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Project
Cardinal Virtues: A virtue-epistemological investigation of the contemporary foundational issues in set theory (FWOAL793)
Set theorists, those mathematicians concerned with the surprisingly difficult issues connected to set-hood, face the problem that there are natural mathematical questions about sets that provably cannot be answered by the formal machinery of mathematics. The resulting debate, set theorists discussing if new axioms should be accepted and if so which ones, is hence based on non-formalised arguments.
The central issues are connected to epistemological concerns and discussion has been going on for over half a century. Recently however, the debate has reached a level of maturity where a resolution of (some of) the open questions seems possible. To answer which arguments are regarded as convincing in the set theory culture and why, it is important to realise that set theory is a human activity and hence part of our intellectual life. Questions about what set theorists value in these debates and what intellectual virtues they aspire to become the focus of the investigation.
In philosophy, the virtue terminology has recently been fruitfully applied to epistemological questions. The young discipline virtue epistemology has shifted the focus from the epistemic value of beliefs to the intellectual virtues of the actor. We propose to connect the insights of virtue epistemology to the epistemological concerns the set theorists are facing, thereby enriching the two disciplines. Hence, we propose to study the values and virtues of set theory from a virtue epistemological perspective.
The central issues are connected to epistemological concerns and discussion has been going on for over half a century. Recently however, the debate has reached a level of maturity where a resolution of (some of) the open questions seems possible. To answer which arguments are regarded as convincing in the set theory culture and why, it is important to realise that set theory is a human activity and hence part of our intellectual life. Questions about what set theorists value in these debates and what intellectual virtues they aspire to become the focus of the investigation.
In philosophy, the virtue terminology has recently been fruitfully applied to epistemological questions. The young discipline virtue epistemology has shifted the focus from the epistemic value of beliefs to the intellectual virtues of the actor. We propose to connect the insights of virtue epistemology to the epistemological concerns the set theorists are facing, thereby enriching the two disciplines. Hence, we propose to study the values and virtues of set theory from a virtue epistemological perspective.
Date:1 Jan 2016 → 31 Dec 2019
Keywords:Virtue
Disciplines:Communication sciences not elsewhere classified