Abductive reasoning

About: Abductive reasoning is a research topic. Over the lifetime, 1917 publications have been published within this topic receiving 44645 citations. The topic is also known as: abduction & abductive inference.

The problem of free will and determinism: an abductive approach

Abstract: This essay begins by dividing the traditional problem of free will and determinism into a “correlation” problem and an “explanation” problem. I then focus on the explanation problem, and argue that a standard form of abductive reasoning (that is, inference to the best explanation) may be useful in solving it. To demonstrate the fruitfulness of the abductive approach, I apply it to three standard accounts of free will. While each account implies the same solution to the correlation problem, each implies a unique solution to the explanationproblem. For example, all libertarian-friendly accounts of free will imply that it is impossible to act freely when determinism is true. However, only a narrow subset of libertarians have the theoretical resources to defend the incompatibilist claim that deterministic laws (qua deterministic) undermine free will, while other libertarians must reject this traditional incompatibilist view.

Musical listening and abductive reasoning: Contributions of C.S. Peirce’s

Abstract: Background in music philosophy. Questions about musical meaning are usually discussed within the area of philosophy of music. These questions gained particular urgencyin the Modern Age, when music had lost its connection with the old cosmologies that assured its position among the other disciplines related to harmony and numbers. In the last centuries philosophers and composers have tried to explain music as art and one of the most prominent attempts was the formalist perspective advocated by Hanslick. From that perspective music is considered on its own without any required connection with something non-musical, and its meaning or its content consists of the very unfolding of musical structures over time that are intelligible to the intellect through some form of reasoning. Background in music psychology. We consider two psychological theories of musical meaning that have been developed by two authors: Leonard Meyer and David Huron. Meyer created a theory of musical meaning based on the Gestalt principles and the practice of music analysis; Huron has constructed a theory based on experimental psychology and statistical analysis of music. On the one hand, both theories are complementary, especially regarding the role hypotheses have in the process of music signification; on the other hand, both lack an explanation of how hypotheses are generated. Aims. This paper aims at connecting the contributions of C.S. Peirce’s philosophy to the studies and investigations of musical meaning. Firstly, we consider his pragmatic concept of meaning; secondly, we analyze the role abductive reasoning has in his logic of discovery, outlining how the generation and evaluation of hypotheses can help to explain an encountered phenomenon. Thirdly, we apply the insights derived from this to an analysis of musical meaning, by indicating how a meaningful interpretation of a musical piece can be provided through the generation of hypotheses about its underlying structure. Main contribution. If the assumption is correct that hypotheses formulation is at the basis of music signification processes, we believe that Peircean philosophy, especially his semiotics, can help to elucidate how hypotheses are generated during music listening, furnishing an interesting and fruitful picture of musical meaning and complementing the psychological perspective on it with a logical and pragmatic point of view. Implications. C.S. Peirce’s thought is extremely interdisciplinary. The Peircean approach to musical meaning in collaboration with empirical studies of music psychology, can offer a more complete logical description of hypothesis generation (the basis of music signification). Moreover, the Peircean approach can strengthen the speculative practice of music philosophy, by providing a pragmatic and logical concept of meaning in music in close dialogue with scientific approaches.

Creativity as a way to innovate successfully

Abstract: Selecting innovative design concepts for further development entails decision making under conditions of sometimes extreme uncertainty pertaining to technical feasibility and market potential. In such situations, decision makers all too often become risk averse and reliant on known metrics that are inherently based on deductive and inductive logics. In prior research, however, good decision making on innovation has been linked with the complementary use of another form of logic: abductive reasoning. Abductive reasoning changes the mind-set of decision makers to become intrinsically forward thinking and explorative towards innovation opportunity. In this paper, we present an experimental study suggesting that the cognitive, creative capabilities of humans correlate positively with their use of abductive reasoning in decision making. We are further able to show that a higher level of abductive reasoning leads to significantly better, i.e. more accurate, decisions in selecting successful innovation concepts. These findings have strong implications for companies seeking to improve their innovative performance, specifically, how and by whom decisions on innovation should be made.

Generating mathematical knowledge in the classroom through proof, refutation, and abductive reasoning

Abstract: Proving and refuting are fundamental aspects of mathematical practice that are intertwined in mathematical activity in which conjectures and proofs are often produced and improved through the back-and-forth transition between attempts to prove and disprove. One aspect underexplored in the education literature is the connection between this activity and the construction by students of knowledge, such as mathematical concepts and theorems, that is new to them. This issue is significant to seeking a better integration of mathematical practice and content, emphasised in curricula in several countries. In this paper, we address this issue by exploring how students generate mathematical knowledge through discovering and handling refutations. We first explicate a model depicting the generation of mathematical knowledge through heuristic refutation (revising conjectures/proofs through discovering and addressing counterexamples) and draw on a model representing different types of abductive reasoning. We employed both models, together with the literature on the teachers’ role in orchestrating whole-class discussion, to analyse a series of classroom lessons involving secondary school students (aged 14–15 years, Grade 9). Our analysis uncovers the process by which the students discovered a counterexample invalidating their proof and then worked via creative abduction where a certain theorem was produced to cope with the counterexample. The paper highlights the roles played by the teacher in supporting the students’ work and the importance of careful task design. One implication is better insight into the form of activity in which students learn mathematical content while engaging in mathematical practice.