Rigorous Deductive Argumentation for Socially Relevant Issues

TL;DR

This paper advocates for using classical first-order logic to construct rigorous deductive arguments on complex societal issues involving vagueness and subjectivity, supported by formal proof frameworks and a collaborative web system.

Contribution

It demonstrates that classical logic suffices for formalizing arguments on vague and subjective issues and develops a framework and web tool for collaborative argumentation.

Findings

Formal proofs can handle vagueness and subjectivity

A framework for criticizing arguments is presented

Progress towards a collaborative web platform is documented

Abstract

The most important problems for society are describable only in vague terms, dependent on subjective positions, and missing highly relevant data. This thesis is intended to revive and further develop the view that giving non-trivial, rigorous deductive arguments concerning such problems -without eliminating the complications of vagueness, subjectivity, and uncertainty- is, though very difficult, not problematic in principle, does not require the invention of new logics -classical first-order logic will do- and is something that more mathematically-inclined people should be pursuing. The framework of interpreted formal proofs is presented for formalizing and criticizing rigorous deductive arguments about vague, subjective, and uncertain issues, and its adequacy is supported largely by a number of major examples. This thesis also documents progress towards a web system for collaboratively authoring and criticizing such arguments, which is the ultimate goal of this project.