The Role of Abduction in Self-Similarity

Based on the Aristotelian criterion referred to as 'abductio', Peirce suggests a method of hypothetical inference, which operates in a different way than the deductive and inductive methods. “Abduction is nothing but guessing” (Peirce, 7.219). This principle is of extreme value for the study of our understanding of mathematical self-similarity in both of its typical presentations: relative or absolute. For the first case, abduction incarnates the quantitative/qualitative relationships of a self-similar object or process; for the second case, abduction makes understandable the statistical treatment of self-similarity, 'guessing' the continuity of geometric features to the infinity through the use of a systematic stereotype (for instance, the assumption that the general shape of the Sierpiński triangle continuates identically into its particular shapes). The metaphor coined by Peirce, of an exact map containig itself the same exact map (a map of itself), is not only the most important precedent of Mandelbrot’s problem of measuring the boundaries of a continuous irregular surface with a logarithmic ruler, but also still being a useful abstraction for the conceptualisation of relative and absolute self-similarity, and its mechanisms of implementation. It is useful, also, for explaining some of the most basic geometric ontologies as mental constructions: in the notion of infinite convergence of points in the corners of a triangle, or the intuition for defining two parallel straight lines as two lines in a plane that 'never' intersect.

Abductive translation studies : The art of marshalling signs

This dissertation contributes to the fields of theoretical translation studies, semiotic translation theory, and the semiotics of translation. The aim of this work is to explore the alternative and potential which the semiotic approaches to translation entail from the viewpoint of contemporary translation studies. The overall objective is thus to show that a general semiotic translation theory, and in particular, a Peircean translation theory, are possible and indispensable. Furthermore, this study contributes to the semiotranslational approach and to its theory-building by developing the concept of abductive translation (studies). The specific theoretical frame of reference adopted in this study is provided by the semiotranslation introduced by Dinda L. Gorlée. This approach is primarily based on the semeiotic of Charles Sanders Peirce (1839 1914), and aims at a fusion of semiotics and translation studies. A more general framework is provided by the threefold background and material: the published and unpublished writings of Peirce, Peirce scholarship and Peircean-semiotic publications, as well as the translation-theoretical literature. Part One of this study concentrates on the justification, existence, and nature of the semiotic approaches to translation. This part provides a historical survey, a status report, and a discussion of this area of research, by employing the findings in a boundary-clearing that is multilayered both conceptually and terminologically. Part Two deals with Peircean semiotranslation. Here Gorlée s semiotranslational research is examined by focusing on the starting points, features, and development of semiotranslation. Attention is also paid to the state-of-the-art of semiotranslation theory and to the possibilities for future elaborations. Part Three focuses on the semiotranslational claim that translation is an abductive activity. The concept of abductive translation is based on abduction, one of Peirce s three modes of reasoning; at the same time Firstness, the category of abduction, becomes foregrounded. So abductive translation as a form of possibilistic translation receives here an extensive theoretical discussion by citing examples in which abduction manifests itself as (scientific) reasoning and as everyday contemplation. During this treatise, translation is first equated with sign action, then with interpretation and finally with reasoning. All these approaches appear to embody different facets of the same phenomenon Peirce s ubiquitous semiosis, and they all suggest that translation is inherently an intersemiotic activity in which a sign is inferred from another sign. Translation is therefore semiosis, semiosis is translation and interpretation, interpretation is reasoning, and so on ad infinitum all being manifestations of the art of marshalling signs. The three parts of this study are linked by the overall goal of abductive translation studies: investigation into abductive translation develops the theory of semiotranslation, and this enrichment of semiotranslation in turn constructs a semiotic paradigm within translation studies.

On the Origin of Ideas : An Abductivist Approach to Discovery

The purpose of this study is to analyze and develop various forms of abduction as a means of conceptualizing processes of discovery. Abduction was originally presented by Charles S. Peirce (1839-1914) as a "weak", third main mode of inference -- besides deduction and induction -- one which, he proposed, is closely related to many kinds of cognitive processes, such as instincts, perception, practices and mediated activity in general. Both abduction and discovery are controversial issues in philosophy of science. It is often claimed that discovery cannot be a proper subject area for conceptual analysis and, accordingly, abduction cannot serve as a "logic of discovery". I argue, however, that abduction gives essential means for understanding processes of discovery although it cannot give rise to a manual or algorithm for making discoveries. In the first part of the study, I briefly present how the main trend in philosophy of science has, for a long time, been critical towards a systematic account of discovery. Various models have, however, been suggested. I outline a short history of abduction; first Peirce's evolving forms of his theory, and then later developments. Although abduction has not been a major area of research until quite recently, I review some critiques of it and look at the ways it has been analyzed, developed and used in various fields of research. Peirce's own writings and later developments, I argue, leave room for various subsequent interpretations of abduction. The second part of the study consists of six research articles. First I treat "classical" arguments against abduction as a logic of discovery. I show that by developing strategic aspects of abductive inference these arguments can be countered. Nowadays the term 'abduction' is often used as a synonym for the Inference to the Best Explanation (IBE) model. I argue, however, that it is useful to distinguish between IBE ("Harmanian abduction") and "Hansonian abduction"; the latter concentrating on analyzing processes of discovery. The distinctions between loveliness and likeliness, and between potential and actual explanations are more fruitful within Hansonian abduction. I clarify the nature of abduction by using Peirce's distinction between three areas of "semeiotic": grammar, critic, and methodeutic. Grammar (emphasizing "Firstnesses" and iconicity) and methodeutic (i.e., a processual approach) especially, give new means for understanding abduction. Peirce himself held a controversial view that new abductive ideas are products of an instinct and an inference at the same time. I maintain that it is beneficial to make a clear distinction between abductive inference and abductive instinct, on the basis of which both can be developed further. Besides these, I analyze abduction as a part of distributed cognition which emphasizes a long-term interaction with the material, social and cultural environment as a source for abductive ideas. This approach suggests a "trialogical" model in which inquirers are fundamentally connected both to other inquirers and to the objects of inquiry. As for the classical Meno paradox about discovery, I show that abduction provides more than one answer. As my main example of abductive methodology, I analyze the process of Ignaz Semmelweis' research on childbed fever. A central basis for abduction is the claim that discovery is not a sequence of events governed only by processes of chance. Abduction treats those processes which both constrain and instigate the search for new ideas; starting from the use of clues as a starting point for discovery, but continuing in considerations like elegance and 'loveliness'. The study then continues a Peircean-Hansonian research programme by developing abduction as a way of analyzing processes of discovery.