Sum of Logic

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Sum of Logic

The "Summa Logicae" is a textbook on logic by William of Ockham. It was written around 1323.

Systematically, it resembles other works of medieval logic, organised under the basic headings of the Aristotelian Predicables, Categories, terms, propositions, and syllogisms. These headings, though often given in a different order, represent the basic arrangement of all scholastic textbooks.

This work is important in that it contains the main account of Ockham's nominalism. The nominalists of the fifteenth century (such as Swineshead, Heytesbury, Gerson and D'Ailly) looked upon him as the founder of their school.

Book I: On Terms

(i) Chapters 1-17 deal with terms: what they are, and how they are divide into categorematic, abstract and concrete, absolute and connotative, 'first intention' and 'second intention'. Ockham also introduces the issue of universals here.

(ii) Chapters 18-25 deal with the five predicables of Porphyry.

(iii) Chapters 26-62 deal with the Categories of Aristotle, known to the medieval philosophers as the 'Praedicamenta'. The first chapters of this section concern definition and description, the notions of subject and predicate, the meaning of terms like 'whole', 'being' and so on. The later chapters deal with the ten Categories themselves, as follows: Substance (42-3), Quantity (44-9), Relation (50-4), Quality (55-6), Action (57), Passion (58), Time (59), Place (60), Position (61), Habit (62).

(iv) Chapters 63-77 onwards deal with the theory of supposition.

Book II: On Propositions

(i) On categorical propositions (1-20)

(ii) On the conversion of propositions (21-9)

(iii) On hypothetical propositions (30-7)

Book III: On Syllogisms

Part I On Syllogisms

(i) On categorical syllogisms (1-19)

(ii) On modal syllogisms (20-30)

(iii) On mixed syllogisms (31-64)

(iv) On syllogisms containing exponible propositions

Part II On Demonstration

These 41 chapters are a systematic exposition of Aristotle's Posterior Analytics.

Part III On the Consequences

These 37 chapters are a systematic exposition of Aristotle's Topics.

Part IV On Obligation (7 chapters)

Part V On the Liar Antinomy (1 chapter)

Part VI On fallacies (in 18 chapters)

* [http://www.iupui.edu/~peirce/writings/v2/w2/w2_32/v2_32.htm Peirce's translation and commentary]
* [http://www.amazon.com/dp/1890318507 Michael Loux's translation of Book I]
* "Ockham's Theory of Propositions": Part II of the Summa Logicae, translated by Alfred J. Freddoso and Henry Schuurman and introduced by Alfred J. Freddoso (Notre Dame, IN: University of Notre Dame Press, 1980), Reprinted: South Bend, IN: St. Augustine's Press, 1998
* Parallel [http://uk.geocities.com/frege@btinternet.com/logicalform/ockhamlogicalform.htm Latin-English translation] of chapters 1, 3, 12 and 13 of the "Summa Logicae " by Edward Buckner, in the Logic Museum.
* [http://home.riise.hiroshima-u.ac.jp/~akyah59/ock.sl.index.html Books I and II online] (Latin only)

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