CHAPTER 1: NATURE OF LOGIC

1. NATURE OF LOGIC

A) Traditional and Modern definitions of Logic
B) Basic features of Inductive and Deductive reasoning. Their uses in Law Courts
C) Some basic logical concepts –Form, Content, Truth , Validity, Inference, Implication.

Logic is a science of valid reasoning.

Logic is a word that comes from the Greek word λογική pronounced as logikē that means, the study of reasoning.

All the places where reasoning is needed, logic is needed. The more accurately we use our reasoning, the more effective is our work in that area. So all those who think, use logic knowingly or unknowingly.

Logic is used in most intellectual activities, but is studied primarily in the disciplines of philosophy, mathematics, and computer science. Logic examines general forms which arguments may take, which forms are valid, and which are fallacies. It is one kind of critical thinking. In philosophy, the study of logic falls in the area of epistemology, which asks: "How do we know what we know?" In mathematics, it is the study of valid inferences within some formal language.

Logic has origins in several ancient civilizations, including ancient India, China and Greece. In west, Logic was established as a discipline by Aristotle, who established its fundamental place in philosophy.

The study of logic was part of the classical trivium. Averroes defined logic as "the tool for distinguishing between the true and the false." Richard Whately, defined logic as "the Science, as well as the Art, of reasoning." Frege, defined logic as "the science of the most general laws of truth."

The concept of logical form is central to logic, it being held that the validity of an argument is determined by its logical form, not by its content. Traditional Aristotelian syllogistic logic and modern symbolic logic are examples of formal logic.

Informal logic is the study of natural language arguments. The study of fallacies is an especially important branch of informal logic. The dialogues of Plato are good examples of informal logic.

Formal logic is the study of inference with purely formal content. An inference possesses a purely formal content if it can be expressed as a particular application of a wholly abstract rule, that is, a rule that is not about any particular thing or property. The works of Aristotle contain the earliest known formal study of logic. Modern formal logic follows and expands on Aristotle. In many definitions of logic, logical inference and inference with purely formal content are the same. This does not render the notion of informal logic vacuous, because no formal logic captures all of the nuances of natural language.

Symbolic logic is the study of symbolic abstractions that capture the formal features of logical inference. Symbolic logic is often divided into two branches: propositional logic and predicate logic.

Mathematical logic is an extension of symbolic logic into other areas, in particular to the study of model theory, proof theory, set theory, and recursion theory.

A) Traditional and Modern definitions of Logic

Traditional Logic is the type of logic propagated by Aristotle. This is popularly known as traditional formal logic. This is because here, the form of statements used in arguments is given total importance. The traditional formal logic is general designation for the systems of deductive logic that do not involve the use of formal languages, or the apparatus of mathematical logic. The basis of traditional logic is syllogistic reasoning.

Traditional logic is defined as “a system of formal logic mainly concerned with the syllogistic forms of deduction that is based on Aristotle and includes some of the changes by contemporary logicians.”

Modern Logic on the other hand contains more form based relationships in the logical thinking. So, the modern logic is not limited to syllogism based arguments, but it goes much beyond them. It becomes mathematical and symbolic. This is the reason why after the modern logic was developed, it started being used practically in every science where thinking in the right way is needed.

Modern logic is defined as “logic where the subject developed into a rigorous and formalistic discipline whose exemplar was the exact method of proof used in mathematics.” The development of the modern "symbolic" or "mathematical" logic is the most significant in the history of logic, and in human intellectual history.

B) Basic features of Deductive and Inductive reasoning.

Logic is divided into two types, these are inductive and deductive reasoning.

The Deductive Reasoning is a reasoning where the conclusion stays within the scope of its supporting statements. It is said that deductive reasoning involves in drawing logical conclusions from definitions and axioms. We can also say that deductive Reasoning involves in deriving known conclusions from known facts. As a result, the conclusions of deductive reasoning are certain.

The Inductive reasoning is a reasoning where conclusion goes beyond the scope of its supporting statements. Many say that inductive reasoning involves in drawing general conclusions from specific examples. We also say that Inductive Reasoning involves in deriving unknown conclusion from known facts. This is the reason why conclusions of Inductive reasoning are probable and not certain.

Though induction and deduction are the two types of logical reasoning, they are not watertight compartments. The general statements that we use as supporting statements in deductive arguments, actually are result of inductive inferences.

So, we find that Induction is of two types, perfect and imperfect.

In perfect induction, we get conclusion from supporting statements, i.e. premises, this conclusion goes beyond the scope of premises, and then we verify and test this conclusion by using some methods that are similar to deduction.

In imperfect induction, we get conclusion from the supporting statements, i.e. premises, this conclusion says something beyond the scope of premises, but then we do not verify and test this conclusion. We just leave it as it is. So, the conclusion of imperfect induction is always probable.

Deduction versus Induction

Aristotle used to classify the type of arguments using syllogism. But all arguments cannot be fitted in the type of syllogism. We can use a simple test for inductive and deductive arguments. The premises in a deductive argument guarantee the truth of the conclusion, so, if the premises are true, the conclusion must be true. The premises in an inductive argument provide some degree of support for the conclusion, but it is possible to have true premises false conclusion.

Aristotle views inductive syllogism as scientific induction and therefore as a more rigorous form of inductive argument. The logical form of the inductive syllogism, after the convertibility maneuver, is the same as the deductive syllogism.

In this sense, induction and deduction possess the same (final) logical form. But, of course, in order to successfully perform an induction, one has to know that convertibility is possible, and this requires an act of intelligence which is able to discern the metaphysical realities between things out in the world. We discuss this issue under non-discursive reasoning below.

Uses of logical reasoning in Law Courts:

In the field of law, we need reasoning in order to present the matter of any litigant effectively, so that we can help him get justice in the existing frames of law. But even the opposite side litigant who has a contrary view also wants justice, so the aim of a good lawyer is always to disclose the truth and just situation. Logical reasoning is absolutely necessary for this as without logical reasoning we cannot find out the truth behind the stories told by the litigants.

C) Some basic logical concepts – Form, Content, Truth , Validity, Inference, Implication.

Logic as we saw, is a science of valid reasoning. In order to know what is valid reasoning, we must first have some concepts clarified. Also, Logic can be best best understood if we understand the basic concepts of logic. So, let us see the definitions of some basic concepts in logic:

Word, is a meaningful group of alphabets used in any language.

Syncatagormatic word, are the words that are used to enhance the meaning of words that can stand on their own. So, the Syncatagormatic words do not make any meaning on their own. They depend on other words for their meaningfulness.

Catagormatic word, is a word that has its own meaning, so it can stand on its own in the process of expressing a meaningful concept.

Sentence, is a meaningful group of words used to convey any meaning.
Statement, is a sentence that asserts some affirmative or negative fact.
Proposition, is a statement used in logical arguments. This means, in logic, a statement is called a proposition.
Form, stands for the relationship of various parts of a statement within itself and in a set of statements called argument.
Content, is the matter of facts mentioned in the statement or argument.
Truth, is the agreement of facts mentioned in an argument with reality.
Validity, is the appropriateness of relationship between various parts of argument.
Inference, is a set of propositions or statements where, on the basis of one or more statements one statement is obtained as a conclusion.

Implication, is a type of statement where the truth of one component is indicated or suggested by the truth of another. Here, the component on which the truth of another component depends is the first component called antecedent and the component that follows from the first component is the consequent.