between abduction and Peirce''s concept of``theorematic reasoning'''' in mathematics (4). Both forms of reasoning could be connected, because both arebased on perception. The last problem concerns therole of instincts in explaining the success ofabductive reasoning in science, and the question whether the concept of instinct might be replaced bymethods of inquiry (5).

Discussions concerning belief revision, theorydevelopment, and ``creativity'' in philosophy andAI, reveal a growing interest in Peirce'sconcept of abduction. Peirce introducedabduction in an attempt to providetheoretical dignity and clarification to thedifficult problem of knowledge generation. Hewrote that ``An Abduction is Originary inrespect to being the only kind of argumentwhich starts a new idea'' (Peirce, CP 2.26).These discussions, however, led to considerabledebates about the precise way in which Peirce'sabduction can be used to explain knowledgegeneration (cf. Magnani, 1999; Hoffmann, 1999).The crucial question is that of understandinghow we can get the new elements capableof enlarging our theories. Under thesecircumstances, it might be helpful to step outof the entanglement and reconsider the basis ofthe problem that originally triggered Peirce'sinterest in abduction. This will lead us toanother Peircean concept, that of ``diagrammaticreasoning,'' which I discuss here in the contextof his ``pragmatism.'' In this way, I hope toreach a better understanding of thecontribution of ``abduction'' to the knowledgegeneration process.

Technology is not only an object of philosophical reflection but also something that can change this reflection. This paper discusses the potential of computer-supported argument visualization tools for coping with the complexity of philosophical arguments. I will show, in particular, how the interactive and web-based argument mapping software “AGORA-net” can change the practice of philosophical reflection, communication, and collaboration. AGORA-net allows the graphical representation of complex argumentations in logical form and the synchronous and asynchronous collaboration on those “argument maps” on the internet. Web-based argument mapping can overcome limits of space, time, and access, and it can empower users from all over the world to clarify their reasoning and to participate in deliberation and debate. Collaborative and web-based argument mapping tools such as AGORA-net can change the practice of arguing in two dimensions. First, arguing on web-based argument maps in both collaborative and adversarial form can lead to a fundamental shift in the way arguments are produced and debated. It can provide an alternative to the traditional four-step process of writing, publishing, debating, and responding in new writing with its clear distinction between individual and social activities by a process in which these four steps happen virtually simultaneously, and individual and social activities become more closely intertwined. Second, by replacing the linear form of arguments through graphical representations of networks of inferential relations which can grow over time in an infinite space, these tools do not only allow a clear visualization of structures and relations, but also forms of collaboration in which, for example, participants work on different “construction zones” of larger argument maps, or debates are performed at specific points of disagreement on those maps. I introduce the term synergetic logosymphysis to describe a practice that combines these two dimensions of collaborative- and web-based argument mapping

Summary. This paper analyzes Frederik Stjernfelt’s recently published Diagrammatology in order to clarify the role of diagrammatic reasoning within an epistemology that focuses on the problem of learning and the growth of knowledge. To achieve this goal, I provide more precise definitions of Peirce’s concepts of “diagram” and “diagrammatic reasoning,” emphasizing in particular the necessity of consistent systems of representation as a precondition for both. The paper starts with a critique of two theses for which Stjernfelt argues based on some remarks by Peirce: first, that it is possible to learn by observing icons and, second, that icons can be defined by similarity

A central challenge for research on how we should prepare students to manage crossing boundaries between different knowledge settings in life long learning processes is to identify those forms of knowledge that are particularly relevant here. In this paper, we develop by philosophical means the concept of a dialectical system as a general framework to describe the de-velopment of knowledge networks that mark the starting point for learning processes, and we use semiotics to discuss the epistemological thesis that any cognitive access to our world of objects is mediated by signs and diagrammatic reasoning and abduction as those forms of practical knowledge that are crucial for the development of knowledge networks. The rich-ness of this theoretical approach becomes evident by applying it to an example of learning in a biological research context. At the same time, we take a new look at the role of mathematical knowledge in this process