WEMSK23

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.

Taxonomy:

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

century.

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

10th.

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

vetus.

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

stages."

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.

Logic

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

1950).

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

edition.

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,

1993).

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!