This volume represents an important contribution to Peirce’s work in mathematics and formal logic. An internationally recognized group of scholars explores and extends understandings of Peirce’s most advanced work. The stimulating depth and originality of Peirce’s thought and the continuing relevance of his ideas are brought out by this major book.
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. (shrink)
Among the many problems posed by Peirce's concept of abduction is how to determine the scope of this form of inference, and how to distinguish different types of abduction. This problem can be illustrated by taking a look at one of his best known definitions of the term:Abduction is the process of forming an explanatory hypothesis. It is the only logical operation which introduces any new idea; for induction does nothing but determine a value, and deduction merely evolves the necessary (...) consequences of a pure hypothesis.The second half of this quote is not part of the definition, but an explanation of it. However, it adds something to this definition because it says implicitly that there are only three logical .. (shrink)
A crucial problem of conflict management is that whatever happens in negotiations will be interpreted and framed by stakeholders based on their different belief-value systems and world views. This problem will be discussed in the first part of this article as the main cognitive problem of conflict management. The second part develops a general semiotic solution of this problem, based on Charles Peirce's concept of "diagrammatic reasoning." The basic idea is that by representing one 's thought in diagrams, the (...) conditions that determine interpretations can become visible, we can "experiment" with them, and we can change them eventually. The third part, finally, focuses on a concrete tool, called Logical Argument Mapping , that can be used in conflict management to perform such diagrammatic reasoning and to cope with the cognitive problems discussed in the first part. The Israeli-Palestinian conflict on the sovereignty over Jerusalem will be used as an example to show how LAM could work in practice. (shrink)
Based on a typology of five basic forms of abduction, I propose a new definition of abductive insight that empha sizes in particular the inferential structure of a belief system that is able to explain a phenomenon after a new, abductive ly created component has been added to this system or the entire system has been abductively restructured. My thesis is, first, that the argumentative structure of the pursued problem solution guides abductive creativity and, second, that diagrammatic reasoning—if conceptualized according (...) to the requirements defined by Charles Peirce—can support this guidance. This support is mainly possible based on the normative power of the system of representation that has to be used to construct diagrams and to perform experiments with them. (shrink)
At the end of I.3, 319a29ff, Aristotle asks a series of questions. This difficult and condensed passage, whose translation is controversial at some points, raises two questions: what is what is not without qualification? and is the matter of earth and fire the same or different? In this essay, I shall focus on the second question.
Signs do not only “represent” something for somebody, as Peirce’s definition goes, but also “mediate” relations between us and our world, including ourselves, as has been elaborated by Vygotsky. We call the first the representational function of a sign and the second the epistemological function since in using signs we make distinctions, specify objects and relations, structure our observations, and organize societal and cognitive activity. The goal of this paper is, on the one hand, to develop a model in which (...) both these functions appear as complementary and, on the other, to show that this complementarity is essential for the dynamics of scientific activity, causing a dialectical process of generating new epistemological and representational means. This will be demonstrated with an example of how two scientists with different background knowledge analyze educational data collaboratively. (shrink)
Why do we formulate arguments? Usually, things such as persuading opponents, finding consensus, and justifying knowledge are listed as functions of arguments. But arguments can also be used to stimulate reflection on one’s own reasoning. Since this cognitive function of arguments should be important to improve the quality of people’s arguments and reasoning, for learning processes, for coping with “wicked problems,” and for the resolution of conflicts, it deserves to be studied in its own right. This contribution develops first steps (...) towards a theory of reflective argumentation. It provides a definition of reflective argumentation, justifies its importance, delineates it from other cognitive functions of argumentation in a new classification of argument functions, and it discusses how reflection on one’s own reasoning can be stimulated by arguments. (shrink)
The primary goal of this chapter is to present a new method—called Logical Argument Mapping —for the analysis of framing processes as they occur in any communication, but especially in conflicts. I start with a distinction between boundary setting, meaning construction, and sensemaking as three forms or aspects of framing, and argue that crucial for the resolution of frame-based controversies is our ability to deal with those “webs” of mutually supporting beliefs that determine sensemaking processes. Since any analysis of framing (...) in conflicts and communication is itself influenced by sensemaking—there is no “frame-neutrality”—the main problem for an analyst is to cope with his or her own cognitive limitations. LAM offers a solution to this problem. The method will be exemplified with an analysis of two conflicting interpretations of how the international community should deal with Hamas after its election victory in 2006. (shrink)
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. (shrink)
Starting from the observation that small children can count more objects than numbers—a phenomenon that I am calling the “lifeworld dependency of cognition”—and an analysis of finger calculation, the paper shows how learning can be explained as the development of cognitive systems. Parts of those systems are not only an individual’s different forms of knowledge and cognitive abilities, but also other people, things, and signs. The paper argues that cognitive systems are first of all semiotic systems since they are dependent (...) on signs and representations as mediators. The two main questions discussed here are how the external world constrains and promotes the development of cognitive abilities, and how we can move from cognitive abilities that are necessarily connected with concrete situations to abstract knowledge. (shrink)
This volume provides new sources of knowledge based on Michael Otte’s fundamental insight that understanding the problems of mathematics education – how to teach, how to learn, how to communicate, how to do, and how to represent ...
A large body of research in cognitive science differentiates human reasoning into two types: fast, intuitive, and emotional “System 1” thinking, and slower, more reflective “System 2” reasoning. According to this research, human reasoning is by default fast and intuitive, but that means that it is prone to error and biases that cloud our judgments and decision making. To improve the quality of reasoning, critical thinking education should develop strategies to slow it down and to become more reflective. The goal (...) of such education should be to enable and motivate students to identify weaknesses, gaps, biases, and limiting perspectives in their own reasoning and to correct them. This contribution discusses how this goal could be achieved with regard to reasoning that involves the construction of arguments; or more precisely: how computer-supported argument visualization tools could be designed that support reflection on the quality of arguments and their improvement. Three types of CSAV approaches are distinguished that focus on reflection and self-correcting reasoning. The first one is to trigger reflection by confronting the user with specific questions that direct attention to critical points. The second approach uses templates that, on the one hand, provide a particular structure to reason about an issue by means of arguments and, on the other, include prompts to enter specific items. And a third approach is realized in specifically designed user guidance that attempts to trigger reflection and self-correction. These types of approaches are currently realized only in very few CSAV tools. In order to inform the future development of what I call reflection tools, this article discusses the potential and limitations of these types and tools with regard to five explanations of the observation that students hardly ever engage in substantial revisions of what they wrote: a lack of strategies how to do it; cognitive overload; certain epistemic beliefs; myside bias; and over-confidence in the quality of one’s own reasoning. The question is: To what degree can each of the CSAV approaches and tools address these five potential obstacles to reflection and self-correction? (shrink)
Background Central to ethically justified clinical trial design is the need for an informed consent process responsive to how potential subjects actually comprehend study participation, especially study goals, risks, and potential benefits. This will be particularly challenging when studying deep brain stimulation and whether it impedes symptom progression in Parkinson’s disease, since potential subjects will be Parkinson’s patients for whom deep brain stimulation will likely have therapeutic value in the future as their disease progresses.Method As part of an expanded informed (...) consent process for a pilot Phase I study of deep brain stimulation in early stage Parkinson’s disease, an ethics questionnaire composed of 13 open-ended questions was distributed to potential subjects. The questionnaire was designed to guide potential subjects in thinking about their potential participation.Results While the purpose of the study was extensively presented during the informed consent process, in returned responses 70 percent focused on effectiveness and 91 percent included personal benefit as potential benefit from enrolling. However, 91 percent also indicated helping other Parkinson’s patients as motivation when considering whether or not to enroll.Conclusions This combination of responses highlights two issues to which investigators need to pay close attention in future trial designs: how, and in what ways, informed consent processes reinforce potential subjects’ preconceived understandings of benefit, and that potential subjects see themselves as part of a community of Parkinson’s sufferers with responsibilities extending beyond self-interest. More importantly, it invites speculation that a different paradigm for informed consent may be needed. (shrink)
There is evidence that problem-based learning (PBL) is an effective approach to teach team and problem-solving skills, but also to acquire content knowledge. However, there is hardly any literature about using PBL in philosophy classes. One problem is that PBL is resource intensive because a facilitator is needed for each group of students to support learning efforts and monitor group dynamics. In order to establish more PBL classes, the question is whether PBL can be provided without the need for facilitators. (...) We present a combination of five strategies—among them the collaborative argument visualization software AGORA-net—to replace facilitators. Additionally, we present evidence that these strategies are sufficient to provide a PBL experience that achieves intended learning goals in an ethics class and is satisfying for students without facilitators. (shrink)
In recent years, semiotics has become an innovative theoretical framework in mathematics education. The purpose of this article is to show that semiotics can be used to explain learning as a process of experimenting with and communicating about one's own representations of mathematical problems. As a paradigmatic example, we apply a Peircean semiotic framework to answer the question of how students learned the concept of "distribution" in a statistics course by "diagrammatic reasoning" and by developing "hypostatic abstractions," that is by (...) forming new mathematical objects which can be used as means for communication and further reasoning. Peirce's semiotic terminology is used as an alternative for notions such as modeling, symbolizing, and reification. We will show that it is a precise instrument of analysis with regard to the complexity of learning and of communication in mathematics classroom. (shrink)
One of the first things President Obama did after coming to office was the establishment of the Office of Public Engagement. As described on its Web site, this office "is the embodiment of the President's goal of making government inclusive, transparent, accountable and responsible." The Office of Public Engagement is supposed to "create and coordinate opportunities for direct dialogue between the Obama Administration and the American public, while bringing new voices to the table and ensuring that everyone can participate and (...) inform the work of the President."1As the president explained in his memorandum on transparency and open government, "Public engagement enhances the Government's effectiveness and improves .. (shrink)
Open peer commentary on the article “Second-Order Science of Interdisciplinary Research: A Polyocular Framework for Wicked Problems” by Hugo F. Alrøe & Egon Noe. Upshot: Alrøe and Noe are right in addressing Rittel and Webber’s notion of “wicked problems” as crucial for interdisciplinary research. However, I can see neither that they are providing a sufficiently clear understanding of “science” in their concept of a “second-order science of interdisciplinary research,” nor that their “polyocular framework” can contribute anything useful to addressing the (...) practical challenges posed by wicked problems. (shrink)
This argument map presents Paul Loewi’s crucial experiment in which he showed that neural transmissions of signals are chemical in nature, not electrical, in form of an argumentation. The map can be used in science education to show how the formulation of hypotheses should be related to a corresponding determination of experimental designs.
This argument map represents the argumentation of Sparrow, R. . "Just say No" to Drones. IEEE Technology and Society Magazine, M 1932-4529/12, 56-63. doi: 10.1109/MTS.2012.2185275. The argument map is open for debate in AGORA-net, search for map ID 9712.
This argument map represents an argumentation from Heyns, C. . Report of the Special Rapporteur on extrajudicial, summary or arbitrary executions, Christof Heyns . S.l.: United Nations. Human Rights Council. The argument map is open for debate in AGORA-net, search for map ID 9206.