CBSE Class 11 Philosophy Elements of Symbolic Logic

Elements of Symbolic Logic

Origin of symbolic logic: In the history of western logic, symbolic logic is a relatively recent development. What sets symbolic logic apart from traditional logic is its leaning towards mathematics. Aristotle, the Greek thinker, in the fourth century BC, laid the foundation of logic as a science of sciences. Logic for him is a science which can serve as the backbone of all other scientific queries. He was the first to propose that logic is the indispensable tool which can provide a set of correct rules for correct reasoning, and that these rules will be applicable in all scientific studies and discussions. Aristotle's conception of logic as a formal study of valid inferences was accepted by all logicians for nearly 2000 years.

In the seventeenth century G.W. Von Leibniz, a mathematician turned philosopher, however, could see that Aristotle and his followers' style of reasoning needs modification. But he merely suggested, and never worked or showed the direction which logic possibly could take. It is only in the nineteenth century that the thinkers started actualizing the ideas conceived by Leibniz. For nearly two thousand years since its inception, logic did not progress so much as it had done in last one hundred and fifty years. This is mostly because of rapid development in mathematics and its use in logic. Since Leibniz’s discovery of Differential Calculus, mathematics developed rapidly. Soon, it became the 'key-science'. With the ascending of the mathematical method, George Boole (1815-1864), an English

mathematician, rediscovered logic and it's potential. He mathematized logic by highlighting the resemblances between disjunction and conjunction of concepts and addition and multiplication operations of mathematics. Through his efforts Class Calculus emerged in logic. While Boole and others like De Morgan (1806-1871), Charles Sanders Pierce (1839-1914) were mathematizing logic, Gottlob Frege (1824-1925), a German mathematician, attempted something revolutionary. He tried to reduce all mathematics into logic by analyzing the concept of number. This is known as the thesis of logicism. In order to achieve this aim he invented a language; a Begriffsschrift (language of thought) to free logical thinking from the dominion of ordinary language and its grammar. The new language which is also called artificial language makes use of logical notations. These notations can express much larger complex sentences than Aristotle's logic could do. This achievement of Frege ushered in the age of symbolic or mathematical logic for which he is rightly called the father of modern symbolic logic.

Arguments presented in natural language whether in English or in any other language are sometimes difficult to evaluate because of the ambiguous, vague and equivocal nature of words and idioms in which they are expressed. To avoid these impurities of ordinary language the logicians as well as some of the mathematicians have developed specialized technical language and vocabulary which is called artificial language or symbolic language.

Elements of Symbolic Logic Nature of symbolic language Ideograms and Phonograms:

In sharing the same platform with mathematics, modern logicians made extensive use of symbols. Symbols are ideograms, written words are phonograms. Ideograms stand directly for ideas whereas phonograms stand for sounds that we make while speaking words. Every word of a language is a phonogram. For example, the written words 'question mark' are phonograms because they are the written characters of the sounds we make while uttering these words. But '?' is an ideogram. This does not represent written characters of the sounds, but stands for the idea directly. Similarly, 'minus' is a phonogram, but '-' is an ideogram; 'Square root of 10' is phonogram, but is an ideogram. Symbolic logic makes use of ideograms instead of phonograms.

There is no doubt the classical logic used symbols like S, P, M which represent minor term, major term and middle term in a categorical syllogism respectively. A, E, I, O symbols were also used to denote categorical propositions by the traditional thinkers. But the use of symbols was very little and it was restricted to a few symbols only. Modern symbolic logic made extensive use of symbols both as variables and constants.

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