You are probably very proud of your grasp of English (unless you live in South Florida, in which case you may not give a damn). And yet I have seen plenty of people whose lack of understanding about basic structures like the “If” statement
Suppose a young child is misbehaving to the point that the caregiving parent decrees “If you don’t knock that off, I’m going to paddle you” (This is an old example; I’m sure nobody would ever actually do that today 😉 ). As young children have been known to do, for whatever reason, the child continues with its behavior. The parent repeats the statement, with added emphasis. Nothing changes. The parent soon throws their hands up and says “wait until (your other parent) gets home”.
The parent’s first decree, like all “if” statements, had two parts; a condition and a consequence (joined by the conjunction “if”), with the understanding that if the condition is true, then the consequence will occur. It’s simple enough that even a young child can understand it. If the condition is met and the consequence is not accomplished, then the statement would be considered false. In short, the child knew that the parent was lying.
Now suppose the non-caregiving parent comes home, sees the objectionable behavior, makes a similar decree, and then the first parent points out that they had already made that decree to no avail. The child, for whatever reason, stops the objectionable behavior. To everybody’s surprise, the second parent paddles the child. Although the child and many of you listeners may think bad thoughts about this parent, one thing you can’t call him/her is a liar.
As you can see here, the problem with the “if” statement is that is incomplete in the sense that it only addresses what happens when the condition is true, remaining completely silent to the possibility that the condition could be false. This allows most people to make the assumption that if the condition is false, the opposite of the consequence must occur. As the young child in our example learned, that assumption would be a mistake.
Don’t make stupid assumptions. As your lawyer would tell you, get it in writing. In the above example, since the second parent didn’t make any promises about what would happen if the behavior did stop, s/he can’t be accused of lying. If this example bothers you, I’m sure the second parent told the child afterward that the paddling was for not obeying the first parent, in which case we would be unable to judge the truthfulness of their claim until after the right set of conditions are met following some later episode of misbehavior (guesstimating any change in likelihood of that future misbehavior based on recent events will be left as an exercise for the reader). To lawyers, mathematicians, and the like, the parent’s explanation doesn’t matter to this case and is unnecessary.
Logicians have named operators (or functions) fulfilling all sixteen patterns of truthfulness or falsehood of expressions based on the truthfulness or falsity of two variables, such as the condition and consequence of the “if” statement described above. Engineers call the statement that yields the results you thought the “if” statement provided the “exclusive nor” function, “nor” being short for not or, meaning “giving the opposite results than the ‘or’ function”. Some refer to it as logical equality. In English, it would be represented by a sentence including the phrase “If, and only if”, such as “I will ground you for the rest of your life if, and only if, you do not stop screaming this very second”. If that type of statement had been the norm in this household, the non-caregiving parent, upon hearing the lack of results achieved by the other parent, was still free to add other (most likely “or”) clauses (to be discussed in a later article) to his/her decree. If you are now totally confused, please do not sign any document containing more than six words before consulting an attorney, or at least a mathematician. On second thought, in cases like this, I would stick with the lawyer.