Abstract

In this chapter, Kit Fine and Errol Martin provide a formal account of non-circular reasoning, i.e. of reasoning in which the conclusion of an argument is not somehow presupposed in its premises. Martin (along with R. Meyer) had previously shown that the implicational system P-W\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\textbf{P}\!\mathbf {-W}$$\end{document} does not contain any theorems of the form A→A\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$A \rightarrow A$$\end{document}. Fine and Martin then extend this result to systems that also contain conjunction.