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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 due to the structure of arguments alone, independent of their topic and content.
- Overview
- Scope and basic concepts
logic, the study of correct reasoning, especially as it involves the drawing of inferences.
This article discusses the basic elements and problems of contemporary logic and provides an overview of its different fields. For treatment of the historical development of logic, see logic, history of. For detailed discussion of specific fields, see the articles applied logic, formal logic, modal logic, and logic, philosophy of.
An inference is a rule-governed step from one or more propositions, called premises, to a new proposition, usually called the conclusion. A rule of inference is said to be truth-preserving if the conclusion derived from the application of the rule is true whenever the premises are true. Inferences based on truth-preserving rules are called deductive, and the study of such inferences is known as deductive logic. An inference rule is said to be valid, or deductively valid, if it is necessarily truth-preserving. That is, in any conceivable case in which the premises are true, the conclusion yielded by the inference rule will also be true. Inferences based on valid inference rules are also said to be valid.
(Read Steven Pinker’s Britannica entry on rationality.)
Logic in a narrow sense is equivalent to deductive logic. By definition, such reasoning cannot produce any information (in the form of a conclusion) that is not already contained in the premises. In a wider sense, which is close to ordinary usage, logic also includes the study of inferences that may produce conclusions that contain genuinely new information. Such inferences are called ampliative or inductive, and their formal study is known as inductive logic. They are illustrated by the inferences drawn by clever detectives, such as the fictional Sherlock Holmes.
The contrast between deductive and ampliative inferences may be illustrated in the following examples. From the premise “somebody envies everybody,” one can validly infer that “everybody is envied by somebody.” There is no conceivable case in which the premise of this inference is true and the conclusion false. However, when a forensic scientist infers from certain properties of a set of human bones the approximate age, height, and sundry other characteristics of the deceased person, the reasoning used is ampliative, because it is at least conceivable that the conclusions yielded by it are mistaken.
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A logic is just a set of rules and techniques for distinguishing good reasoning from bad. A logic must formulate precise standards for evaluating reasoning and develop methods for applying those standards to particular instances. Basic Notions.
18. März 2000 · Aristotle’s Logic. First published Sat Mar 18, 2000; substantive revision Tue Nov 22, 2022. Aristotle’s logic, especially his theory of the syllogism, has had an unparalleled influence on the history of Western thought.
Logical reasoning (or just “logic” for short) is one of the fundamental skills of effective thinking. It works by raising questions like: If this is true, what else must be true? If this is true, what else is probably true? If this isn’t true, what else can’t be true?
Logic is the study of information encoded in the form of logical sentences. Each logical sentence divides the set of all possible world into two subsets - the set of worlds in which the sentence is true and the set of worlds in which the set of sentences is false.
16. Sept. 2000 · Classical Logic. First published Sat Sep 16, 2000; substantive revision Wed Jun 29, 2022. Typically, a logic consists of a formal or informal language together with a deductive system and/or a model-theoretic semantics. The language has components that correspond to a part of a natural language like English or Greek.
