Now, Boys and Girls, Let’s Look at Some Syllogisms
by David Kennedy Bird
Is it just me, or has it been entirely too long since we’ve explored the exciting world of how to construct a sound logical syllogism?
A Voice from Near the Back of the Auditorium: Pretty sure it’s just you.
Heh heh. Terrific. Thanks. Ahem. So, why don’t we refresh our memories regarding what a ‘logical syllogism’ is and how they function as components in an argument.
A Voice from Near the Back of the Auditorium: Let’s not, and say we did.
Mmmmm. Pardon me one moment.
“Ushers? We appear to have a situ — very good. Yes. Thank you.”
Glad that’s taken care of. You can’t always control who ends up in your audience.
So, anyway, for those of us who could use a reminder, or are perhaps new to the blog, a syllogism is like the basic building block of a logical argument. Each syllogism is made up of three statements: the first two are the ‘premises,’ and the third statement is the ‘conclusion.’ The two premises introduce a set of ideas which, if understood correctly, lead necessarily to the conclusion.
Here, let me show you.
1. All flockbinkers are treadknicious.
2. Some wamwams are flockbinkers.
3. Therefore, some wamwams are treadknicious.
As you can clearly see, if the first two statements — the premises — are true, then the conclusion is bang-on. This is how a syllogism is supposed to work. The premises give you all the information you need to start out with, and if everything is set up right, the conclusion should naturally follow.
Here’s another example.
1. All Republicrats are freemish.
2. Some Democricans are Republicrats.
3. Therefore, some Democricans are freemish.
“But wait a second!” you say. “This is the same exact thing as that ‘All flockbinkers are treadknicious’ syllogism, but with a different set of silly words inserted into it.”
Ah, excellent reader, how good of you to pick up on that! And, indeed, the two syllogisms might be, sort of, the same thing — if all of the ‘silly words’ (as you have so uncharitably labeled them) are not only functionally but semantically equivalent. But that’s assuming an awful lot, isn’t it! (And you know what happens when we assume.) What makes you so sure, good reader, that a ‘flockbinker’ and a ‘Republicrat’ are the same thing?
The Good Reader: All meaningless words are the same thing. They all mean, and i quote, ‘diddly-squat.’
The Blogger: But i disagree. Perhaps different nonsense terms indicate different categories of nonsense?
The Good Reader: Nonsense is nonsense! How can there be different ‘categories’ of nonsense? It’s all nonsense! Nonsense nonsense nonsense.
The Blogger: Well, what if the term ‘wamwam’ occupies a certain semantic territory, albeit one that does not correspond to any actual existent thing or category of things, while the term ‘republicrat’ occupies a different semantic territory?
The Good Reader: That did not EVEN mean anything. You’re stalling.
The Blogger: Of course it did! Perhaps if i were to use more simple language… in deference to your elementary grasp of philosophy….
The Good Reader: [mutters something under her breath that does not sound nice]
The Blogger: Allright. Try this. What if there are modalities of meaning, some of which are attached to existent entities and some of which are attached merely to mental images, or even to nodules of possibility that correspond to no intelligible image or idea?
The Good Reader: You’re boring me.
Okay, okay, enough. We probably need to cut our losses on that one. Jeepers. Our first examples seem not to have gone over very well.
So here’s a syllogism in which all of the terms are ordinary, recognizable words.
1. If James is a good boy, he will be pelted with frozen waffles by a mob of crazed orangutans.
2. James is not a good boy.
3. Therefore, James need not worry about being pelted with frozen waffles by a mob of crazed orangutans.
Random Reader of the Blog, Who Is Not Specifically ‘The Good Reader’, But Who Is Nevertheless a Good Reader, and Who Raises His hand, Indicating That He Wishes to Volunteer to Analyze This Syllogism:
I’ve got this.
Um, right off the top of my head, i can see three problems with your… oh, what was the word you used? Syllogism? I think that was the word. And here they are.
Problem #1: Being pelted with frozen waffles by a mob of crazed orangutans is not a real thing. This does not ever happen. It just doesn’t. Literally no one has experienced this. The Blogger is scraping the bottom of a nonexistent barrel.
Problem #2: Even if it were a thing, it is highly unlikely that being pelted with frozen waffles by a mob of crazed orangutans would be the consequence of being a good boy. When you’re a good boy, the teacher gives you an ‘S’ for ‘satisfactory’ in the behavior section of your report card. Orangutans, crazed or sober, are not involved.
Problem #3: Even if crazed orangutans throwing frozen waffles were a real thing, and even if this were the sort of thing a good boy might expect to happen to him, there’s no reason to assume that one could not be pelted with frozen waffles (by a mob of crazed orangutans) even if one were not a good boy. Maybe there just happens to be a mob of crazed orangutans roaming the neighborhood, pelting people indiscriminately with frozen waffles. They don’t care whether you’ve been a good boy or not. They don’t know. They can’t even tell the difference. Dude. They are crazed orangutans.
So for those three reasons, and probably some more that i haven’t noticed, this syllogism is a disaster.
Back to you, Blogger.
Darn it. I hate to admit it, but Random Reader of the Blog has scored some decent points there. Hey, fella, toss me an email later on… i may have a job for you on this blog.
So. That syllogism turns out to have been a wash; let’s try one last one.
1. No flockbinkers are unicorns.
2. A unicorn is a small slippery fish with eight legs and a stinger.
3. Therefore, a flockbinker is not a small slippery fish with eight legs and a stinger.
And i’ll just go ahead and start you out with a hint: The syllogism is invalid.
The Good Reader: Invalid! Duh. Of course it’s not valid. There are so many things wrong with that one, i don’t EVEN know where to begin!”
The Blogger: I see that The Good Reader has once again made an appearance. Well, Good Reader, lay it on us. What’s the problem here?
The Good Reader: There are skoozoos of problems. To begin with…
The Blogger: One moment, please. Did you actually say, “skoozoos of problems”…?
The Good Reader: I did.
The Blogger: I’ve never heard that one before. Hmmm. Interesting. Well, okay, carry on.
The Good Reader: Right. First off, how can we know that no flockbinkers are unicorns?
The Blogger: Well, i mean, golly, they just aren’t!
The Good Reader: That’s the best you’ve got…?
The Blogger: Let’s just say this: say we are positing, for the sake of argument, that ‘flockbinker’ and ‘unicorn’ are mutually exclusive categories.
The Good Reader: Fine. That’s pretty arbitrary, but whatever. So then let’s go on to the next thing, which is your totally false definition of ‘unicorn’.
The Blogger: False definition? What? Where?
The Good Reader: You claim in this syllogism that a unicorn is “a small slippery fish with eight legs and a stinger.”
The Blogger: Okay. So?
The Good Reader: That’s not even a good definition of a fish, much less a unicorn! A fish can’t have eight legs. It wouldn’t be a fish. It would be… an arachnid? Or something.
The Blogger: But unicorns don’t exist, so how can there be a true or a false definition of one? Hah! I’ve got you there.
The Good Reader: So… Okay. Here’s this. Dumbo the Elephant has a six-cylinder engine, seventeen heads, ginger ale for blood, and he eats postal delivery workers for breakfast.
The Blogger: What? That’s not right! Dumbo isn’t anything like that!
The Good Reader: Ah, but he’s a fictional character, he doesn’t exist, so, according to you, i can define him any way i want to. [makes a highly unattractive ‘neener, neener’ face that her mother would find most frightfully disappointing]
The Blogger: Well, um, we could discuss at some length the issue of what it means to say that Dumbo ‘does not exist’….
The Good Reader: …and we could apply the exact same criteria to whether unicorns exist or not. Surely you’re not saying that Dumbo the Ohmigosh Stupid Fictional Elephant is somehow more real than a unicorn…?
The Blogger: Well…no.
The Good Reader: I didn’t think so.
The Blogger: So, for the sake of the argument, a unicorn could STILL be a “small, slippery fish with eight legs and a stinger.” We just define him that way, by fiat. In this syllogism, that’s what a unicorn is.
The Good Reader: So syllogisms don’t have to have even a remote connection to reality. Logic is for dreamers and drug users and Tim Burton and people in psychiatric hospitals.
The Blogger: Um, no.
The Good Reader: And anyway, you yourself said that this particular syllogism is invalid. Right?
The Blogger: I did. You just haven’t discovered the reason why it’s invalid yet.
The Good Reader: I’ve pointed out that it’s made up of bizarre garbled incoherent hash. You want more than that?
The Blogger: Well, to be exact, you haven’t really….
The Good Reader: So, Mister Blogger, why would you say that it’s invalid, if not for the fact that you haven’t defined a single thing correctly in it?
The Blogger: Well, a flockbinker could still be a small slippery fish with eight legs and a stinger, even if it’s not a unicorn. Maybe there’s more than one kind of animal that’s a small slippery fish with eight legs and a stinger. A unicorn is one kind, and a flockbinker is a different kind.
The Good Reader: I hereby accuse you of the excessive use of alcohol.
The Blogger: No, really, it works. Think it through. Draw a diagram if you have to.
The Good Reader: If you want to represent logic to your readers as being a truckload of absurdity that’s completely useless for actually figuring anything out in the real world, go right ahead. [*sigh*]
The Blogger: See, here’s the circle that includes all of the unicorns, and here’s the circle that includes all of the flockbinkers —
The Good Reader: Someone kill me now.
The Blogger: And notice that, even though the two circles don’t overlap, they could still both contain different kinds of small slippery fish with —
The Good Reader: Make it painless, if possible, but i’m ready to go.