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

Creative Commons Attribution 4.0 License
This work is licensed under a Creative Commons Attribution 4.0 License.

Reader's Reactions

Daniel H. Cohen, Commentary on Ami Mamolo on argumentation and infinity (May 2016)

 
May 18th, 9:00 AM May 21st, 5:00 PM

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.