Location
University of Windsor
Document Type
Paper
Keywords
ambiguity, bias, infinity, intuitive and formal reasoning, nonstandard analysis, objectivity, paradox, set theory
Start Date
2016 9:00 AM
End Date
2016 5:00 PM
Abstract
This paper presents an overview of several years of my research into individuals’ reasoning, argumentation, and bias when addressing problems, scenarios, and symbols related to mathematical infinity. There is a long history of debate around what constitutes “objective truth” in the realm of mathematical infinity, dating back to ancient Greece (e.g., Dubinsky et al., 2005). Modes of argumentation, hindrances, and intuitions have been largely consistent over the years and across levels of expertise (e.g., Brown et al., 2010; Fischbein et al., 1979, Tsamir, 1999). This presentation examines the interrelated complexities of notions of objectivity, bias, and argumentation as manifested in different presentations and normative interpretations or resolutions of well-known paradoxes of infinity. Paradoxes have been described as occasioning major epistemological reconstructions (e.g., Quine, 1966), and I highlight such occasions as they emerged for both novices and experts with connection to current conceptualisations of objectivity (e.g., Daston, 1992). Of interest is the perception that one single objective truth about “actual” mathematical infinity exists – indeed, this is brought to question at an axiomatic level with both theoretical and empirical research implications.
Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.
Reader's Reactions
Daniel H. Cohen, Commentary on Ami Mamolo on argumentation and infinity (May 2016)
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Exploring argumentation, objectivity, and bias: The case of mathematical infinity
University of Windsor
This paper presents an overview of several years of my research into individuals’ reasoning, argumentation, and bias when addressing problems, scenarios, and symbols related to mathematical infinity. There is a long history of debate around what constitutes “objective truth” in the realm of mathematical infinity, dating back to ancient Greece (e.g., Dubinsky et al., 2005). Modes of argumentation, hindrances, and intuitions have been largely consistent over the years and across levels of expertise (e.g., Brown et al., 2010; Fischbein et al., 1979, Tsamir, 1999). This presentation examines the interrelated complexities of notions of objectivity, bias, and argumentation as manifested in different presentations and normative interpretations or resolutions of well-known paradoxes of infinity. Paradoxes have been described as occasioning major epistemological reconstructions (e.g., Quine, 1966), and I highlight such occasions as they emerged for both novices and experts with connection to current conceptualisations of objectivity (e.g., Daston, 1992). Of interest is the perception that one single objective truth about “actual” mathematical infinity exists – indeed, this is brought to question at an axiomatic level with both theoretical and empirical research implications.
