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Laws of Nature are a stated regularity in the relations or order of phenomena in the world that holds, under a stipulated set of conditions, either universally or in a stated proportion of instances.

Laws of nature are of two basic forms: (1) a law is universal if it states that some conditions, so far as are known, invariably are found together with certain other conditions; and (2) a law is probabilistic if it affirms that, on the average, a stated fraction of cases displaying a given condition will display a certain other condition as well. In either case, a law may be valid even though it obtains only under special circumstances or as a convenient approximation. Moreover, a law of nature has no logical necessity; rather, it rests directly or indirectly upon the evidence of experience.

Laws of universal form must be distinguished from generalizations, such as "All chairs in this office are gray," which appear to be accidental. Generalizations, for example, cannot support counterfactual conditional statements such as "If this chair had been in my office, it would be gray" nor subjunctive conditionals such as "If this chair were put in my office, it would be gray." On the other hand, the statement "All planetary objects move in nearly elliptical paths about their star" does provide this support. All scientific laws appear to give similar results. The class of universal statements that can be candidates for the status of laws, however, is determined at any time in history by the theories of science then current.

Several positive attributes are commonly required of a natural law. Statements about things or events limited to one location or one date cannot be lawlike. Also, most scientists hold that the predicate must apply to evidence not used in deriving the law: though the law is founded upon experience, it must predict or help one to understand matters not included among these experiences. Finally, it is normally expected that a law will be explainable by more embracing laws or by some theory. Thus, a regularity for which there are general theoretical grounds for expecting it will be more readily called a natural law than an empirical regularity that cannot be subsumed under more general laws or theories.

Universal laws are of several types. Many assert a dependence between varying quantities measuring certain properties, as in the law that the pressure of a gas under steady temperature is inversely proportional to its volume. Others state that events occur in an invariant order, as in "Vertebrates always occur in the fossil record after the rise of invertebrates." Lastly, there are laws affirming that if an object is of a stated sort it will have certain observable properties. Part of the reason for the ambiguity of the term law of nature lies in the temptation to apply the term only to statements of one of these sorts of laws, as in the claim that science deals solely with cause and effect relationships, when in fact all three kinds are equally valid.

Everyone is subject to the laws of Nature whether or not they believe in them, agree with them, or accept them. There is no trial, no jury, no argument, and no appeal.

Excerpt from the Encyclopedia Britannica without permission.

Logic is the the study of propositions and of their use in argumentation. This study may be carried on at a very abstract level, as in formal logic, or it may focus on the practical art of right reasoning, as in applied logic.

Valid arguments have two basic forms. Those that draw some new proposition (the conclusion) from a given proposition or set of propositions (the premises) in which it may be thought to lie latent are called deductive. These arguments make the strong claim that the conclusion follows by strict necessity from the premises, or in other words that to assert the premises but deny the conclusion would be inconsistent and self-contradictory. Arguments that venture general conclusions from particular facts that appear to serve as evidence for them are called inductive. These arguments make the weaker claim that the premises lend a certain degree of probability or reasonableness to the conclusion. The logic of inductive argumentation has become virtually synonymous with the methodology of the physical, social, and historical sciences and is no longer treated under logic. Logic as currently understood concerns itself with deductive processes. As such it encompasses the principles by which propositions are related to one another and the techniques of thought by which these relationships can be explored and valid statements made about them.

In its narrowest sense deductive logic divides into the logic of propositions (also called sentential logic) and the logic of predicates (or noun expressions). In its widest sense it embraces various theories of language (such as logical syntax and semantics), metalogic (the methodology of formal systems), theories of modalities (the analyses of the notions of necessity, possibility, impossibility, and contingency), and the study of paradoxes and logical fallacies. Both of these senses may be called formal or pure logic, in that they construct and analyze an abstract body of symbols, rules for stringing these symbols together into formulas, and rules for manipulating these formulas. When certain meanings are attached to these symbols and formulas, and this machinery is adapted and deployed over the concrete issues of a certain range of special subjects, logic is said to be applied. The analysis of questions that transcend the formal concerns of either pure or applied logic, such as the examination of the meaning and implications of the concepts and assumptions of either discipline, is the domain of the philosophy of logic.

Logic was developed independently and brought to some degree of systematization in China (5th to 3rd century BC) and India (from the 5th century BC through the 16th and 17th centuries AD). Logic as it is known in the West comes from Greece. Building on an important tradition of mathematics and rhetorical and philosophical argumentation, Aristotle in the 4th century BC worked out the first system of the logic of noun expressions. The logic of propositions originated in the work of Aristotle's pupil Theophrastus and in that of the 4th-century Megarian school of dialecticians and logicians and the school of the Stoics. After the decline of Greek culture, logic reemerged first among Arab scholars in the 10th century. Medieval interest in logic dated from the work of St. Anselm of Canterbury and Peter Abelard. Its high point was the 14th century, when the Scholastics developed logic, especially the analysis of propositions, well beyond what was known to the ancients. Rhetoric and natural science largely eclipsed logic during the Renaissance. Modern logic began to develop with the work of the mathematician G.W. Leibniz, who attempted to create a universal calculus of reason. Great strides were made in the 19th century in the development of symbolic logic, leading to the highly fruitful merging of logic and mathematics in formal analysis.

Modern formal logic is the study of inference and proposition forms. Its simplest and most basic branch is that of the propositional calculus (or PC). In this logic, propositions or sentences form the only semantic category. These are dealt with as simple and remain unanalyzed; attention is focused on how they are related to other propositions by propositional connectives (such as "if . . . then," "and," "or," "it is not the case that," etc.) and thus formed into arguments. By representing propositions with symbols called variables and connectives with symbolic operators, and by deciding on a set of transformation rules (axioms that define validity and provide starting points for the derivation of further rules called theorems), it is possible to model and study the abstract characteristics and consequences of this formal system in a way similar to the investigations of pure mathematics. When the variables refer not to whole propositions but to noun expressions (or predicates) within propositions, the resulting formal system is known as a lower predicate calculus (or LPC).

Changing the operators, variables, or rules of such formal systems yields different logics. Certain systems of PC, for example, add a third "neuter" value to the two traditional possible values--true or false--of propositions. A major step in modern logic is the discovery that it is possible to examine and characterize other formal systems in terms of the logic resulting from their elements, operations, and rules of formation; such is the study of the logical foundations of mathematics, set theory, and logic itself.

Logic is said to be applied when it systematizes the forms of sound reasoning or a body of universal truths in some restricted field of thought or discourse. Usually this is done by adding extra axioms and special constants to some preestablished pure logic such as PC or LPC. Examples of applied logics are practical logic, which is concerned with the logic of choices, commands, and values; epistemic logic, which analyzes the logic of belief, knowing, and questions; the logics of physical application, such as temporal logic and mereology; and the logics of correct argumentation, fallacies, hypothetical reasoning, and so on.

Varieties of logical semantics have become the central area of study in the philosophy of logic. Some of the more important contemporary philosophical issues concerning logic are the following: What is the relation between logical systems and the real world? What are the limitations of logic, especially with regard to some of the assumptions of its wider senses and the incompleteness of first-order logic? What consequences stem from the nonrecursive nature of many mathematical functions?

Excerpt from the Encyclopedia Britannica without permission.