Today’s installment comes from someone we all enjoy reading – and his knowledge shared has made all of us better informed, if not better thinkers.
Thanks to .
So, the other day I’m on a site where I offered the following thought: “The writer Ayn Rand once observed that whenever you are attempting to use logic to show someone where their argument misses the mark, and they concede the logic of your point but say, ‘It’s logical, but logic has nothing to do with it,’ what they’re really saying is, ‘It’s logical, but I have nothing to do with logic’.” Sure enough, some commenter says to me, “What about aesthetics? There’s no logic to THAT!” I was just about to go “meta” on his ass and say, “You just proved Ayn Rand’s point,” i.e., he hadn’t met Rand’s point with any sort of logical argument against it, and so, he was having nothing to do with logic at that point, but I figured, why bother?
What that conversation prompted in me was a bit of a callback to a conversation I had had with Mark of “rhetoric versus eristic in argumentation,” “rhetoric” being defined as “attempts at persuasion” and “eristic” being “attempts at debunking.” The two are important in ANY sort of “dialectic,” defined as “the give-and-take on a particular subject.” Eristic ideally is supposed to say to rhetoric, “You MAY have a valid point, but you’re not making it validly.” Eristic practitioners may resort to all sorts of “counter-rhetoric” which fails as a valid argument if all they want to do is to shut up the rhetorician with all sorts of fallacious argumentation in “debaters’ tricks” kinds of ways. There are lists of fallacies, and you can find them on any search engine, and so I won’t bother listing any, but we all know SOME, and we will often think when hearing/reading them, “Hey wait, that doesn’t follow!”, in a Potter Stewart maybe-I-don’t-know-the-technical-term-name-for-them-but-I-know-them-when-I-hear-them sort of way.
So, I just thought I’d brush everybody up on logic real quick:
- There are what are called the Laws of Thought, which are:
- “For every A such that it has quality x, A is an A with quality x if and only if it’s an A with quality x.”;
- “An A with quality x either is one or else it isn’t”; and
- “There’s no such thing as something that is both an A with quality x and NOT an A with quality x”
Now it may seem that these are just three different ways of explaining the same thing, and perhaps they are, but just to make sure everyone gets the point, the original philosophers of logic broke them up into those three different formulations.
But you kind of need to know what the “logical operators” in those laws are– for example, what does “if and only if”, “either/or”, “both/and” mean when used in a logical proof? We know what those signify in colloquial speech, of course, or else (“or else”!) we couldn’t even converse with each other– but what do they signify?
“Both/and” = the two (or more, for that matter) conjoined things are true, or the statement fails;
“Either/or” at least one (maybe two) of the disjoined things are true, and fails if none of them are true.
“If and only if” = the two things are either both true or both false, but if one is true and the other is not, the statement fails.
There’s also a deal called “modus ponens” which involves a process called “material implication”– it goes essentially “Given, A, and given, if A then B, then B.” The “and” here means that if the two givens are true, it logically follows that B is true, this because material implication says that “You don’t start out with true premises and end up with a false conclusion.” And there’s another deal called “modus tollens” which goes “Given, if A then B, and given, not-B, then not-A”, because for it to logically follow if both givens are true, you can’t have A implying both B and not-B, refer back to Laws of Thought– A cannot be true if it implies both B and not-B, therefore it is not-A (defined as “something which negates A”) as being what logically follows.
What happens is that many people often fallaciously think, “If A then B, but not A, so, therefore not B.” This may factually be the case, but it does not logically follow. Likewise, “If A then B, and B, so therefore A” again, it may factually be the case, but it does not logically follow.
The last paragraph here gets us into a whole ‘nuther realm of logic called “modal logic” which I won’t delve into right now (perhaps in a later post, if you really want me to), but suffice it to say that it deals with things that are “necessary” and things that are “possible”– and THAT’s where a lot of the argumentation in things like, e.g., politics takes place. And that’s also where a lot of the fallacious argumentation occurs as well..
I can get deeper into this in replies to any comments, if anyone wants to ask me. I’m kinda hoping everyone has learned this sorta thing in life if they didn’t do so in the formal classroom setting, but all I’m doing, for those who “know it without having learned it in school” is to teach you the technical terms.
