Proofs, proofs, proofs, and proofs

TL;DR

This paper explores the concept of proof in logic and sociology, examining various forms of proofs and their formal representation to clarify what constitutes a proof in different contexts.

Contribution

It provides a comparative analysis of formal and sociological notions of proof, proposing a broader understanding and implications for formal representation.

Findings

Different forms of proofs are analyzed and contrasted.

A broader, sociological perspective on proofs is proposed.

Implications for formal proof representation are discussed.

Abstract

In logic there is a clear concept of what constitutes a proof and what not. A proof is essentially defined as a finite sequence of formulae which are either axioms or derived by proof rules from formulae earlier in the sequence. Sociologically, however, it is more difficult to say what should constitute a proof and what not. In this paper we will look at different forms of proofs and try to clarify the concept of proof in the wider meaning of the term. This has implications on how proofs should be represented formally.