Symbolic Logic
INTRODUCTION
Logic is the theory of the way in which people reason, with the aim of studying the principles of valid reasoning. The study of logic is the effort to determine the conditions under which one is justified in passing from given statements, called premises, to a conclusion that is claimed to follow from them. Logical validity is a relationship between the premises and the conclusion such that if the premises are true then the conclusion is true.
There are several types of logic. The earliest and simplest of these is known as classical or traditional logic which was introduced by Aristotle who developed rules for correct syllogistic reasoning.
Modern Logic: In the middle of the 19th century, the British mathematicians George Boole and Augustus De Morgan opened a new field of logic, now known as symbolic or modern logic, which was further developed by the German mathematician Gottlob Frege and especially by the British mathematicians Bertrand Russell and Alfred North Whitehead in Principia Mathematica (3 volumes, 1910-13). The logical system of Russell and Whitehead covers a far greater range of possible arguments than those that can be cast into syllogistic form. It introduces symbols for complete sentences and for the conjunctions that connect them, such as “or,””and,” and “If . . . then. . . .” It has different symbols for the logical subject and the logical predicate of a sentence; and it has symbols for classes, for members of classes, and for the relationships of class membership and class inclusion. It also differs from classical logic in its assumptions as to the existence of the things referred to in its universal statements.
Both classical logic and modern logic are systems of deductive logic. In a sense, the premises of a valid argument contain the conclusion, and the truth of the conclusion follows from the truth of the premises with certainty.
Both classical and modern logic in their usual forms assume that any well-formed sentence is
Logic is the theory of the way in which people reason, with the aim of studying the principles of valid reasoning. The study of logic is the effort to determine the conditions under which one is justified in passing from given statements, called premises, to a conclusion that is claimed to follow from them. Logical validity is a relationship between the premises and the conclusion such that if the premises are true then the conclusion is true.
There are several types of logic. The earliest and simplest of these is known as classical or traditional logic which was introduced by Aristotle who developed rules for correct syllogistic reasoning.
Modern Logic: In the middle of the 19th century, the British mathematicians George Boole and Augustus De Morgan opened a new field of logic, now known as symbolic or modern logic, which was further developed by the German mathematician Gottlob Frege and especially by the British mathematicians Bertrand Russell and Alfred North Whitehead in Principia Mathematica (3 volumes, 1910-13). The logical system of Russell and Whitehead covers a far greater range of possible arguments than those that can be cast into syllogistic form. It introduces symbols for complete sentences and for the conjunctions that connect them, such as “or,””and,” and “If . . . then. . . .” It has different symbols for the logical subject and the logical predicate of a sentence; and it has symbols for classes, for members of classes, and for the relationships of class membership and class inclusion. It also differs from classical logic in its assumptions as to the existence of the things referred to in its universal statements.
Both classical logic and modern logic are systems of deductive logic. In a sense, the premises of a valid argument contain the conclusion, and the truth of the conclusion follows from the truth of the premises with certainty.
Both classical and modern logic in their usual forms assume that any well-formed sentence is