This is a work in progress
on Medieval Logic. Elsewhere, I have described part of the tradition of
medieval logic in relatively non-technical terms ("The Development of
Supposition Theory in the Later 12th through 14th Centuries," Gabbay,
Dov and John Woods, Handbook of the History of Logic, vol
2, Elsevier 2008). The point of the present project is to work
out the formal logical details. I see a rich system of logic in the various discussions
by medieval logicians. The point of this project is to articulate their ideas
in comtemporary terms, while being accurate about
their doctrines. I am making parts of this work available here because I
believe that there is much here that will be of interest to others, and which
they will be able to refine and extend, even lacking a finished project on my
part. If I try to hold off until I have a completed document, I'll likely
never finish, and nobody will ever see it. So here it is (part of it anyway).
More parts will be added, and existing ones revised. You get what I have at
the moment.
Some Logicians in the Aristotelian
Tradition
1 An Overview of Aristotle's Logic
1 Categorical Propositions
2 Logical Relations among Categorical Propositions
3 The Square of Opposition
4 Issues Concerning Empty Terms
5 Conversions
6 Syllogisms
7 Infinite Negation
8 Formal Validity
2 Aristotle's Proofs of Conversions and
Syllogisms
1 Formal Derivations
2 Proofs of the Conversion Principles
3 Reduction of all Syllogisms to Perfect Ones
4 Proving the First Figure Syllogisms
5 Propositions with Repeated Terms
6 The Indispensability of Exposition and Expository Syllogism
7 A Contemporary Assessment of Aristotle’s Basic Theory
8 Singular Propositions
Appendix: Summary of Aristotle's Rules of Proof
3 Molecular Propositions in Ancient Logic
4 Syllogistic in 13th Century
Textbooks and Later
1 13th
Century Texts
2 14th Century Short Works
3 Algorithms without Figure and Mood
5 Quantifying Predicates, Singular Term
Predicates, Negative Terms
1 Expanded Notation
2 Equipollences
3 Semantics and Rules
4 Singular Terms as Predicates
5 Infinitizing Negation and Conversion
6 Completeness of the Rules
Appendix: Summary of the Rules of Proof used so far
6 Basic Linguish
1 Basics
2 Categorical Propositional Logical Forms
3 Rules of Inference
4 Signification and Supposition
5 Truth Conditions
6 Validity
7 Completeness of the Rules
8 Soundness of the Rules
7 Expanding the Notation
1 Adjectives
2 Intransitive Verbs
3 Transitive Verbs
4 Additional Rules for Parasitic Terms
5 Some Complex Terms
6 Relative Clauses
7 Genitives
8 Demonstratives
9 Molecular propositions
8 Some Illustrative Cases
1 Relational Expressions
and DeMorgan's Challenge
2 Buridan on Subjects and Predicates
3 Simple and Complex Terms
9 Modes of Personal Supposition
0 Introduction
1 The Fourteenth Century Definitions of the Modes
2 Clarification of the Definitions
3 Causes of the modes
4 Restricted Descent and Parasitic Terms
5 A Variant Account of Merely Confused Supposition
6 Useful Inferences
7 Refining the Theory
8 Causes of the Refined Modes
9 Useful Inferences Again
10 Modes of Supposition as Analyses of Quantification
11 Global Quantificational Import
10 Relatives (Anaphoric Words)
1 Relatives of Identity
2 Reflexive Pronouns
3 Bound-Variable Relatives in Linguish
4 Non-Reflexive Relatives of Identity
5 Complex Propositions in Linguish
6 An Application of Relatives to Syllogistic
7 Donkey Anaphora
8 Common term Relatives of Identity and Diversity
11 Comparison of Medieval Logic with
Contemporary Logic
1 The Expressive Power of
Medieval Logic
2 Representing Medieval Logic within Modern Predicate Logic with Identity
3 Representing Modern Logic with Medieval Logic; The Problem of Existential
Import
4 Representing Modern Logic with Medieval Logic; Grammatical Issues
5 First-Order Arithmetic in Medieval Logic
12 Ampliation
and Restriction
1 Univocation
as the Source of Ampliation and Restriction
2 Ampliation and Restriction by Tenses
3 Ampliation by Modal Terms
4 Ampliation due to Words which Pertain to the Soul
5 Promising
6 Ampliation due to Semantic Terms
13 Artificial Quantifiers in Early 16th
Century Logic
1 The Signs
2 What the Signs Mean
3 The Signs are, in a sense, Logically Dispensible
4 A Doubt: Certain Examples do not work as advertised
5 Another Doubt: The paradigm use of the sign 'd' is incoherent
6 Some Examples from John Major
Bibliography