Two questions frequently asked by students are:
(1) What is logic? and (2) Why
study logic?
Logic is the science of necessary inference. An inference is the forming of a conclusion from premises by logical methods -- the conclusion itself. The adjective necessary in necessary inference or necessary consequence means there is no way to avoid the conclusion of an argument. We define an argument as one or more propositions in support of another proposition. The propositions in support of the other proposition are called premises; the proposition supported by the premises is called the conclusion. More about necessary inference later, but first, what is a proposition?
A proposition is a form of words in which the predicate is affirmed or denied of the subject of a declarative sentence. A proposition is the meaning of a declarative sentence. Declarative sentences are either true or false. Propositions are the premises and conclusions of arguments. Other sentences, in expressing commands, posing questions, or conveying exhortations are neither true nor false. Some questions, rhetorical questions, are intended as propositions; but if a question is not rhetorical, then it is neither true nor false.
Arguments divide into two classes: deductive arguments and inductive arguments. This classification amounts to two different claims. The premises of Inductive Arguments claim to provide incomplete or partial reasons in support of the conclusion. The premises of Deductive Arguments claim to provide conclusive reasons for the conclusion. In Inductive Argument, the conclusion is said to be either probable or improbable. With Deductive Argument the conclusion either follows necessarily or it does not. That is to say, the conclusion is either a necessary consequence of the premises or it is not a necessary consequence of the premises. Another way of stating the same thing: A Deductive Argument consists of a conclusion presumably deduced from premises. The deduction of conclusions from premises is at the heart of logic.
The phrases necessary consequence and necessary implication mean necessary inference . The use of one or the other phrase depends on the emphasis. If one stresses that the premises imply a conclusion, one speaks of necessary implication. If one stresses the conclusion resulting from premises, one speaks of necessary consequence. With either phrase, the reference is a claim of necessary inference between premises and conclusion of a Deductive Argument. If the conclusion of a Deductive Argument is a necessary consequence of the premises, then the argument is valid; otherwise, invalid. Using other words: If the premises of a Deductive Argument necessarily imply the conclusion, then the argument is valid; otherwise, invalid.
Summarizing this section. Logic is the study of the relation between premises and conclusion in Deductive Arguments. If the conclusion follows from premisesnecessarily (that is, the conclusion is unavoidable), then the argument enjoys valid status; if not (that is, the conclusion can be avoided), then the argument is invalid. Every Deductive Argument is either valid or invalid.
There are at least three reasons.
First. To the question what is more basic than the three R's of Reading, wRiting, and aRithmetic, we answerTHOUGHT. To engage in any one of the three activities, you must think! Thinking, if it is correct, follows rules. Sometimes we think incorrectly, when we neglect the rules for correct thinking. Other times, we make mistakes in thinking or reasoning. The rules for correct thinking and methods for avoiding mistakes in reasoning belong to the subject of logic.
Second. The study of logic trains the mind to distinguish logical from emotional (psychological) appeals offered in support of a conclusion or a position. To opt for a course of action confusing an emotional appeal with a logical appeal is to fall victim to incorrect thinking. It is a fallacy to accept an emotional-inference as a necessary-inference. Logic is the irreplaceable means for correct thinking and avoiding fallacious reasoning.
Third. The structure of Man's mind is the same as his Creator's. God is not insane; He is a rational being; the structure of God's mind is logic. For these reasons, we say not only that logic is irreplaceable and universal, but logic is necessary and fixed. It is not one scheme of things among others. It is not something optional, for Man's mind was formed on the principles of identity, excluded middle, and contradiction.
The three laws of thought are universal, irrefutable, and true for reasons already stated. Without these laws, it is impossible to imagine how anything written or spoken could be intelligible. More to the point, the laws are the basis of necessary inference, for without them, necessary inference vanishes! To repeat, the laws of logic are universal, irrefutable, and true. By "universal," we mean allows for no exception. "Irrefutable" means that any attempt to refute them, makes use of them; thus, establishing them as necessary for argument. "True" means not only "not-false," but not-false because they are grounded in the Logos of God, the source and determiner of all truth. Moreover, the laws stand together as a trinity; to fault one, is to fault all, and to uphold one, upholds the others. Together, these laws establish and clarify the meaning of necessary inference for logic and all intelligible discourse.
Here is a brief statement of each.
| 1 | The law of identity states that if any statement is true, then it is true; or, every proposition implies itself: A implies A. |
| 2 | The law of excluded middle states that everything must either be or not be; or, everything is A or not-A. |
| 3 | The law of contradiction states that no statement can be both true and false; or, A and not-A is a contradiction and always false: thus, not both A and not-A. |
Without the first, identity or sameness is lost; without the second, confusion begins; and without the last, irrationalism is in full residence.
To recapitulate. Logic is the science of necessary inference. The basic elements are propositions in arguments. A proposition is the meaning of a declarative sentence. An argument is composed of propositions some of which are premises, one of which is the conclusion. The premises are reasons given to support the conclusion of an argument or a position. Arguments are classified as either inductive or deductive. With Deductive Argument, we ask: "Does this conclusion follow as a necessary consequence from these premises?" If the answer is affirmative, the Deductive Argument is valid; otherwise, the argument is invalid. Deductive Arguments are either valid or invalid. Also, if the argument is not invalid, then it is valid. If the argument is not valid, then it is invalid.
Three reasons for the study of logic are (1) correct thinking requires it; (2) discerning minds necessarily depend on it; and (3) man is a rational being in the image of his Creator. Logic is universal, necessary, and irreplaceable. Man's mind was formed on the principles of identity, excluded middle, and contradiction. These three laws are the basis for all intelligible thought. Without them, all rational discourse vanishes.