The difference between being Logical and being Right

Logic is the math of ideas. That is, given the same input ideas, and the same series of logical statements, the end result will always be true or untrue, no matter who does the calculation. That’s one of the most beautiful things about math, is that opinion or personal experience doesn’t matter. Math is math, and if you disagree with it, you’re wrong. Your teacher can’t argue with the result, because, as long as your math is correct, so is your answer. The same is true for logic. Just like 2 + 2 + 4 will always equal 8, so, too, will “If I weigh 400 pounds then I am fat,” “I weigh 400 pounds,” “Therefore I am fat” will always be true. However, just like math, if you start with incorrect inputs, then most likely your outputs will also be wrong (unless you somehow manage to cancel out your own errors with other errors).

This can often be confused with other unrelated concepts. It’s common to see people use “logical” as a synonym for “reasonable,” “rational,” or “right.” It is none of those things. The word “logical” speaks only to whether or not the argument adheres to the established rules of logic. It does not speak to the intrinsic truth of the conclusion. For example, the following is a perfectly logical set of statements: “All black people are good runners.” “Being a good runner gives you good teeth.” “Good teeth make you eat more vegetables.” “Therefore, all black people eat lots of vegetables.” It is perfectly logical, even though it is obviously a ridiculous thing to say. That’s because the inputs were wrong, which means the output is wrong. Something can be perfectly logical, and still be incorrect. And likewise, something can be correct, and still be illogical. Take this example: “Most doctors are men.” “Most men are tall.” “Therefore, most doctors are tall.” This is not logically sound, because doctors could, for example, be the minority of men who are short. To see this more clearly, just replace “Doctors” with “Jockeys”, and the problem becomes more obvious.

That’s not to say that logic isn’t valuable in discerning truth. Logic is, in fact, more a method of double-checking a truth once it has occurred to us. You can safely assume that, if all of your input statements are true, and if you rigorously follow the rules of logic in laying out your argument, then your conclusion will also be true. You just can’t reasonably object to a logical argument with such soft rebuttals as “Well, I just don’t see it that way.” If you accept the premises, and you cannot find fault with the logic, then (if you’re intellectually honest), you must concede the conclusion. It doesn’t matter how you feel about it or whether you want it to be true. Truth is truth. But the veracity of a conclusion is always a function of both: the validity of your inputs, and the extent to which you stick to valid logic.

Never ascribe either more or less to logic than it deserves.