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DEFINITION OF LOGIC
The terms logic is derived from the Greek word "logos", which means reason or expression of reason in words that is discourse. Etymologically. therefore, Logic is the science of reasoning or argument According to Dewey and Stebbing, reasoning or reflective thinking is a process of finding way out of some difficulty or problem by weighing the evidence on the basis of a tentive hypothesis and thereby reaching some conclusion. The reasoning can be either deductive or inductive. In the deductive reasoning we argue from a general principle to a particular conclusion. For example if we say that since all men are mortal, and X who is a man is mortal. But if we argue that since X, Y, Z, who are men are subject to death, every man must be subject to death, we are arguing inductive In logic we study the general principles governing both type of reasoning. Accordingly, we may define Logic as the science of taws of thought and reason.

J.S.MiII:- "Logic is the science of operations of understanding which are subsequent to the estimation of evidence of both the process itself of advancing from known truth to unknown and all other intellectual operations in so far as ancillary to this." The definition by Mill brings out the main characteristics of logic, namely ( i ) logic helps in evaluating the evidence in order to arrive at a proof; (ii) logic helps to discover unknown facts on the basis of known and (iii) logic deals with all intellectual processes pertaining to deduction and induction.

SCOPE AND SUBJECT MATTER OF LOGIC
The definition of logic given by Mill clearly indicates the scope of logic. According to Mill, "logic is the science of the operations of the understanding which are subsequent to the estimation of evidence, both the process itself of advancing from known truth to unknown and all other intellectual operations in so far as ancillary to this". This definition brings our following facts:

(1) That logic studies various intellectual processes such as thinking, reasoning and judgment.
(2) That logic studies processes necessary for evaluating evidence.
(3) That logic studies how to move from known to the unknown. This can be done in two ways: by moving from general to particular, as in the example "All men are rational, Ram is a man, therefore, Ram is rational", or by moving from particular instances to a general conclusion as in "Apples, bananas, mangoes etc. fall to ground because they are heavy and, therefore, all heavy things must fall to the ground". The first example illustrates the deductive reasoning while the second illustrates inductive reasoning, and both are within the scope of logic.
 
(4) That logic studies all intellectual processes involved in deduction and induction.
(a) In deduction we study laws of thought, viz., law of identity, law of non- contradiction and law of exclused middle. We also study the different types
of terms. We also study genus differential and accidental properties of terms. We also study formal rules of deduction, the immediate and mediate inferences. And, finally we study various fallacies in argumentation.

(b) In induction we study the difference between form and matter, the nature of definition, hypothesis, evidence, experimental techniques, probability etc.
We also study rules of classification, taxonomy (giving new names) etc. Finally, we study the fallacies incidental to inductive reasoning.
 
IMPORTANCE OF LOGIC
Though it is true that the knowledge of rules of logic is no guarantee against false reasoning, this is no serious objection against logic. The worth of any science is to be judged not by its actual practice but by the nature of facts it is about. For instance, the science of medicine is not to be condemned as some doctors fail to diagnose diseases properly. The study of logic cannot ensure that logicians will never^make in argument; but the chance of making mistake is certainly much less in their case.

LOGIC AND PSYCHOLOGY

Though there exists a close and strong relation between Logic and Psychology, the two are quite distinct and it is not possible to reduce one to the other or treat logic as a branch of psychology, which primarily deals with thinking and judgment. Again, it will be equally false to assert that since all arguments are decidable by logic principles, psychology is nothing but the logic "of mental process.

A general confusion about the relation of logic and psychology stems from the fact that traditionally logic is defined to be a science of laws of thought but now it is generally accepted that any investigation into the laws or ways in which we actually think belongs to psychology. Logic has little concern as to how^one thinks and arrives at conclusions, -It is only concerned with whether two propositions imply each other and what can be the valid inference, To illustrate: it may not be possible for someone to conceive the existence of mermaids. But irrespective of the fact whether we are able to imagine mermaids or not, logically it is valid to assert, that if there are mermaids then they are females with human head and the body of a fish.

It has been aptly observed by Cohen and Nagel that it is very important to distinguish between logic and psychology if we are to avoid the confusion of logic with certain allied subject which though occurring along with logic are nevertheless very different. The realization that logic cannot be restricted to psychological phenomena, therefore, will help us to discriminate between logic and rhetoric. The rhetoric is an art of persuasion. While it is true that if a ailed argument is put effectively by employing words like 'indubitably', beyond a shadow of doubt', 'clear as day which do not militate against them no amount of rhetoric can transform an invalid argument into valid. This does not mean that rhetoric is useless. It helps harmonious social relation. But it must be realized that the validity of an argument is quite independent of what goes in our head or how we put it forward. The validity in short is extra human. Therefore, psychology has to bearing upon the essential subject matter of logic, However, psychology does have an important role. It helps us appreciate how the social and personal prejudices block effective argument and also that personal or subjective assurance is no guarantee about the validity of an argument. As Nagel says, "The history of human error shows that the assertion 'I am absolutely certain' or 'I cannot help believing" in regard to any proposition is no adequate evidence of its truth."

LOGIC AND PHILOSOPHY

Philosophy is the philosophical process, which deals with certain specific problems from the philosophical viewpoint with the help of philosophical methods and arrives at certain philosophical conclusion. This definition of philosophy, abstract though it is, shows the distinction between philosophy and science. Science is a systematic study of a limited field of experience. Thus philosophy and a science differ in connection with methods, problems, viewpoints and conclusions. The most important branches of philosophy are metaphysics, epistemology and axiology of those logic comes within the fields of axioloav.' Axiology is the study of values. These values are generally of three kinds - truth, good and beauty. While ethics studies good. aesthetics studies beauty. Logic studies truth. It is the science which discriminates between true and untrue among the oppositions It is the method of arriving at the implication or meaning of propositions- It is the science of the value of truth. Thus logic is a branch of philosophy. Its knowledge is absolutely necessary for a philosopher, though it cannot be said that the logician equally necessarily requires the knowledge of philosophy.
Philosophy depends upon logic, though in its turn logic does not depend upon philosophy.

Phylosophical and Logical method
Logic and philosophy are most intimately related in the field of methods. The two most important methods of philosophical thinking are induction and deduction - the two branches of logic. It is here that philosophy and logic are intimately related since the former depends upon the later. Logic is concerned with the laws of induction and deduction, their merits and demerits and the fallacies to their wrong use. In the absence of logic, the methods of analysis and synthesis cannot be properly used in philosophy. It is hence that Logical Positivism one of the most important contemporary school of philosophy, has considered logical analysis as the chief method of philosophical thinking. This has been admitted by most of the contemporary philosophers. It has been accepted that philosophizing is impossible in the absence of a sound knowledge of logic.

Value of Logic in Philosophy
Thus the relationship or logic with philosophy the same as its relation with science, Every science requires logic for the proper presentation of scientific theory and cultivation of induction and deduction. In the absence of the knowledge of logic proper thinking in the field of philosophy is not possible. Neither can a philosopher arrive at logical conclusions.

Need of Philosophy in Logic
Logic discovers the laws of thought. It is on the basis of these laws that correct thinking is possible. Each science is based upon certain fundamental postulates. For example the law of causation is a postulate in physics. Similarly in logic the fundamental laws of though such as law of non-contradiction, law of identity and law of excluded middle or the law of sufficient cause are postulates, they are not proved but accepted. Logic does not example the truth of, these laws of thought. However this is precisely the function of philosophy. Philosophy examines the fundamental postulates of logic as all other positive and normative sciences. Thus philosophy provides the foundation to logic, therefore, depends upon philosophy.

Thus philosophy and Logic are closely related. According to logical positives, the function of philosophy is to examine the fundamental postulates of all the science and to show as to how far they are valid. It is so since science is limited to the field of facts while critical evaluation is the function of philosophy. This again is the function of philosophy in the fields of logic.                         

           FUNDAMENTAL LAWS OF THOUGHT

"Logic has often been defined as the study of 'Laws of thought' and in particular three principles:-

(1) The principle of identity. 
(2) The principle of contradiction.
(3) The principle of excluded middle.
Besides the above-mentioned three laws, Leibnitz considers Law of sufficient Reason, an additional law.

LAW OF IDENTITY
I. According to this law, if anything is A it is A, or if any proposition is true. In accordance with this we know that in a deductive argument, the meaning of the terms must remain same throughout. For example if we say that since books are meant to be read, the books in a bank must be read, we violate the law of in the usual sense. Heraclitus and Buddhists deny the validity of this law, because, according to them nothing remain same at any two moments.
But this criticism is invalid because there is fundamental difference in the realm of things and the realm of thinking. For instance though we cannot step into the same river again, this assertion itself is either true or false and if true it is true now as it was true when Heraclitus Asserted it. Therefore ideas and natural objects are not subject to same laws.
 
Meaning of the Law of Identity
The law of identity can be expressed as follows"-

(1) What is. is - It has been pointed out by the author of Bhagwadgita, that whatever exists cannot be non-existent and whatever is non-existent cannot exist. In other words what is, is and what is not, is not.

(2) Each object is equal to itself - Every thing is identical. Each object should be taken as it is. For example a kilogram is a kilogram and a pound is a pound. If we do not stick to their fixed meaning and take each to be identical with itself, we cannot use them for the purpose of thinking.

(3) A thing is what is - The nature of a thing has some fundamental elements, which show its basic properties and functions. For example, if it is said that a man, it may be tautology and yet one means by it that the human nature is like human nature and different form the nature of a thing, animal or God.

(4) Everything is according to itself - Leibnitz has pointed out to a law of identity of indiscernible in his monadotogy. This means that each monad represents only itself and no one else since each monads windowless and develops from within.
Thus in nature one finds different levels of things and living beings. No two things are identical. This is know/n as the law of identity of indiscernibles. In order words, every things is according to itself. Had there been two things of the same nature it would have been better to call them one rather than to. There can be no dualiam without distinction. If there is no distinction between two things they are one. Thus the analogy of a thing is only itself. A lion is a lion and different from all other animals. The only analogy of man is man.

(5) Truth is coherent- Every principle must be explained in consistency with is basic postulate since truth lies in coherence. While examining a philosophical thought it should not be compared with other philosophical thinking since the two are different. In order to examine the truth of a philosophy we have to enquire about its self-consistency. The logical implication of its basic postulate should be the same form the beginning to the end. Otherwise, it is far from consistent. It may be noted here that in that in the field of nature the above-mentioned however law may have certain exceptions. In the realm of thinking however, no such exception is possible.

Value of the Law of Identity
The law of identity does not mean that nothing is chargeable but it insists upon a uniformity and continuity in this change which is responsible for the identity of the object.
Every thing is this world is changeable. But while we think about an object we take it as something is not identical. If a thing is constantly changed, thought upon this thing is not possible,. This may lead to the dilemma that thought is not actually applicable to the changing nature, but in the realm of thought thinking is not possible without acceptance of the law of identity.

Again nothing can be defined without taking recourse to the law of identity. A thing is defined in terms of its properties and nature. Thus, though we may admit with the philosophers like F.H.Bradlley and Henry Bergson that the physical world is the result of the thought and the world of thought does represent the actual world, it must be admitted  that philosophies were not also possible without abstraction. Intact the world of thought should be considered as distinct from the world of things through the two are interrelated. It is them that we will be able to understand that just as the world of physical things follows the law of nature, similarly the world of thought follows the taw of thought.

LAW OF NON CONTRADICTION
The law of Contradiction has been expressed as A cannot be B and not B at the same time. In other works, a thing cannot both exist and non-exist at the same time. If you say that Ram is in the house, it cannot be said that the is out of the house. One cannot assert that Ram is both in the house and out of it unless the words, in and out are taken in some special sence. If it means physical existence with in. the same physical existence without is not possible.

Hamilton has called the law of contradiction as the law of non-contradiction. According to him correct thinking is non-contradicted. For example, a thing cannot be white and non white. If a thing exists it cannot be said to be non-existence. In other words either A is B however not-B at the time. Nothing can have contradictory qualities in the same space-time. It is possible that a shield is white on one side and non-white on the other side, but it cannot be white and non-white on the same side. The law of contradiction can be better called the law of non-contradiction since it shows that non-contradiction is a necessary condition for correct thinking. It may be remembered here that though one may find contradictory things in nature, the same is not possible in the world of thought. Coherence,though no virtue of the physical world, is certainly a condition for human thinking.

LAW OF EXCLUDED MIDDLE
According to this law anything must be either true or false, i.e. A or not A. For example, a piece of the toffee can either be sweet or not sweet. According to Jeyons, "The very name of the taw expresses the fact that (here is no third or middle course". Though in a way these laws of thought are related to each other because what law of non-contradiction states is implied in law of identity. But, we cannot by any means derive from 'A is A" and 'A is not A". For example to say that sun will not rise tomorrow. The truth of a proposition dies imply the falsehood of its opposite, but to bring out this implication we need another statement which is independent. Hegel's criticism of the law of non contradiction we need another statement is metaphysical and not logical. Since the prepositions of logic are independent of space and time they are formal in nature, they cannot be regarded to behave in the same manner as facts. Warm water may feel both not and cold, because what we mean is that warm is cool in relation to hot and hot in relation to cold. This will require two propositions. Therefore a proposition of logic can not have contradictory or contrary predicates.

LAW OF SUFFICIENT REASON
It has been pointed out by Leibniz that if there is no sufficient reason for a thing or statement to be what is and not to be different from it, then its actual existence cannot be real. Thus everything in the world has a sufficient reason of its existence. According to leibniz the law of sufficient reason is applicable both in the field of metaphysics as well as of logic. In metaphysics there should be some sufficient reason for each for the innumerable things found in the world. God is the cause of the world and each instance in the world has its sufficient cause. In logic every Judgment has some or the other basis, without which it cannot be logical. Thus different judgments have different basis. Even where there is change, it has a sufficient reason.

The law of sufficient reason is complimentary to the law of identity. According to the law of identity. According to the law of identity the date should remain unchanged. The law of sufficient reason, on he other hand, points out that a thing is as it is. The law of sufficient reason, points out that a thing can change only when there is a sufficient reason for the change. In the absence of such a sufficient reason no change is possible. In other words, other things being the same a thing remains as it is- As the law of sufficient reason is complimentary to the law of identity, some scholars do not lake it part from the taw of identity and consider it as a part of it.

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