Jeff Hampton, age 16, of Paterson, N.J., for his question:
WHAT IS THE SCIENCE OF LOGIC?
Logic is the science that investigates the principles governing correct or reliable inference. It deals with the principles of valid reasoning and argument.
The study of logic is the effort to determine the conditions under which one is justified in passing from given statements, called premises, to a conclusion that is claimed to follow from them.
Logical validity is a relationship between the premises and the conclusion such that if the premises are true then the conclusion is true.
The validity of an argument should be distinguished from the truth of the conclusion. If one or more of the premises is false, the conclusion of a valid argument may be false. As an example: "All mammals are four footed animals; all people are mammals; therefore, all people are four footed animals." This is a valid argument with a false conclusion.
On the other hand, an invalid argument may by chance have a true conclusion. Try this: "Some animals are two footed; all people are animals; therefore, all people are two footed." this happens to have a true conclusion, but the argument is not valid.
What is now known as classical or traditional logic was first formulated by Aristotle, who developed rules for correct syllogistic reasoning. A well formed syllogism consists of two premises and a conclusion, each premise having one term in common with the conclusion, and one in common with the other premise. In classical logic, rules are formulated by which all well formed syllogisms are identified as valid or invalid forms of argument.
In the middle of the 19th Century, the British mathematicians George Boole and Augustus DeMorgan opened a new field of logic, now known as modern logic. It covers a far greater range of possible arguments than those than can be cast into syllogistic form.
Both classical logic and modern logic are systems of deductive logic.
Logic tells us what would be true if the premises were true. In deductive logic, the conclusion is a necessary consequence of the premises. In inductive logic, the conclusion is only more or less probable on the basis of the premises. Grounds for belief may be based on generalizations, analogies or causal connections.
A person may observe the planet Mars in a number of positions in the sky and infer that it is moving in an elliptical path. This is a "generalization," or a general principle which makes an assertion about all members of a class of objects.
A person may argue that student A is good at mathematics because he is like student B in temperament. He argues using an "analogy," or a comparison of two or more things which agree in some respects.
A person may observe that he gets restless as the temperature rises. He may then draw the conclusion that the heat makes him restless. He is arguing from a "causal connection," or from cause and effect.