The ''Summa Logicae'' ("Sum of Logic") is a textbook on

logic Logic is the study of correct reasoning. It includes both formal and informal logic. Formal logic is the study of deductively valid inferences or logical truths. It examines how conclusions follow from premises based on the structure o ...

William of Ockham William of Ockham or Occam ( ; ; 9/10 April 1347) was an English Franciscan friar, scholastic philosopher, apologist, and theologian, who was born in Ockham, a small village in Surrey. He is considered to be one of the major figures of medie ...

. It was written around 1323. Systematically, it resembles other works of medieval logic, organised under the basic headings of the Aristotelian Predicables, Categories, terms,

proposition A proposition is a statement that can be either true or false. It is a central concept in the philosophy of language, semantics, logic, and related fields. Propositions are the object s denoted by declarative sentences; for example, "The sky ...

s, and

syllogism A syllogism (, ''syllogismos'', 'conclusion, inference') is a kind of logical argument that applies deductive reasoning to arrive at a conclusion based on two propositions that are asserted or assumed to be true. In its earliest form (defin ...

s. These headings, though often given in a different order, represent the basic arrangement of scholastic works on logic. This work is important in that it contains the main account of Ockham's

nominalism In metaphysics, nominalism is the view that universals and abstract objects do not actually exist other than being merely names or labels. There are two main versions of nominalism. One denies the existence of universals—that which can be inst ...

, a position related to the

problem of universals The problem of universals is an ancient question from metaphysics that has inspired a range of philosophical topics and disputes: "Should the properties an object has in common with other objects, such as color and shape, be considered to exist ...

Book I. On Terms

Book II. On Propositions

Book III. On Syllogisms

Part I. On Syllogisms

Part II. On Demonstration

* These 41 chapters are a systematic exposition of Aristotle's

Posterior Analytics The ''Posterior Analytics'' (; ) is a text from Aristotle's '' Organon'' that deals with demonstration, definition, and scientific knowledge. The demonstration is distinguished as ''a syllogism productive of scientific knowledge'', while the de ...

Part III. On Consequences

* The first 37 chapters of Part II are a systematic exposition of Aristotle's Topics. In Part III, Ockham deals with the definition and division of consequences, and provides a treatment of Aristotle's Topical rules. According to Ockham a consequence is a conditional proposition, composed of two categorical propositions by the terms 'if' and 'then'. For example, 'if a man runs, then God exists' (''Si homo currit, Deus est'').Boehner pp. 54–5 A consequence is 'true' when the antecedent implies the consequent. Ockham distinguishes between 'material' and 'formal' consequences, which are roughly equivalent to the modern material implication and

logical implication Logic is the study of correct reasoning. It includes both formal and informal logic. Formal logic is the study of deductively valid inferences or logical truths. It examines how conclusions follow from premises based on the structure of ...

respectively. Similar accounts are given by

Jean Buridan Jean Buridan (; ; Latin: ''Johannes Buridanus''; – ) was an influential 14thcentury French scholastic philosopher. Buridan taught in the faculty of arts at the University of Paris for his entire career and focused in particular on logic and ...

and Albert of Saxony. * Chapters 38 to 45 deal with the Theory of obligationes. *Chapter 46 deals with the

Liar Paradox In philosophy and logic, the classical liar paradox or liar's paradox or antinomy of the liar is the statement of a liar that they are lying: for instance, declaring that "I am lying". If the liar is indeed lying, then the liar is telling the trut ...

Part VI. On Fallacies (in 18 chapters)

Part IV, in eighteen chapters, deals with the different species of fallacy enumerated by Aristotle in

Sophistical Refutations ''Sophistical Refutations'' (; ) is a text in Aristotle's ''Organon'' in which he identified thirteen fallacies.Sometimes listed as twelve. According to Aristotle, this is the first work to treat the subject of deductive reasoning in ancient Gree ...

(''De sophisticis elenchis''). *Chapters 2-4 deal with the three modes of

equivocation In logic, equivocation ("calling two different things by the same name") is an informal fallacy resulting from the use of a particular word or expression in multiple senses within an argument. It is a type of ambiguity that stems from a phrase ...

. *Chapters 5-7 deal with the three types of amphiboly. *Chapter 8 deals with the fallacies of

composition Composition or Compositions may refer to: Arts and literature *Composition (dance), practice and teaching of choreography * Composition (language), in literature and rhetoric, producing a work in spoken tradition and written discourse, to include ...

, and division. *Chapter 9 deals with the fallacy of accent. *Chapter 10 deals with the fallacy of 'figure of speech'. *Chapter 11 deals with the fallacy of accident. *Chapter 12 deals with the fallacy of

affirming the consequent In propositional logic, affirming the consequent (also known as converse error, fallacy of the converse, or confusion of necessity and sufficiency) is a formal fallacy (or an invalid form of argument) that is committed when, in the context of a ...

. *Chapter 13 deals with '' secundum quid et simpliciter''. *Chapter 14 deals with Ignoratio elenchi or irrelevant thesis. *Chapter 15 deals with

begging the question In classical rhetoric and logic, begging the question or assuming the conclusion (Latin: ) is an informal fallacy that occurs when an argument's premises assume the truth of the conclusion. Historically, begging the question refers to a fault i ...

(''petitio principii''). *Chapter 16 deals with false cause (''non-causam ut causam'') *Chapter 17 deals with the fallacy of many questions (''plures interrogationes ut unam facere'')> *Ockham ends (chapter 18) by showing how all these fallacies err against the syllogism.

Notes

References

* ''Ockham's Theory of Terms'' : Part I of the ''Summa Logicae'', translated and introduced by Michael J. Loux, University of Notre Dame Press, Notre Dame, IN, 1974. Reprinted, St. Augustine's Press, South Bend, IN, 1998. * ''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, University of Notre Dame Press, Notre Dame, IN, 1980. Reprinted, St. Augustine's Press, South Bend, IN, 1998. * Longeway, John Lee (2007), ''Demonstration and Scientific Knowledge in William of Ockham'', University of Notre Dame Press, Notre Dame, IN. A translation of ''Summa Logicae III-II : De Syllogismo Demonstrativo'', with selections from the ''Prologue'' to the ''Ordinatio''. * Boehner, P. (1952), ''Medieval Logic'', Manchester University Press.

External links

Charles Sanders Peirce Charles Sanders Peirce ( ; September 10, 1839 – April 19, 1914) was an American scientist, mathematician, logician, and philosopher who is sometimes known as "the father of pragmatism". According to philosopher Paul Weiss (philosopher), Paul ...

(1869)
Translation and commentary on selected passages from OckhamPeirce Edition Project

Spade's translation of parts of ''Summa'' Book I

''Summa Logicae'', full text in Latin - partially in English
{{DEFAULTSORT:Sum Of Logic Occamism Logic books Term logic History of logic 1320s books Medieval philosophical literature Scholasticism Treatises