Entitlement theories: a non-evidentialist Epistemology of Mathematics

seminaria monograficzne

This course introduces and discusses a novel approach in the epistemology of mathematics: Entitlement theories. Inspired by the work of Crispin Wright, entitlement theories take a new perspective on general, well-known issues in the Epistemology of Mathematics.

In a nutshell, entitlement theories introduce a new notion of mathematical justification, which - contrary to our ordinary mathematical justification - is non-evidential. Originally, philosophers developed the idea of entitlement in the context of mainstream epistemology as a response to scepticism about perceptual justification. Since then, entitlement has helped philosophers provide a more fine-grained epistemology of perception. Recently, philosophers started to employ this very notion of entitlement to tackle essential questions in the epistemology of mathematics. The introduction of this additional type of justification helps us have a better, more fine-grained understanding of the epistemology of mathematics, more in harmony with our epistemology of science. Finally, the addition of entitlement opens several crucial philosophical questions: how does entitlement relate to ordinary evidential justification? How does it relate to the possibility of defeaters? Is it rational to believe our entitlements? What is the logic of entitlement? Can entitlements be known? This course aims to introduce entitlement theories and their connection to the original literature by Wright, Pryor, and others to provide the students with the knowledge and understanding needed to tackle these research questions.

Audience: The seminar is open to everyone. However, the course is tailored for advanced philosophy students interested in the philosophy of mathematics or epistemology. Basic knowledge of epistemology and (some) questions in the philosophy of mathematics is helpful but optional. The seminar's topic is philosophical, and the seminar aims to be accessible to those without a strong background in mathematical logic.

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Burge, T. (2020). Entitlement: The basis for empirical epistemic warrant. In Pedersen, N. and Graham, P., editors, Epistemic Entitlement, pages 37–142. Oxford University Press.

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Fischer, M., Horsten, L., and Nicolai, C. (2019). Hypatia's silence truth justification and entitlement. Noˆus. online first doi: 10.1111/nous.12292.

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– 300

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fregean programme. In Ebert, P. and Rossberg, M., editors, Abstractionism. Oxford University Press.

Pedersen, N. J. L. L. (2021). Cornerstone epistemology: scepticism, mathematics,non- evidentialism, consequentialism, pluralism. In Pedersen, N. J. L. L. and Moretti , L., editors, Non-Evidentialist epistemology. Brill

Pryor, J. (2000). The skeptic and the dogmatist. Noˆus, 34(4):517–549.

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Wright, C. (2003). Some reflections on the acquisition of warrant by inference. In Nuccetelli, S., editor, New Essays on Semantic Externalism and Self-Knowledge, pages 57–78. MIT Press.

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Wright, C. (2012). Replies part iv: Warrant, transmission and entitlement. In Coliva, A., editor, Mind, Meaning, and Knowledge. Themes from the Philosophy of Crispin Wright, pages 451–486. Oxford University Press.

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Wright, C. (2016). Abstraction and epistemic entitlement: On the epistemological status of hume's principle. In Ebert, P. A. and Rossberg, M., editors, Abstractionism: Essays in Philosophy of Mathematics, pages 161–185. Oxford University Press.

Acquired knowledge:

• Know the basic notion involved in entitlement theories in their original context: the

epistemology of perception.

• Understand how entitlement theories work in a mathematical context. Have acquaintance with the relevant literature on mathematical entitlement.

• Know the basic positions concerning the structure of justification: conservativism and liberalism.

• Know the relevant distinctions between closure and transmission of justification across valid arguments.

Acquired skills

• The ability to apply tools and context from pure epistemology to within the context of the philosophy of mathematics.

• The ability to evaluate the epistemic good standing of arguments (from the perspective of transmission)

Acquired social competences:

• Has the ability to work in a team.

• Understands and appreciates the need for training and professional development

Assessment methods and criteria: a seminar presentation or a submitted essay.

Number of absences: 2