Project Description

The philosophy of mathematical practice is an endeavor that:

• treats mathematics as a dynamic human activity rather than a static body of results,

• emphasizes the role of human agents, individuals and communities, their practices, cognitive abilities and activities, and how these affect mathematics, 

• engages with “real” mathematics, in contrast to starting from idealized views, such as the idea that “mathematical statements describe a realm of abstract objects” or that “all mathematical proofs are formal proofs”, and

• draws on relevant mathematical content that goes beyond arithmetic and set theory, shifting away from the foundational issues that have dominated 19th- and 20th-century philosophies of mathematics, thus delivering a variety of case studies across a vast range of mathematical disciplines and sub-disciplines. 

Yet, as it stands, the philosophy of mathematical practice has not fully integrated logic. As a result, accounts of logic do not take logicians’ practices and activities into account, and the relationship between logic and philosophy lies almost entirely within the boundaries of “philosophical logic”. This means that the discussion of logic as a discipline and an activity is overshadowed by the application of formal systems to philosophical problems. It follows that the philosophy of logic mostly overlaps with philosophical logic, and questions about logic as an interdisciplinary human endeavor remain unanswered.

PHILPROOF addresses three interconnected dimensions of logic and proof theory, particularly focusing on:

• Epistemology of proofs and proof-theoretic practices.

• Social philosophy of logic and proof-theoretic practices.

• Educational aspects of logic teaching and proof-theoretic practices.

Combining philosophy, social studies, and educational research, the project aims to establish what we refer to as the philosophy of proof-theoretic practice as a novel line of inquiry.