Logic / Dialectic

The student should not get the idea that there is such a thing as
a medieval logic which is hermetically sealed off from the other
parts of the trivium.  Medieval logic is for the most part language
logic (almost any text in logic before Boole can be said to be
'medieval' in its outlook and formulations).  Look also at the
sections on medieval rhetoric and grammar.


    The study and history of medieval logic can be divided into
many parts (cf: M. Grabmann, "Aristoteles im 12. Jh.," Medieval
Studies 12 (1950) 123-162.  The basis for logical study in the 12th
and 13th century was formed by the logical works of Aristotle and
Boethius, together with the Isagoge of Porphyry.  This corpus
logicum is divided into two parts, the Logica vetus and the Logica
nova, the latter becoming known during the course of the 12th

   I. Logica vetus: Isagoge of Porphyry, the Categories and the
Perihermeneias of Aristot1e, the commentaries of Boethius on
the Isagoge as translated by Marius Victorinus and Boethius'
own translations, the commentary of Boethius on the Categories
in 4 books, the commentaries of Boethius on the Perihermeneias, an
elementary one in two books and a more complete one in 5 books,
finally the logical tractates of Boethius himself: Introductio ad
syllogismos categoricos, De Syllogismo categorico, De Syllogismo
hypothetico, De Divisione, De Differentiis Topicis and an
incomplete (up to chap. 76) commentary on Cicero's Topica.

2. Logica nova: Aristotle's other logical writings: Analytica
prioria, Analytica posteriora, Topica and De Sophisticis Elenchis
plus Gilbert de la Porree's Liber sex princip.  In the course of
the 12th century, there developed a logica modernorum, in which
Aristotle's Organon was extended by the following: De
Suppositionibus, De Fallaciis, de Relativis, De Ampliationibus,
De appellationibus, De Restrictionibus, De Distributionibus. The
authors who are members of the logica modernorum movement; to name
Just a few, are: William of Shyrewood, Petrus Hispanus, Lambert of
Auxerre, Abelard, Ockham.

Following A. van den Vyver ("Les etapes du developpement
philosophique du haut moyen-age," Revue belge de philolophie et
d'histoire VIII (1929) 425-52, we may set up the following stages
in the development of Aristotelian/Boethian logic:

I.  The first period (7th and 8th centuries) is an alogical period,
in which we find preferred the Etymologiae of Isidor of Seville,
Cassiodor, Martianus Capella and the pseudo-Augustine Categoriae.

2.  In the 9th and 10th also we find the above works, but already
in Alcuin and John Scotus we find the Isagoge of Porphyry, the
Perihermenias and the Topica of Cicero, along with Boethius'
commentaries.  Boethius' translation of the Isagoge, the Categories
and the Perihermenias, as well as Boethius' commentaries on ths
first parts of the Organon become known first at the end of the

3. In the 11th and the first part of the 12th, the commentaries
and the logical tractates of Boethius become more and more used.
Manuscripts of the logica vetus (Isagoge, Categories,
Interpretation and Boethius) become more and more common.  As
example, let us take Notker of St. Gall (died 1022): He translated
the following works: Ancient authors (Cato, Virgil, Terence, etc.),
the Psalms, The Book of Job, The Moralia of Gregory the Great, the
Consolation of Philosophy of Boethius, the Aristotelian writings
Categories and Interpretation, adding the commentaries of Boethius.

He also wrote logical tractates of his own, De partibus logicae and
De Syllogismo, along with a Dialectica.  We may consider him to be
a representative of the age, these books represent the logica

4 The most important event in the influence of Aristotle was the
introduction, during the 12th century, of the rest of his logical
writings: The prior and posterior analytics, the topics and the
sophistic refutations, in other words, the logica nova.

5. All kinds of `splinter' groups arose, e.g. the Modistae, from
which we have Langland's _ex vi transitionis_.  A
logician/grammarian even became Pope.

6. Just a TAN PS on Aristotle and class logic: Susan Stebbing, A
Modern Introduction to Logic, p. 435:

"Principles regulating a logical division...
l. There must be only one fundamentum divisionis at each step.
2. The division must be exhaustive.
3. The successive steps of the division must proceed by gradual

All of this merely to assure that the definition is _per proximum
genus et differentiam (vel differentias)_, the only way to have a
watertight definition.

NB: In working with the syllogism, remember the sorites, a piling
up of propositions, an extended syllogism if you will, and the
enthymeme, a syllogism with one of the propositions suppressed,
e.g. `she is a woman and may be won' (= All women may be won, she
is a woman, ergo, she may be won).

Learn your Barbara celarent.


It is important that one keep in mind that there are many kinds of
logic.  Nowadays, there is an unfortunate tendency to equate logic
with `formal logic', `sentential calculus' and the like, with its
Aristotelian bias.  There are many other types, such as deontic
logic, language logic, modal logic, etc.  A good place to look for
a general taxonomy would be the various "Maps of Logic" put out by
Nicholas Rescher, e.g. "A Map of Logic" and "A Concise Bibliography
of Philosophical Logic" in his Topics in Philosophical Logic.
Synthese Library (Dordrecht: Reidel, 1968), 6-13.

1. If you need an easy survey of logic, look at Susan Stebbing, A
Modern Introduction to Logic. Harper Torchbooks.  The Science
Library, TB 538 (NY: Harper, 1961; a repr. of the 7th edition of

2. Guides:

a. For a quick guide to medieval logic, you cannot beat Earline J.
Ashworth, "Logic, Medieval," in Routledge Encyclopedia of
Philosophy, gen. ed. Edward Craig, vol. 5 (London: Routledge,
1998), 746-759. Also available on CD-ROM.  In fact, one ought to
read the whole series of works on logic in this encyclopedia.

b. Alexander Broadie, Introduction to Medieval Logic, 2d ed.
(Oxford: Clarendon, 1993). Ashworth warns against the first

c. Philotheus Boehner, Medieval Logic. An Outline of its
Development from 1250 - c. 1400 (Manchester: University of
Manchester Press, 1952). A good, readable survey.

d. Desmond Paul Henry, Medieval Logic and Metaphysics: A Modern
Introduction (London: Hutchinson, 1972). Short, solid.

e. Ernest A. Moody, Truth and Consequence in Mediaeval Logic.
Studies in Logic and the Foundaitons of Mathematics (Amsterdam:
North Holland, 1953). In spite of its title, a good introduction to
medieval logic in general; unfortunately uses some modern notation;
if this confuses you, skip that part.

3. A good bibliographical guide is: Earline J. Ashworth, The
Tradition of Medieval Logic and Speculative Grammar from Anselm to
the End of the 17th Century: A Bibliography from 1836 Onwards
(Toronto: Pontifical Institute of Medieval Studies, 1978).  Good
annotations; good index.

4. History of logic:

a. Carl Prantl, Geschichte der Logik im Abendlande, 4 vol. in 3
(Berlin: Akademie-Verlage, 1955; repr. of the 1855 ed.). Excellent
history with copious citations in the original language.

b. William and Martha Kneale, The Development of Logic (Oxford:
Clarendon, 1962; corrected, 1964). The standard text.

5. Readers:

a. Norman Kretzmann and Eleonore Stump, The Cambridge Translations
of Medieval Philosophical Texts, vol. 1: Logic and the Philosophy
of Language (Cambridge: CUP, 1988).  The translations are designed
to supplement The Cambridge History of Later Medieval Philosophy,
ed. Norman Kretzmann and Jan Pinborg (Cambridge: CUP, 1982), which
is devoted to a great extent to logic between 1200 and 1350.  The
selections are good, but the book seems a little expensive to me.

b. Innocentius M. Bochenski, Formale Logik, 2d ed.
(Freiburg/Munich: Orbis Academicus, 1956). Engl. Translation by Ivo
Thomas, A History of Formal Logic (Notre Dame University Press,
1961). An excellent collection of sources, with a large
bibliographical supplement.  First port of call.

c. A good selection of somewhat earlier texts is offered by:
Classics in Logic, ed. Dagobert D. Runes (NY: Philosophical
Library, 1962).

d. Lambertus Marie de Rijk, Logica modernorum; a contribution to
the history of early terminist logic. Wijsgerige teksten en studies
6. 2 vols. in 3 (Assen, Van Gorcum, 1962-67). TOC: v. 1. On the
twelfth century theories of fallacy. -- v. 2. The origin and early
development of the theory of supposition. Vol.1 includes the full
Latin texts of the main treatises on which the author's study is
based. Vol. 2.1 is mostly on grammar. Discussion and examples.

e. Lorenzo Minio-Paluello, Twelfth Century Logic. Texts and Studies
(Rome: Edizioni di Storia e Letteratura, 1956-58). TOC: 1. Adamus
Balsamiensis, Parvipontani. Ars disserendi (dialectica Alexandri)
-- 2. Abaelardiana inedita. Super Periermenias XII-XIV. Sententie
secundum M. Petrum.

6. With these you have a good history of the subject and detailed
treatment.  There are also good treatments of individual authors
and problems, of which I can only cite a few:

a. Henryk Lagerlund, Modal Syllogistics in the Middle Ages (Leiden:
Brill, 2000).

b. Norman Kretzmann, William of Sherwood's Introduction to Logic
(Minneapolis: Univ. of Minnesota Press, 1966).

c. Joseph P. Mullally, The Summulae Logicales of Peter of Spain
(Notre Dame University Press, 1945).

d.  Philotheus Boehner, William Ockham: Philosophical Writings: A
Selection. Library of Liberal Arts 193 (Indianapolis: Bobbs-
Merrill, 1964; original Nelson's Philosophical Texts, 1957).

e. Peter of Spain, Tractatus syncategorematum and Selected
Anonymous Treatises, tr. Joseph P. Mullally (Milwaukee: Marquette
U. Press, 1964).

f. John Buridan, Sophisms on Meaning and Truth, tr. Kermit Scott.
Century Philosophy Sourcebooks (NYP: Meredith, 1966).

g. Curtis Wilson, William Heytesbury, Medieval Logic and the Rise
of Mathematical Physics. University of Wisconsin Publications in
Medieval Science 3 (Madison: UWiscPress, 1960).

9. The study of logic infected everything, as we know from the
mention of the moods of the syllogism, such things as Piers
Plowman's ex vi transitionis, etc.

a. P. Osmund Lewry, "Grammar, Logic and Rhetoric 1220-1320," The
History of the University of Oxford, Vol. 1: The Early Oxford
Schools, ed. J. I. Catto (Oxford: Clarendon, 1984), 401-33. Good on
the teaching of logic.

b. Alfonso Maieru, University Training in Medieval Europe, tr.
Darleen N. Pryds. Education and Society in the Middle Ages and
Renaissance 3 (Leiden: Brill, 1994). Particularly Chapter 2:
"Academic Exercises in Italian Universities" and Chapter 5:
"Methods of Teaching Logic during the Period of the Universities."

c. Eugene Vance, From Topic to Tale: Logic and Narrativity int he
Middle Ages. Theory and History of Literature 47 (Minneapolis:
University of Minnesota Press, 1987). Strongly influenced by
Kretzmann and Stump.

d. J. Stephen Russell, Chaucer and the Trivium: The Mindsong of the
Canterbury Tales (Gainesville: University Press of Florida, 1998).
I liked his Chapter 1: "A Medieval Education and Its Implications."

e. Ross G. Arthur, Medieval Sign Theory and Sir Gawain and the
Green Knight (Toronto: UToronto Press, 1987).

10. It is good to look at collected papers of conventions, to get
a notion of directions in which the field is going.  I just name a
few, which will lead you to others:

a. European Symposium on Medieval Logic and Semantics (9th: 1990:
St. Andrews, Scotland). Title: Sophisms in Medieval Logic and
Grammar: Acts of The Ninth European Symposium for Medieval Logic
and Semantics, held at St. Andrews, June 1990, ed. Stephen Read.
Nijhoff International Philosophy Series 48 (Dordrecht: Kluwer,

b. European Symposium on Medieval Logic and Semantics (12th: 1997:
Pamplona, Spain) Title: Medieval and Renaissance Logic in Spain:
Acts of The 12th European Symposium on Medieval Logic and
Semantics, held at the University of Navarre (Pamplona, 26-30 May
1997), edited by Ignacio Angelelli and Paloma Perez-Ilzarbe.
Philosophische Texte und Studien 54 (Hildesheim: Olms, 2000.

c. Studies on the History of Logic. Proceedings of the III.
Symposium on the History of Logic, ed. Ignacio Angelelli and Maria
Cerezo. Perspektiven der Analytischen Philosophie 8 (Berlin: de
Gruyter, 1996).

11. If the syllogism and its ramificaitons confuse you:

a. Otto Bird, Syllogistic and Its Extensions. Prentice-Hall
Fundamentals of Logic Series (Englewood Cliffs, NJ: Prentice-Hall,
1964). Uses modern notation.

b. A fundamental work on the syllogism is: Jan Lukasiewicz,
Aristotle's Syllogistic from the Standpoint of Modern Formal Logic,
2d ed. (Oxford: Clarendon, 1957). A famous book. {If it is
important, note that his name begins with L/ "Polish l"). Damned ASCII!