THE BOOK The book titled, An Introduction to Logic, introduces students and other readers, interested in Logic and Philosophy, to some important aspects of the discipline of Logic. It gives an account of the historical development of Logic, the main systems of it, its inductive, deductive and symbolic dimensions, and it examines the logical fallacies. The treatment of logic enables the reader to acquire a broad picture of the discipline of logic.
THE AUTHOR Professor A.S. Thakur was educated in India, England and Nigeria. He has written many books, published by leading publishers like National Publishing House, New Delhi and Macmillan, London. He has had a long experience of teaching in India and Africa. At present, he is the Dean, Faculty of Education, University of Maiduguri, Nigeria.
The book titled : "An Introduction to Logic;" is written to meet the needs of students, staff and general public who are interested in acquiring the knowledge of the important features of the discipline of "Logic". In a way, Logic in its general context interests us all, for we would not like to make statements which are adjudged to be illogical. The knowledge of logic is also vital to the students of Logic and Philosophy, for logic is a discipline on its own and it is also an important tool to the understanding of philosophy.
Chapter 1 of the book defines logic and identifies its relationship with language; in the nature and the scope of logic are discussed its theoretical and practical values. Logic as a study of argument engages our attention and makes us examine its advantages.
Chapter 2 introduces the readers to a brief history of logic. The Greek contributions in general and those of Aristotle in particular are still relevant and thought-provoking. A long medieval period has been a period of the stunted growth for logic, because the Church did not permit arguments which were unacceptable to it. From the 13th century onward, the scholastic logicians accupied themselves with the problem of ambiguity. They also developed new logical principles. Modem logic began at the onset of the 16th century and was later developed by the authors of the Port-Royal Logic in the middle of the 19th century. They developed the metalogical theory of Syllogistic, which remained popular up to the mid-19th century. Later on, Leibniz developed mathematical logic, anticipating the use of quantifiers. French and British logicians expanded the syllogistic. George Boole presented new ideas on logic, known as the "algebra of logic." The German logician, Frege, elucidated the notion of number, thus, laying the foundation of logic of mathematics. In the twentieth century, Russell, Brouwer and Hilbert have made contributions to the logic of mathematics. Of particular interest is Hilbert's "metalogic" in which the problems of the constancy and completeness of deductive systems and their decidability have been discussed.
Chapter 3 gives a brief account of three systems of logic - the formal, the metalogic, and the applied. Formal logic is an a priori study. It uses deduction. Metalogic studies syntax and semantics of formal languages and formal systems. Applied logic develops the machinery of syllogism in vast ranges of subjects like sciences and philosophy and also in every day discourse. Inductive and Deductive Reasoning is the subject of Chapter 4. In inductive reasoning, an attempt has been made to illustrate it by first identifying the principles in the facts that occur in our experience, and then organizing facts and laws with a view to arriving at generalizations. In deductive reasoning, data are combined to yield a conclusion which is new. That simplest form of deductive reasoning is the "syllogism."
Symbolic Logic is the theme of Chapter 5. Logicians have developed symbols which enable us to make transitions almost mechanically by the eye. There are also testing procedures and operating rules for the symbols. Chapter 6 deals briefly with the use of some of the truth-functional operators like the tilde, dot, wedge, horse-shoe and triple-bar. The conjunction, negation, punctuation and disjunction are also discussed in this chapter. "
Quantifiers" is the subject matter of Chapter 7. The two types of quantifiers - an existential quantifier and a universal quantifier -are illustrated with symbols. Quantifier rules are discussed in some detail.
In Chapter 8 is examined the logic of four philosophies -Naturalism, Idealism, Realism and Pragmatism. The logic of Naturalism is the logic of science. The logic of Idealism emphasises the formal logic, including both induction and deduction. The Realists attach importance to formal logic but emphasise relations in Nature and human mind. The Pragmatists highlight the logic which is based on experimental method, and which stresses flexibility, continuity, and relation to the culture and society.
Chapter 9 concludes the various sub-themes of the book by focussing attention on the logical fallacies. It is interesting to note that a good deal of the classification of Aristotle as well as Bacon is still relevant to our times.
**Contents and Sample Pages**
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