Logical and reasonable

Something being logical does not mean it is reasonable, and the reverse does not hold either. Many people confuse the logical with the reasonable. It is a fairly common mistake.

One of the things we cannot forgive Gene Roddenberry and Mr. Spock for is the meaning they give to the word logic.

The problem is that when Mr. Spock says “that would not be logical”, what he really means is “that would not be reasonable”. This is one more example of how television, even quality television, ruins people’s education.

Almost always, when someone says a fact is logical, they actually mean the opposite: that the fact seems right based on intuition and common sense.

Strictly speaking, when we say that something is logical in and of itself we are talking nonsense. Because what it means for a statement to be logical is that the statement is inferred from a set of axioms by means of a formal system of reasoning. If you don’t know the formal system, or the axioms, then you cannot say whether the statement is logical, and calling something logical is meaningless.

Besides, the things people call “logical” are not even inferable from any axioms.

They may be reasonable things, but they are not logical, unless someone shows you the chain of inferences and prior reasoning.

Logic is not one thing, but a name for a family of formal proof systems with their inference rules.

There are many logics, as Mark Chu Carroll explains in “Mr. Spock is not logical”

There are many logics, and a statement that is a valid inference (meaning that it is logical) in one system may not be valid in another. To give you a very simple example, think about a statement like “The house on the corner is red”. Most people would say that it’s logical that that statement is either true or false: after all, either the house is red, or the house isn’t red. In fact, most people would agree that the statement “Either the house is red, or it isn’t red” must be true.

In the most common logic, called predicate logic, that’s absolutely correct. The original statement is either true or false; the statement with an “or” in it must be true. But in another common logic, called intuitionistic logic, that’s not true. In intuitionistic logic, there are three possible truth values: something can be true (which means that there is a proof that it is true); something can be false (which means that there is a proof that it is false); and something can be unknown so far (which means that there’s no proof either way).

In addition to having different ways of defining what’s true or provable, different logics can describe different things. Our good old familiar predicate logic is awful at describing things involving time – there’s really no good particularly good way in predicate logic to say “I’m always hungry at 6pm”. But there are other logics, called temporal logics which are designed specifically for making statements about time.

Now, the interesting thing about logic is that it is entirely mechanizable. You don’t need to understand the statements in an argument to be able to draw inferences. That is important to understand, because many people get tangled up and don’t notice that their reasoning does not follow a logical chain, and it is easy to show them they are wrong without having to pass any value judgment on what they said. You can do that, but it would not necessarily be reasonable, especially if you are arguing with your friends.