Structural realism, mathematics, and ontology.

Area of Science:

• Philosophy of Science
• Metaphysics
• Philosophy of Mathematics

Background:

• Structural realism has evolved significantly over the past two decades.
• Steven French's work, particularly "The Structure of the World" (2014), offers a sophisticated and historically informed version of ontic structural realism.
• Ontic structural realism posits that structure is the fundamental constituent of reality.

Purpose of the Study:

• To analyze the specific role and status of mathematics within Steven French's ontic structural realism.
• To critically evaluate the compatibility and coherence of mathematical entities within the realist framework of French's theory.
• To identify and discuss potential concerns regarding the understanding of mathematics in relation to the core tenets of ontic structural realism.

Main Methods:

• Conceptual analysis of Steven French's ontic structural realism.
• Examination of the implications of ontic structural realism for the philosophy of mathematics.
• Critical engagement with the realist components of French's view concerning mathematical structures.

Main Results:

• French's ontic structural realism provides novel insights into issues like underdetermination, scientific representation, and laws of nature.
• The paper identifies specific challenges in fully integrating the understanding of mathematics within French's ontic structural realism.
• Concerns are raised regarding the precise realist interpretation of mathematical elements in the context of structuralism.

Conclusions:

• Steven French's ontic structural realism offers a powerful lens for understanding scientific phenomena.
• The paper highlights a tension between the realist commitments of ontic structural realism and the philosophical treatment of mathematics.
• Further philosophical inquiry is needed to resolve the status of mathematics within this influential scientific realism framework.