Today’s post comes to us from TheRealGuyFaux. Thanks, Guy for a well-written and intelligent piece.
In the previous installment lo these many months ago, I mentioned “modal logic” in passing, defining it as “propositions that deal with ‘necessary’ versus ‘possible’.”
A quick definition of terms is in order:
“Necessary” => “being the case in any and all situations,” and;
“Possible” => “being the case in some situation whether or not it is presently the case in this situation.”
It is usually considered an axiom of this sort of logic that if something is “necessary,” then it is the case, and that if something IS the case, that it is “possible” for it to be the case. It does not work in the other direction, however. Simply because something is not prevented from being the case, i.e., “possible” (which we would then term “impossible” if it were somehow metaphysically prevented) doesn’t mean it is the actual current case, and just because something is now the case, we have no guarantee it will remain so unless there’s no other way it COULD be, i.e., “necessary.”.
There are different types of modal logics, depending on what sort of subject you are discussing. In a modal logic of ethics, for example, you would not expect that someone would be required to do something that is forbidden. To do so is to invite abandonment of any standard of what should and should not be done. Thus, you can believe that a transgression may be forgivable, i.e., Jean Valjean stealing bread, but Valjean was not being ordered to steal the bread by any moral code– rather, it was from self-preservation. You can get into discussions of whether self-preservation trumps all other ethical strictures, but you must first agree that, even in that extreme situation, Valjean could have stopped and not done it, in the sense that nothing prevented him from stopping, just as no one compelled him to do as he did other than himself.
There’s a logic of epistemology, i.e., “how do you know something?” Nobody seriously argues that one can “know” that which one does not believe. Oh, we may use a colloquialism like, “I know something happened, but I don’t believe it,” by which we mean, “Something must be so, despite my incredulousness.” But we would not persist in our disbelief after the initial wariness wore off, would we? And then we get into the Gettier Problem– what if our conclusion is correct, but that which induced us to come to that conclusion is faulty? In other words, “lucky guesses”? We believed something that turned out right in the end, but for the wrong reason– we do not “know” that right answer, said Gettier, because we didn’t believe the right evidence. You’ve got to be “right” all the way down the line to “know” something.
Where we usually encounter modal logic is in the form of the subjunctive mood and/or counterfactuals. For example, “If the Queen had balls, she’d be/would have been the King.” We laugh, because this makes intuitive sense– had the Queen been born male, the heir to George VI would have been a king instead of who it is, namely the Queen. And what we mean by this is, “It is entailed in the definition of ‘monarch’ that to be born male makes you the ‘King,’ while being born female makes you the ‘Queen’.” We have no problem understanding that sort of logic. Where we invite trouble is when the conclusion is not a “necessary” one, but rather a “possible” one.
“If the South had won the Battle of Gettysburg, they would have won the War..” Much as many Lost Causers might have wanted to believe it, it would not have logically followed. It could have turned out that way, mind you, in the sense that nothing we know of at that moment prevented it from happening, but there was no “necessary” about it. “…[T]hey MAY have won the War…” is a fairer and more defensible statement for which evidence could be adduced either way, I suppose. A lot might have changed, but once you’ve changed the timeline, you then need to introduce a lot more variables than just your favorite hobby-horse ones. (This sort of “temporal logic” would get us into a discussion longer than this essay, I fear!)
Where I’m going with all this is, just as in the discussion about enthymemes (unstated premises), a person hearing a modal logic argument does not come in with a clean slate, usually. They come in with some built-in assumptions, some of which, like Will Rogers (or Mark Twain, or Artemus Ward, or Ronald Reagan) said, are the things that you “know” but that aren’t so, and those will get you into trouble.
We need only look to what’s going on around us to see that we’re being told plenty of things that are not so, and from material implication, discussed in my first post on the subject, we know that anything can follow from a false premise. What an understanding of what modal logic is and does leads you to your asking yourself whether what follows is “necessary,” or merely “possible,” or void, even if we were to grant the truth of the premise.
You will notice that I’ve sorta assumed that you DO understand how it works, even in the last sentence of the previous paragraph, by saying “even if it were true.” But like the Bourgeois Gentleman from Moliere’s play with prose, you’ve been doing it all your life, even if you didn’t know it had a name (and the “even if” clause in this sentence is yet another example!)
Feel free to offer examples!
