Some early thinkers, after having defined logic as “the science of the laws of thought”, went on to assert that there are exactly three basic laws of thought, laws so fundamental that obedience to them is both the necessary and the sufficient condition of correct thinking. In the western tradition, the concept of laws of thought can be traced back to Aristotle (384-322BC) the eminent Greek thinker, who is considered to be pioneer of western logic. As part of his project, Aristotle was trying to describe the basic laws by which human thought (and reasoning) can occur. As an examples of foundational laws, he identified the following three laws:
Principle of Identity: This principle asserts that if any statement is true, then it is true. Using our notation we may rephrase it by saying that the principle of identity asserts that every statement of the from p implication p must be true, that every such statement is tautology.
Principle of Noncontradiction: This principle asserts that no statement can be both true and false. Using our notation we may rephrase it by saying that the principle of noncontradiction asserts that every statement of the form p ·~p must be false, that every such statement is self-contradictory.
Principle of Excluded Middle: This principle asserts that every statement is either true or false. Using our notation we may rephrase it by saying that the principle p disjunction ~p must be true, that every such statement is a tautology.
Law of Sufficient Reason : In Leibniz , the view that nothing takes place without a reason sufficient to determine why it is as it is and not otherwise. He held that criteria of truth are clarity and absence of contradiction. Thus, to test the truths of reason it was enough to apply the logic of Aristotle (the law of identity, contradiction and the excluded middle) while the law of sufficient reason was needed to test “truths of fact.” This law comes very near to the harmony of truth according to which statement is true which harmonizes will all things known.
These laws are sometimes misunderstood. The first does not imply nothing ever changes. The second does not imply that a thing can have only one property. The third does not imply that everything is black or white: it implies only that either everything is black or something is not black. Aristotle identified these laws as the necessary condition of human thought: without them, thought cannot occur. He also held them as laws of thought, i.e. as fundamental principles for human rational thinking. George Boole, one of the greatest mathematicians of 19th century and one of the founders of mathematical logic, fully supported these Aristotelian notions.