THOUGHT, LAWS OK Logicians usually formulate cer tain ultimate principles or assumptions implied in all consistent thinking and reasoning. These principles are known as the "laws of thought" in the narrower and more usual sense of the expres sion, though in a wider sense the rules of the syllogism and of induction, etc., might be called laws of thought. Three or four such fundamental principles are usually formulated. Perhaps a fifth ought to be added. They are as follows. (1) The Principle of Identity: "A is A," or "a thing is what it is" or "everything has a certain character which it retains more or less" (see IDENTITY). ( 2) The Principle of Contradiction: "A is not non-A," or "A can not both be B and not be B," or "A cannot be both B and non-B," "a thing cannot both have and not have a certain at tribute," or "the same predicate cannot be both affirmed and denied of the same subject." (3) The Principle of Excluded Middle: "A either is or is not B," or "A is either B or non-B," or "a thing must either have or not have a certain character," or "of two contradictory predicates one can be asserted of every relevant subject." (4) The Principle of Sufficient Reason: "Noth ing occurs for which one having sufficient knowledge might not be able to give a reason sufficient to determine why it is as it is and not otherwise" (Leibniz) . (5) The Principle of Uniformity of Reasons: "Whatever is regarded as a sufficient reason in any one case must be regarded as a sufficient reason in all cases which are essentially of the same kind," or, expressed negatively, "noth ing can be regarded as a sufficient reason in any one case unless it can also be regarded as a sufficient reason in all cases of that kind" (A. Wolf).
These principles are indemonstrable assumptions or postulates. If they cannot be proved, neither can they be disproved. Any one, who chooses to challenge, say, the principle of contradiction, would only put himself in an absurd position. For, by refusing to accept its validity, he admits the possibility that those who accept it and those who reject it may both be right. So he has nothing to object to. Again, in describing these principles as laws of thought it is not intended to contrast thought with things, and to suggest that they are mere peculiarities of human ways of thinking without foundation in objective fact—as Nietzsche and some prag matists or sceptics would maintain. Normally what we really think we believe to be true of the facts referred to. The laws of thought were originally assumed to hold good of things as well as of thought ; and they are still so regarded by many thinkers. Sea Locic and the bibliography given there.