Robert Kilwardby’s Science of Logic

A Thirteenth-Century Intensional Logic


Author: Paul Thom
Paul Thom’s book presents Kilwardby’s science of logic as a body of demonstrative knowledge about inferences and their validity, about the semantics of non-modal and modal propositions, and about the logic of genus and species. This science is thoroughly intensional. It grounds the logic of inference on that in virtue of which the inference holds. It bases the truth conditions of propositions on relations between conceptual entities. It explains the logic of genus and species through the notion of essence.
Thom interprets this science as a formal logic of intensions with its own proof theory and semantics. This comprehensive reconstruction of Kilwardby’s logic shows the medieval master to be one of the most interesting logicians of the thirteenth century.

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Paul Thom, B.Phil. (Oxford), is Honorary Professor of Philosophy at the University of Sydney and a Fellow of the Australian Academy of Humanities. He has authored numerous books on the history of logic.
"Robert Kilwardby (d. 1279) was almost always of interest to medieval philosophers. This interest, however, has seldom been replicated by modern editorial initiatives, leaving our appreciation of the Oxford master’s intellectual profile incomplete, and perhaps uneven. We are aware of the different contributions that Kilwardby made to metaphysics and to the natural philosophy of his time, and we know that he was a dedicated and influential logician. We may even claim that Kilwardby was a fortunate logician, for he was one of the first scholars in the Latin West to read and to comment on the newly discovered books of Aristotle’s logic. This feature is greatly stressed in Paul Thom’s second book devoted exclusively to Kilwardby’s "science of logic", as described in the title.[...] Thom’s volume already stands as a great and inspiring work for the almost timeless interpretative potential he fairly attributes to Robert Kilwardby’s logic." Edit Anna Lukacs, in Speculum 96/1 , (January 2021).

List of Figures and Tables
1Logic as Science and Art
 1 The Evolution of Logic
 2 The Art of Logic
 3 Branches of the Science of Logic
 4 The Science of Logic as Sermocinal
 5The Science of Logic Distinguished from Other Content in the Organon
 6 Kilwardby’s Writings on Logic
 7 Aspects of Kilwardby’s Thought
 8 Formalisation
2 The Logic of Terms: Categories and Complex Terms
 1 The Categories
 2 Complex Terms
 3 Formal Language
 4 Models
 5 Theorems
3The Logic of Terms: Relations between Terms
 1 The Predicables
 2 Genus and Species
 3 Differentia
 4 Proprium
 5 Accident
 6 Formal Analysis
 7 Formal Language
 8 Models
 9 Truth in a Model
 10 Postulates
 11 Theorems
4 The Logic of Statements: Assertoric Statements
 1 Propositions and Statements
 2 Assertoric Statements
 3 Truth
 4 Ut nunc assertorics
 5 Simpliciter Assertorics
 6 Natural simpliciter Assertorics
 7 Opposition and Equipollence
 8 Conversion
 9 Non-Aristotelian Consequences among Assertorics
 10 Formal Analysis
 11 Theorems
5 The Logic of Statements: Necessity and Possibility Statements
 1 Modal Statements
 2 Necessity Statements
 3 Possibility Statements
 4 Formal Analysis
 5 Formal Language
 6 Models
 7 Theorems
6 The Logic of Statements: Contingency Statements
 1 Unampliated Contingencies
 2 Kilwardby’s Examples
 3 Ampliated Contingencies
 4 Kilwardby’s Rules for the Truth of Ampliated Contingency Statements
 5 Kilwardby’s Examples
 6 Formal Analysis
 7 Theorems
7 The Logic of Inferences: Consequences
 1 Consequences According to the Relations between Terms
 2 Formal Consequences
 3Pure Rules of Consequence
 4Rules of Consequence and Conversion
 5Rules of Consequence and Opposition
 6Rules of Consequence, Opposition and Repugnance
 7Rules of Consequence and Possibility
 8Rules of Consequence and Assertion
 9Rules of Consequence and Denial
 10Essential Consequences
 11Essential Consequence and Essential Inseparability
 12Syllogistic Consequences
 13Formal Analysis
 14Truth Conditions
8The Logic of Inferences: Assertoric Syllogisms
 1Syllogistic Figures and Moods
 4Being Said of All
 5Families of Syllogism
 6Principles, Validity, Perfectibility
 7Mixed ut nunc / simpliciter Inferences
 9Formal Analysis
 10Generative Rules
9The Logic of Inferences: Necessity Syllogisms
 1Family 3. The LLL Family
 2Principles for LL Premises
 3Being Said of All
 6Family 4. The LXlL Family
 7Principles for L / Xl Premises
 8Being Said of All
 9Inferences Related to the Perfect Syllogisms
 12Formal Analysis
10The Logic of Inferences: Contingency Syllogisms
 1Unrestricted Syllogistic Conversion in Family 3
 2Unrestricted Syllogistic Conversion in Family 4
 3Family 5. The Q’ Q’ Q’ Family
 4Family 6. The QXlQ Family
 5Family 7. The QLQ Family
 6Formal Analysis
11The Logic of Inferences: Non-perfectible Inferences
 1xq Premises
 2Realised Modals
 3Formal Analysis
Modern Author Index
Subject Index
Ancient an Medieval Author Index
Anyone interested in the history of medieval logic, anyone interested in Kilwardby’s thought, and anyone interested in ways to develop intensional logics.