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a theory of logic presented in Logic, or the Art of Thinking (1662), a book by A. Arnauld and P. Nicole, abbots at the Port-Royal monastery and followers of Descartes. The book was divided into four basic parts, devoted to conception, judgment, reasoning, and ordering (method).
In the Port-Royal logic, a distinction is made for the first time between the content of a concept (that is, the totality of characteristics included in it) and its scope (the class of objects possessing these characteristics). The authors of the Port-Royal logic proposed the creation of a special logical language (formal language), which, when used in scientific research and in the presentation of experimental results, would make it possible to avoid the most common logical errors. The language of logic would be devoid of polysemy and homonymy. Each term would have a single, precise meaning stated in a definition.
In general, the Port-Royal logic pays considerable attention to the theory of definitions (originated chiefly by B. Pascal), strictly differentiating between nominal definition (the introduction of terms that have no meaning or significance prior to their definition) and real definition (the clarification of the meaning of the names of certain “real” objects, using terms associated with other real objects). The acceptance of a nominal definition is merely a question of agreement on terminology. In general, a real definition is a sentence that requires substantiation.
From a modern point of view, the central problems of the Port-Royal logic are considered to be completely unrelated to logic. For example, the Port-Royal logic develops an idea introduced by Descartes in his Discourse on Method: scientific truth emerges as a result of the analysis of data but is transmitted and ordered by means of synthesis. The Port-Royal logic developed a system of methodological recommendations for working out definitions, axioms, conclusions, proofs, and scientific methods as such.
From the standpoint of logic (in the modern sense of the term), the Port-Royal logic may be viewed as a rationalistic critique of Scholastic logic and a reconstruction of logic in the Aristotelian tradition, even though it subjects Aristotle’s ideas (particularly the doctrine of categories) to critical examination. The Port-Royal grammar and the Port-Royal logic anticipated certain basic principles of contemporary formal (symbolic or mathematical) logic—for example, the problem of the structure of complex judgments (propositions).