Uploaded April 2026 | Updated September 2026, 2 days ago
Carl Friedrich von Weizsäcker Colloquium - April 29, 2026
The determinacy challenge constitutes one of the most forceful objections to the feasibility of a naturalistically acceptable mathematical realism. It asks how mathematical realists can claim to have achieved successful reference to intended mathematical structures in light of the existence of non-standard models of important mathematical theories. Any attempt to overcome the issue is rejected on account of merely shifting the indeterminacy but not resolving it. As a result, moderate mathematical realism is deemed unstable and untenable. Despite its frequent invocation in criticizing realist accounts in the philosophy of mathematics central aspects of the determinacy challenge remain under-investigated. In this talk, I want to clarify the scope and force of the challenge. In doing so, I argue that the mathematical realist has the resources to escape the regress argument and meet the challenge in a naturalistically acceptable manner. Nonetheless, it puts into focus the inherent limitations on what a moderate mathematical realism can hope to achieve.
Carl Friedrich von Weizsäcker Colloquium - April 29, 2026
The determinacy challenge constitutes one of the most forceful objections to the feasibility of a naturalistically acceptable mathematical realism. It asks how mathematical realists can claim to have achieved successful reference to intended mathematical structures in light of the existence of non-standard models of important mathematical theories. Any attempt to overcome the issue is rejected on account of merely shifting the indeterminacy but not resolving it. As a result, moderate mathematical realism is deemed unstable and untenable. Despite its frequent invocation in criticizing realist accounts in the philosophy of mathematics central aspects of the determinacy challenge remain under-investigated. In this talk, I want to clarify the scope and force of the challenge. In doing so, I argue that the mathematical realist has the resources to escape the regress argument and meet the challenge in a naturalistically acceptable manner. Nonetheless, it puts into focus the inherent limitations on what a moderate mathematical realism can hope to achieve.
