The Summa Logicae is a textbook on logic

Logic

In philosophy, Logic is the formal systematic study of the principles of valid inference and correct reasoning. Logic is used in most intellectual activities, but is studied primarily in the disciplines of philosophy, mathematics, semantics, and computer science...

 by William of Ockham

William of Ockham

William of Ockham was an English Franciscan friar and scholastic philosopher, who is believed to have been born in Ockham, a small village in Surrey. He is considered to be one of the major figures of medieval thought and was at the centre of the major intellectual and political controversies of...

. It was written around 1323.

Systematically, it resembles other works of medieval logic, organised under the basic headings of the Aristotelian

Aristotelianism

Aristotelianism is a tradition of philosophy that takes its defining inspiration from the work of Aristotle. The works of Aristotle were initially defended by the members of the Peripatetic school, and, later on, by the Neoplatonists, who produced many commentaries on Aristotle's writings...

 Predicables

Predicables

Predicables is, in scholastic logic, a term applied to a classification of the possible relations in which a predicate may stand to its subject. It is not to be confused with 'praedicamenta', the schoolmen's term for Aristotle's ten Categories...

, Categories, terms

Terminology

Terminology is the study of terms and their use. Terms are words and compound words that in specific contexts are given specific meanings, meanings that may deviate from the meaning the same words have in other contexts and in everyday language. The discipline Terminology studies among other...

, proposition

Proposition

In logic and philosophy, the term proposition refers to either the "content" or "meaning" of a meaningful declarative sentence or the pattern of symbols, marks, or sounds that make up a meaningful declarative sentence...

s, and syllogism

Syllogism

A syllogism is a kind of logical argument in which one proposition is inferred from two or more others of a certain form...

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

Nominalism

Nominalism is a metaphysical view in philosophy according to which general or abstract terms and predicates exist, while universals or abstract objects, which are sometimes thought to correspond to these terms, do not exist. Thus, there are at least two main versions of nominalism...

.

Book I. On Terms

1. 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.


2. Chapters 18–25 deal with the five predicables
   Predicables
   Predicables is, in scholastic logic, a term applied to a classification of the possible relations in which a predicate may stand to its subject. It is not to be confused with 'praedicamenta', the schoolmen's term for Aristotle's ten Categories...
   
    of Porphyry
   Porphyry (philosopher)
   Porphyry of Tyre , Porphyrios, AD 234–c. 305) was a Neoplatonic philosopher who was born in Tyre. He edited and published the Enneads, the only collection of the work of his teacher Plotinus. He also wrote many works himself on a wide variety of topics...
   
   .


3. Chapters 26–62 deal with the Categories
   Categories (Aristotle)
   The Categories is a text from Aristotle's Organon that enumerates all the possible kinds of thing that can be the subject or the predicate of a proposition...
   
    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 (42–43), Quantity (44–49), Relation (50–54), Quality (55–56), Action (57), Passion (58), Time (59), Place (60), Position (61), Habit (62).


4. Chapters 63–77 onwards deal with the theory of supposition.

Book II. On Propositions

1. On categorical propositions (1–20)


2. On the conversion of propositions (21–9)


3. On hypothetical propositions (30–7)

Part I. On Syllogisms

1. On categorical syllogisms (1–19)


2. On modal syllogisms (20–30)


3. On mixed syllogisms (31–64)


4. On syllogisms containing exponible propositions

Part II. On Demonstration

• These 41 chapters are a systematic exposition of Aristotle's Posterior Analytics
  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 definition marked as the statement of a thing's nature, .....
  
  .

Part III. On Consequences

• The first 37 chapters of Part II are a systematic exposition of Aristotle's Topics
  Topics (Aristotle)
  The Topics is the name given to one of Aristotle's six works on logic collectively known as the Organon. The other five are:*Categories*De Interpretatione*Prior Analytics*Posterior Analytics*On Sophistical Refutations...
  
  . 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).. 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
  Material conditional
  The material conditional, also known as material implication, is a binary truth function, such that the compound sentence p→q is logically equivalent to the negative compound: not . A material conditional compound itself is often simply called a conditional...
  
   and logical implication respectively. Similar accounts are given by Jean Buridan
  Jean Buridan
  Jean Buridan was a French priest who sowed the seeds of the Copernican revolution in Europe. Although he was one of the most famous and influential philosophers of the late Middle Ages, he is today among the least well known...
  
   and Albert of Saxony
  Albert of Saxony
  Albert of Saxony may refer to:* Albert of Saxony * Albert I, Duke of Saxony * Albert, Duke of Saxony * Prince Albert of Saxony, Duke of Teschen * Albert of Saxony...
  
  .
• Chapters 38 to 45 deal with the theory of obligationes
  Theory of Obligationes
  Obligationes or disputations de obligationibus were a medieval disputation format common in the XIIIth and XIVth centuries, which had nothing to do with ethics or morals but rather with logical formalisms. The name comes from the fact that the participants were "obliged" to follow the rules...
  
  .

• Chapter 46 deals with the Liar Paradox
  Liar paradox
  In philosophy and logic, the liar paradox or liar's paradox , is the statement "this sentence is false"...
  
  

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 (De sophisticis elenchis).

• Chapters 2-4 deal with the three modes of equivocation
  Equivocation
  Equivocation is classified as both a formal and informal logical fallacy. It is the misleading use of a term with more than one meaning or sense...
  
  .
• Chapters 5-7 deal with the three types of amphiboly.
• Chapter 8 deals with the fallacies of composition
  Fallacy of composition
  The fallacy of composition arises when one infers that something is true of the whole from the fact that it is true of some part of the whole...
  
  , and division
  Fallacy of division
  A fallacy of division occurs when one reasons logically that something true of a thing must also be true of all or some of its parts.An example:# A Boeing 747 can fly unaided across the ocean.# A Boeing 747 has jet engines....
  
  .
• 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
  Accident (fallacy)
  The logical fallacy of accident is a deductive fallacy occurring in statistical syllogisms when an exception to a rule of thumb is ignored. It is one of the thirteen fallacies originally identified by Aristotle...
  
  .
• Chapter 12 deals with the fallacy of affirming the consequent
  Affirming the consequent
  Affirming the consequent, sometimes called converse error, is a formal fallacy, committed by reasoning in the form:#If P, then Q.#Q.#Therefore, P....
  
  .
• Chapter 13 deals with converse accident
  Converse accident
  The logical fallacy of converse accident is a deductive fallacy that can occur in a statistical syllogism when an exception to a generalization is wrongly called for.For example:The inductive version of this fallacy is called hasty generalization...
  
   or secundum quid et simpliciter.
• Chapter 14 deals with Ignoratio elenchi
  Ignoratio elenchi
  Ignoratio elenchi is the informal fallacy of presenting an argument that may in itself be valid, but does not address the issue in question...
  
   or irrelevant thesis.
• Chapter 15 deals with begging the question
  Begging the question
  Begging the question is a type of logical fallacy in which the proposition to be proven is assumed implicitly or explicitly in the premise....
  
   (petitio principii).
• Chapter 16 deals with false cause
  Questionable cause
  Fallacies of questionable cause, also known as causal fallacies, non causa pro causa or false cause, are informal fallacies where a cause is incorrectly identified...
  
   (non-causam ut causam)
• Chapter 17 deals with the fallacy of many questions
  Complex question
  Complex question, trick question, multiple question or plurium interrogationum is a question that has a presupposition that is complex. The presupposition is a proposition that is presumed to be acceptable to the respondent when the question is asked. The respondent becomes committed to this...
  
   (plures interrogationes ut unam facere)>
• Ockham ends (chapter 18) by showing how all these fallacies err against the syllogism.

See also

• Summa logicae by Lambert d'Auxerre
• Summa Theologica
  Summa Theologica
  The Summa Theologiæ is the best-known work of Thomas Aquinas , and although unfinished, "one of the classics of the history of philosophy and one of the most influential works of Western literature." It is intended as a manual for beginners in theology and a compendium of all of the main...
  
   by Thomas Aquinas
  Thomas Aquinas
  Thomas Aquinas, O.P. , also Thomas of Aquin or Aquino, was an Italian Dominican priest of the Catholic Church, and an immensely influential philosopher and theologian in the tradition of scholasticism, known as Doctor Angelicus, Doctor Communis, or Doctor Universalis...
  
  

External links

• Charles Sanders Peirce (1869), Translation and commentary on selected passages from Ockham, Peirce Edition Project.
• Spade's translation of parts of Summa Book I.