TRUTH
To be true or false is a property of a statement. Usually we say that a statement is true when it expresses a fact. For example, take the statement “Salt dissolves in water.” We consider this statement to be true because it expresses a fact. Actually, in this case we can roughly prove the fact ourselves. We take a bowl, put some water in it, and put in a little salt. After a while we look into the water and notice that no salt whatever is to be seen.
Of course, this statement, like many another, occurs in a context where certain things are understood. One of the understandings here, for example, is “a small amount of salt in a much larger amount of water.” For if we put a whole bag full of salt in just a little water, not all the salt will dissolve. Nearly every statement occurs in a context that we must know if we are to decide whether the statement is true or false.
LOGICAL TRUTH
Logical truth is different from ordinary truth. With logical truth we appeal not to facts but to suppositions. Usually we say that a statement is logically true when it follows logically from certain suppositions. In other words, we play a game that has useful, even wonderful, results. The game starts with “if” or “suppose” or “let us assume.” While the game lasts, any statement is logically true if it follows logically from the suppositions.
For example, let us take five statements:
- 1. “The earth is flat like a sheet of paper.”
- 2. “The earth is round like a ball.”
- 3. “John Doe travels as fast as he can, without turning
- to left or to right, for many days.”
- 4. “John Doe will fall off the earth.”
- 5. “John Doe will arrive back at his starting point.”
Let us also take a certain context in which: We know what we mean by such words as “earth,” “flat,” “falling,” etc.; we have other statements and understandings such as “if John Doe walks off the edge of a cliff, he will fall,” “a flat sheet of paper has an edge,” etc. In this context, if statements 1 and 3 are supposed, then statement 4 is logically true. On the other hand, if statements 2 and 3 are supposed, then statement 5 is logically true. Of course, for many centuries, nearly all men believed statement 1; and the importance of the years 1492 to 1521 (Columbus to Magellan) is linked with the final proof that statement 2 expresses a fact. So, depending on the game, or the context, whichever we wish to call it, almost any statement can be logically true. What we become interested in, therefore, is the connections between statements which make them follow logically.
LOGICAL PATTERNS
Perhaps the most familiar example of “following logically” is a pattern of words like the following: