The term logic is used to describe the totality of all laws guiding the human thought. It is a truism that humans are rational beings whose thinking processes are based on certain principles. These principles and techniques of logic that have been developed to distinguish correct from incorrect reasoning are not however arbitrary. This is because there are certain fundamental laws guiding the operation of these principles and techniques and every thinking process, for it to be correct, it must comply with these laws: ‘the law of identity’, ‘the law of excluded middle’, and ‘the law of contradiction’ (also known as the law of non-contradiction).
The first principle or law asserts that a statement cannot be true and false at the same time. For example, a person could not logically make the statement: “it is raining and it is not raining”. Statement of this form are internally contradictory and cannot even be true. The second law says that a statement must be true or false. “It is raining or it is not raining” is an example. It is called “the law of excluded middle” because it is either raining or not, there is no third or middle possibility. The third law asserts that everything is equal to itself. The statement “X is equal to X” is true without exception. As with the first two laws, one immediately apprehends this principle. That is, one has an intuitive grasp of its truth, quite apart from any knowledge about the facts of sense experience.
The aim of logic is to make explicit the rules by which inferences may be drawn, rather than to study the actual reasoning processes that people use, which may or may not conform to these laws. Logic is to relate that holds between propositions, namely those which depend on combinations of truth and the falsity are possible. These relations are called logical relations. Two which are of central concern are consistency and consequences. A proposition is consistent with others when it is possible for them all collectively to be true, and consequences is the relation that holds between the premises and the conclusion of a valid argument.
There are two uncontroversial entrenched forms of justification: inductive and deductive justifications. These shows validity, at best that a rule of inference usually leads from true premises to a true conclusion (or that it is sufficiently likely to do so). This is too weak; a valid rule of inference, as noted above, necessarily leads from true premises to true conclusions. So it appears that the justification of validity must be deductive.
To say that an argument is valid is to say that the premises logically imply the conclusion. This does not tell us whether the premises are true or false. Indeed, it is possible to have a deductively valid argument which made up of false premises. This, then is one of the limitations of logic.