Symbolic Logic

Logic deals with statements, and statements vary extensively in the precision with which they may be made. If someone says, "That is a good book," that is a statement. It is far less precise, however, than a statement such as "Albany is the capital of New York." A good book could be good because it is well printed and bound. It could be good because it is written in good style. It could tell a good story. It could be good in the opinion of one person but mediocre in the opinion of another.

The statements that logic handles with the greatest certainty are those that obey the law of the excluded middle, i.e., which are unambiguously true or false, not somewhere in between. It doesn't offer much help in areas such as literary criticism or history where statements simple enough to be unequivocally true or false tend also to be of little significance. As an antidote to illogical thinking, however, logic can be of value in any discipline.

By a "statement" in logic one means an assertion which is true or false. One may not know whether the statement is true or false, but it must be one or the other. For example, the Goldbach conjecture, "Every even number greater than two is the sum of two primes," is either true or false, but no one knows which. It is a suitable statement for logical analysis.

Other words that are synonyms for "statement" are "sentence," "premise," and "proposition."