What is Logic?
Logic is the science of correct reasoning. The purpose of logic is to help people to think without making mistakes and to reason easily and in an orderly manner. Logic is used, consciously or unconsciously, by every human being. It is applied in everyday life, as well as in technical fields, such as the physical sciences, mathematics, philosophy, theology, and law.
Although people think about different subjects, they all think in basically the same way. They begin by conceiving ideas, which they express in such terms as "man," "mortal," and "Socrates." They then combine their ideas to form judgments that are expressed in propositions, such as "All men are mortal" and "Socrates is a man." Finally, they combine their judgments in a logical argument, such as "All men are mortal; Socrates is a man; therefore, Socrates is mortal." Usually, however, the argument is thought or expressed in a shortened form, such as "Socrates is mortal because he is a man."
The argument about Socrates is an instance of a deductive argument. The same kind of argument is employed when a person reasons: "All metals are conductors of electricity; copper is a metal; therefore, copper is a conductor of electricity." Such arguments, called syllogisms, were first analyzed scientifically by the ancient Greek philosopher Aristotle and were further developed in the Middle Ages by such Scholastic philosophers as Peter of Spain (later Pope John XXI) and Peter Abelard. A syllogism contains two premises, or initially given propositions, and a conclusion that is logically drawn from them. The argument is valid, or correct, because anyone who accepts the premises as true must also accept the conclusion as true.
The validity of an argument results from its form, or structure. The form is usually illustrated by symbols, called placeholders, that indicate where sets of words or suitable expressions can be inserted to produce the argument. For example, the syllogisms about Socrates and conductors of electricity are categorical, or declarative, syllogisms. The subject of the conclusion appears in one premise, and the predicate of the conclusion appears in the other; a third term, called the middle term, appears in both premises, linking them together and making possible a conclusion: "All M(iddle term) are P(redicate); S(ubject) is M; therefore, S is P." Categorical syllogisms may also be based on the propositions "No M is P;" "some M is P;" and "some M is not P." An example is the argument "No teachers are manual laborers; some men are teachers; therefore, some men are not manual laborers." The conditional syllogism, first developed by Stoic philosophers, has the form: "If A is B, then C is D; A is B; therefore, C is D." The disjunctive syllogism has the form: "Either A is B or C is D; A is not B; therefore, C is D."
Further developments in deductive reasoning occurred as early as the 17th century, when men like Baron Gottfried von Leibniz became concerned with the relation of logic to the new mathematical sciences. Such 19th-century logicians as George Boole, Friedrich Wilhelm Schroder, and Gottlob Frege began to apply mathematical methods to logic. Elaborate systems of symbols have made it possible to develop an algebra of logic and thus to handle complicated arguments easily. In the 20th century, Bertrand Russell and Alfred North Whitehead showed in Principia Mathe-matica (1910-1913) that the basic ideas of mathematics can be derived from the basic concepts of logic. Modern mathematical, or symbolic, logic has many applications in subjects as diverse as the theories of computers and the philosophy of science.
Thus, logic is concerned with the deductive procedures by which a person can validly derive a conclusion from a set of premises. However, some arguments are invalid because they contain a fallacy, or error in reasoning. The fallacy may arise from using terms whose meaning is ambiguous, from employing vague or obscure propositions, or from some other cause. For example, it would be a fallacy for a person to argue: "A pen is a writing instrument; an animal enclosure is a pen; therefore, an animal enclosure is a writing instrument."
In addition, even valid form in an argument does not guarantee a true conclusion. If even one of the premises is false, the conclusion may also be false. For example, a person could argue: "No one who disagrees with the majority is right; every heretic disagrees with the majority; therefore, no heretic is right." In this instance, one must reject the first premise as false. Reasoning is sometimes classified as a priori or a posteriori depending on whether the premises are independent of (prior to) experience or derived from (posterior to) experience. Mathematical reasoning, for example, is a priori.
The process of reasoning directly from experience is called inductive reasoning. It consists of observing and mentally organizing data and then making a generalization about the data. In making such generalizations, a person always draws heavily on past experience. When they have no reason to believe otherwise, human beings assume that the future will be similar to the past and that their past experience provides a reliable guide for their thinking. Some philosophers, such as Nicholas of Autrecourt in the 14th century and David Hume in the 18th century, have held that even such scientific laws as those of cause and effect are based primarily on inductive reasoning from past experience.
Many thinkers stress that the conclusions of inductive reasoning cannot be logically demonstrated. They hold that the truth of the premise, which is concerned exclusively with the past, provides only a good reason for thinking that the conclusion, which is concerned with the present and future, is also true. The degree of probability of the conclusion depends in part on how much experience the speaker has had and how varied such experience has been. The study of inductive arguments was carried on by such men as John Stuart Mill in the 19th century. The study has led to the development of elaborate and sophisticated theories of probability and statistical inference.
Both inductive and deductive reasoning have certain limits when used alone. Deductive reasoning may produce a false conclusion, and inductive reasoning cannot produce more than a probable conclusion. Most people naturally combine the two methods of thought, as can be seen in Albert Einstein's theory on the effect of gravity on the movement of light. From certain peculiarities in mathematical equations that expressed inductively observed characteristics of light, Einstein generalized that all light rays are affected in their travels by the gravitational pull of heavenly bodies. The inductive generalization became the first premise in a line of deduction. Einstein then selected a star whose light rays would pass near the sun and could be observed from earth during a solar eclipse. Applying his first premise to the particular case of this star, he concluded deductively that its light rays passing near the sun would be bent by the pull of the sun's gravity. Observations at the time of the eclipse confirmed this theory inductively, thus lending extra weight to its probable accuracy.
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