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 science of deductively valid inferences or of logical truths. It is a formal science investigating how conclusions follow from prem ...

William of Ockham William of Ockham, OFM (; also Occam, from la, Gulielmus Occamus; 1287 – 10 April 1347) was an English Franciscan friar, scholastic philosopher, apologist, and Catholic theologian, who is believed to have been born in Ockham, a small vil ...

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

Predicable Predicable (Lat. praedicabilis, that which may be stated or affirmed, sometimes called ''quinque voces'' or ''five words'') is, in scholastic logic, a term applied to a classification of the possible relations in which a predicate may stand to its ...

s, Categories, terms,

proposition In logic and linguistics, a proposition is the meaning of a declarative sentence. In philosophy, " meaning" is understood to be a non-linguistic entity which is shared by all sentences with the same meaning. Equivalently, a proposition is the no ...

s, and

syllogism A syllogism ( grc-gre, συλλογισμός, ''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 tru ...

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 at least two main versions of nominalism. One version denies the existence of universalsthings ...

, 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 be ...

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'' ( grc-gre, Ἀναλυτικὰ Ὕστερα; la, Analytica Posteriora) is a text from Aristotle's '' Organon'' that deals with demonstration, definition, and scientific knowledge. The demonstration is distinguis ...

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 A consequent is the second half of a hypothetical proposition. In the standard form of such a proposition, it is the part that follows "then". In an implication, if ''P'' implies ''Q'', then ''P'' is called the antecedent and ''Q'' is called ...

. Ockham distinguishes between 'material' and 'formal' consequences, which are roughly equivalent to the modern material implication and

logical implication Logical consequence (also entailment) is a fundamental concept in logic, which describes the relationship between statements that hold true when one statement logically ''follows from'' one or more statements. A valid logical argument is one ...

respectively. Similar accounts are given by

Jean Buridan Jean Buridan (; Latin: ''Johannes Buridanus''; – ) was an influential 14th-century French philosopher. Buridan was a teacher in the faculty of arts at the University of Paris for his entire career who focused in particular on logic and the wor ...

and

Albert of Saxony en, Frederick Augustus Albert Anthony Ferdinand Joseph Charles Maria Baptist Nepomuk William Xavier George Fidelis , image = Albert of Saxony by Nicola Perscheid c1900.jpg , image_size = , caption = Photograph by Nicola Persch ...

. * Chapters 38 to 45 deal with the

Theory of obligationes ''Obligationes'' or disputations ''de obligationibus'' were a medieval disputation format common in the 13th and 14th centuries. Despite the name, they had nothing to do with ethics or morals but rather dealt with logical formalisms; the name comes ...

. *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 truth ...

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'' ( el, Σοφιστικοὶ Ἔλεγχοι, Sophistikoi Elenchoi; la, De Sophisticis Elenchis) is a text in Aristotle's ''Organon'' in which he identified thirteen fallacies.Sometimes listed as twelve. According to ...

(''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/expression in multiple senses within an argument. It is a type of ambiguity that stems from a phrase havin ...

. *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 v ...

, and

division Division or divider may refer to: Mathematics *Division (mathematics), the inverse of multiplication *Division algorithm, a method for computing the result of mathematical division Military *Division (military), a formation typically consisting ...

. *Chapter 9 deals with the

fallacy of accent The fallacy of accent (also referred to as ''accentus'', from its Latin denomination, and misleading accent) is a type of ambiguity that arises when the meaning of a sentence is changed by placing an unusual prosodic stress, or when, in a written p ...

. *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 Affirming the consequent, sometimes called converse error, fallacy of the converse, or confusion of necessity and sufficiency, is a formal fallacy of taking a true conditional statement (e.g., "If the lamp were broken, then the room would be dar ...

. *Chapter 13 deals with '' secundum quid et simpliciter''. *Chapter 14 deals with

Ignoratio elenchi An irrelevant conclusion, also known as ''ignoratio elenchi'' () or missing the point, is the informal fallacy of presenting an argument that may or may not be logically valid and sound, but (whose conclusion) fails to address the issue in quest ...

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, instead of supporting it. For example: * "Green is t ...

(''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 philosopher, logician, mathematician and scientist who is sometimes known as "the father of pragmatism". Educated as a chemist and employed as a scientist for ...

(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 and English
{{DEFAULTSORT:Sum Of Logic Occamism Logic books Term logic History of logic 1320s books Medieval philosophical literature Scholasticism Treatises