# A Class-Room Introduction to Logic

## May 5, 2009

### Unit-I: Nature of Logic

Filed under: Logic,Nature of Logic — Dr. Desh Raj Sirswal @ 6:29 am

Logic: Logic is a branch of Philosophy, dedicated to the study of reasoning The word ;Logic ‘ derives from Greek  logike, means “possessed of reason, intellectual, dialectical, argumentative”, from logos equivalent to “word, thought, idea, argument, account, reason, or principle”. Logic is the study of the methods and principles used to distinguish correct reasoning from incorrect reasoning.

The aim of the logic is to provide methods, techniques and devices which help in differentiating right reasoning from wrong reasoning and good reasoning from bad. But it does not mean that only those who study logic can reason correctly. However it is true that those who study logic certainly make less errors while arguing. Knowledge of logic helps one to face a problem in a more orderly and systematic way and in many cases makes the solution less difficult and more certain. Like any other active field of study, it too has grown in many directions.

Kinds of Logic

Today, logic is both a branch of philosophy and a branch of mathematics. Its applications as well known in the area of artificial intelligence. This page aims primarily to acquaint the readers with the basics of what is known as classical logic or classical first order logic and sometime also called as formal logic, because proponents of this logic mostly believe that statements in natural language have underlying logical forms. In their view, the expression in logic exhibit these latent deep structures or the logical forms. If the deep structures of the form is correct, only then a piece of reasoning in natural language is valid. Here we will also study Informal Logic (Fallacies). There are many other kinds of logic: Many-Valued Logic, Fuzzy Logic, Non-Monotonic Logic, Modal Logic and Paraconsistent Logic. You can find a short note and suggested books about kinds of logic in Chhanda Chakraborti : Logic: Informal, Symbolic & Inductive.

## History of Logic

The earliest sustained work on the subject of logic is that of Aristotle, In contrast with other traditions, Aristotelian logic became widely accepted in science and mathematics, ultimately giving rise to the formally sophisticated systems of modern logic.

Several ancient civilizations have employed intricate systems of reasoning and asked questions about logic or propounded logical paradoxes. In India, the Nasadiya Sukta of the Rigveda (RV 10.129) contains ontological speculation in terms of various logical divisions that were later recast formally as the four circles of catuskoti: “A”, “not A”, “A and not A”, and “not A and not not A”. The Chinese philosopher Gongsun Long(ca. 325–250 BC) proposed the paradox “One and one cannot become two, since neither becomes two.” Also, the Chinese ‘School of Names’ is recorded as having examined logical puzzles such as “A White Horse is not a Horse” as early as the fifth century BCE. In China, the tradition of scholarly investigation into logic, however, was repressed by the Qin dynasty following the legalist philosophy of Han Feizi.

Logic in Islamic philosophy also contributed to the development of modern logic, which included the development of “Avicennian logic” as an alternative to Aristotelian logic. Avicenna’s system of logic was responsible for the introduction of hypothetical syllogism, temporal modal logic, and inductive logic. The rise of the Asharite school, however, limited original work on logic in Islamic philosophy, though it did continue into the 15th century and had a significant influence on European logic during the Renaissance.

In India, innovations in the scholastic school, called Nyaya, continued from ancient times into the early 18th century, though it did not survive long into the colonial period. In the 20th century, Western philosophers like Stanislaw Schayer and Klaus Glashoff have tried to explore certain aspects of the Indian tradition of logic.

During the later medieval period, major efforts were made to show that Aristotle’s ideas were compatible with Christian faith. During the later period of the Middle Ages, logic became a main focus of philosophers, who would engage in critical logical analyses of philosophical arguments.

The syllogistic logic developed by Aristotle predominated until the mid-nineteenth century when interest in the foundations of mathematics stimulated the development of symbolic logic (now called mathematical logic). In 1854, George Boole published An Investigation of the Laws of Thought on Which are Founded the Mathematical Theories of Logic and Probabilities, introducing symbolic logic and the principles of what is now known as Boolean logic. In 1879 Frege published Begriffsschrift which inaugurated modern logic with the invention of quantifier notation. In 1903 Alfred North Whitehead and Bertrand Russell  published Principia Mathematica  on the foundations of mathematics, attempting to derive mathematical truths from axioms and inference rules in symbolic logic. In 1931 Gödel raised serious problems with the foundationalist program and logic ceased to focus on such issues.

The development of logic since Frege, Russell and Wittgenstein had a profound influence on the practice of philosophy and the perceived nature of philosophical problems (see Analytic philosophy), and Philosophy of mathematics. Logic, especially sentential logic, is implemented in computer logic circuits and is fundamental to computer science. Logic is commonly taught by university philosophy departments often as a compulsory discipline. (From Wikipedia, the free encyclopedia)

Utility of Logic

}There are some points which highlights the utility of logic :

}Logic develop intellectual capacity.

}We can rectify the mistakes in our arguments.

}Logic is the Science of Sciences.

}The study of logic is a part of true Education.

}Logic is useful in everyday life.

Logic can help us in explaining and demonstrating truth.

Conclusion

}Our course primarily to acquaint the students with the basics of what is known as classical logic or classical first order logic and sometime also called as formal logic, because proponents of this logic mostly believe that statements in natural language have underlying logical forms. In their view, the expression in logic exhibit these latent deep structures or the logical forms. If the deep structures of the form is correct, only then a piece of reasoning in natural language is valid.

}References:

}A Class-Room Introduction to Logic

}Copi, Cohen, Jetli  & Prabhakar: Introduction to Logic.

}Chhanda Chakraborti : Logic: Informal, Symbolic & Inductive.

Krishana Jain:A Text Book of Logic.