Line Diagrams for Logic. Drawing Conclusions

This book makes two important contributions to philosophical scholarship. It presents a number of reasons for the reinstatement of a traditional terminist logic, contributing to the ongoing debate concerning the proper connections between formal logic, natural language, artificial reasoning, and mathematics. This debate touches of number of crucial areas in logic, cognitive psychology, artificial intelligence research, and linguistics. As well, the system of linear diagrams for logic presented here allows for the first time ever the diagrammatic analysis of all the kinds of inferences (in particular, those involving relationals) within the scope of modern standard logic.


". . . a remarkable work. . . . it presents every essential element of term logic, presented concisely and persuasively. It also lays out an ingenious new system of representing inferences diagrammatically. Having so concise and thorough a work available will make it significantly easier for scholars to acquaint themselves with this body of knowledge." – David Kelley, author of The Art of Reasoning (W. W. Norton) "The diagram system – along with the analyses of the historical problems it is proposed to resolve, the discussion of the wider philosophical implications of the approach, and the cases he makes against the alternatives – are, in my opinion, masterfully woven together into an organic whole." – Wallace A. Murphree

"Englebretsen has developed a new system of linear diagrams for representing and testing syllogisms and syllogistic types of arguments with relations. His work is groundbreaking and extremely innovative. It has not yet received the attention it deserves. I predict that ‘Englebretson Diagrams' will, eventually, be recognized to be just as important as Edwards Diagrams' and ‘Venn diagrams'. " – Philip L. Peterson

Table of Contents

Table of Contents:

Preface, Introduction

1.Reasoning with diagrams

2.Syntax and diagrams

3.A word about truth

4.Diagramming categoricals and singulars

5.Compound terms and negative names

6.Compound names

7.Syllogistic inference


9.Reflexive and personal pronouns

10.The dictum de omni

11.Statement logic as a special part of term logic

12.Diagramming unanalyzed statements

13.Final Remarks

Appendix, References