4 Day 3: Third Degree
Chorus: The darkness inside the P‘s & Q‘s is unexpectedly challenged by the darkness outside. The late afternoon storm caught most by surprise; umbrellas are rare, but patrons taking refuge are not. The wind bellows as it bends trees and snaps limbs. The rain, often hard enough to fall straight down, pounds on windows and walls, and forms impromptu snakes of water flowing over and around everything. An occasional barrage of ball lightning flashes from one dark pregnant cloud to another, followed shortly by its muffled roars of thunder that seem to swirl around in the darkness left over.
Inside, Socrates X sits on a stool at the corner of the bar. Behind him, deeper into the dark shelter, foul-weather visitors play pool, video games, pinball; others watch. Many nurse a glass or a cigarette, and Philonius Daunting is beside himself trying to keep up with business. Behind the bar, he is constantly slinging happy-hour cups and bottles and exchanging bills over the constant din. The clack of pool balls, the clink of glass, the clank of a pinball special — three of a thousand sounds that swirl around the room and minds alike.
Socrates X sees and hears all of this as a grand play, the characters of which displaying the greatest of all acting skills. Like every intricate mechanism of nature, from the singular dance of a honeybee to the powerful forces of a thunderstorm, the buzz of activity in the P‘s & Q‘s is a fascinating subject of study. As he turns and takes in the activity, a reflective smile slowly and surely emerges, until his gaze rests on a clock on a far wall. A gaudy affair meant to remind all of some brand of beer, typical of a distributor’s free gifts, its glowing message had been painted black, and the only light left was around the face; Socrates X smiles broadly. As if fate were disguised as accident, Hatch enters the pub. Leaving a trail of water, he finds his way to the empty stool next to his new friend, and sits; a fresh lager coincidentally appearing before him.
Hatch: [Waving] Thanks, Phil! Hi’ya, SocX!
SocX: Hello, Hatch. [With a raised eyebrow, and a wry smile] Staying dry?
Hatch: Hardly! Nothing out there is dry.
SocX: [Glancing around, the smile widening] Nothing is dry in here, either. [Pointing at the nearest one] This booth is empty. Shall we?
Hatch: [As they both move to the booth] Yes. [After they are both settled] Either I’m dreaming, or it’s damn crowded in here!
SocX: [As Hatch lights a cigarette] You are not dreaming.
Hatch: So, it’s crowded in here.
SocX: Damn crowded, actually. Hatch, do you realize we just made an argument?
SocX: Yes. Your first statement gave us two options, and then I eliminated one of them, leaving us a conclusion.
Hatch: That it’s crowded? [Socrates X gives a half-nod as he drinks] That’s a good trick! I bet that always works!
SocX: Not always, and not this time either. We will talk later about why an argument like this works well [TBD], and why this one does not [TBD]. We will have to cover more fundamental aspects of an argument as well, like its parts [TBD], but for now let us concentrate on the first statement. It is called a disjunctive statement.
Hatch: [With hesitation] Disjunctive? Sounds broken, like it’s in pieces.
SocX: Well, it is. This statement is in two pieces (we call them disjuncts), each of which is itself a statement. They are separated by the word “or.”
Hatch: “Either…or.” Like two choices. This or that.
SocX: Yes, but we have to be careful here. There are two different ways to read such a statement. We can mean that the choices are exclusive, and that one and only one of the choices must be made; or, we can mean that one or both can be made. We call the second kind inclusive.
Hatch: So, it can be “this or that” or “this and that?” I’m not sure I understand.
SocX: Well, think of it in terms of what makes the statement true or false. If the statement is exclusive, only one disjunct can be true. For example, consider this statement: At this very time and place, either it is day or it is night. There is no chance it can be both day and night, right?
Hatch: When one side is true, the other is excluded.
SocX: Exactly. On the other hand, in an inclusive statement, both disjuncts can be true. Take this statement: Either the sun rises at dawn or the sun sets at dusk. Both disjuncts are true, and they do not conflict with each other.
Hatch: I get it now. Both can be included as true. [Smoking, as Socrates X nods and lifts his cup] But, why is that important?
SocX: Well, as a general rule we assume that disjunctive statements in arguments are inclusive.
Hatch: Really? Why?
SocX: [Chuckling] Good question. I suppose the simplest explanation is that we should try to be precise in the language we use in arguments. It is cumbersome to try to express inclusivity every time, but it is relatively easy to make it obvious that a disjunctive statement is explicitly exclusive.
Hatch: It is? How?
SocX: Actually, this brings us to another kind of statement, the conjunctive statement. This one is formed when two or more statements (called conjuncts) are joined by the word “and” or other words (implied or otherwise) that serve the same purpose, and is true only when all conjuncts are true. So, when we want to show that a disjunctive statement is exclusive, we can add this: “and not both.”
Hatch: [With awed understanding] Oh, that’s slick!
SocX: [With a chuckle] Yes it is, and it gets better. You will learn later that each of these have logical equivalents, and can be expressed as different statements that mean the same thing [TBD]. First, however, there are two more kinds of statements we need to identify. These will take some time to fully explain and understand. For now, we must be content with an introduction, and on some other occasion, we will discuss all of these statements more completely [TBD].
Hatch: I can’t wait. [Smoking] What statements are left?
SocX: Well, the final two kinds of statements are extremely important, and it is equally important to recognize them. The next kind of statement is the conditional — or “if…then” — statement.
Hatch: I know those: [Animated] If you’re late for work one more time, then you’ll be fired. If you don’t pay your taxes, they’ll take your house. Wait! There was no “then” in that last one. Is that okay?
SocX: Actually, it is. The word “then” is often left out, and sometimes that part of the statement can come before the “if” part.
Hatch: They’ll take your house if you don’t pay your taxes.
SocX: Exactly. Regardless of the order, a conditional statement always has two parts: the antecedent, which is after the “if;” and the consequent, which follows the “then.” These two parts, which are usually statements themselves, are always present, even if the indicator words (like “if” and “then”) are not. [Noticing a vaguely panicked look come across his friend’s face as he inhales] Do not be concerned, Hatch — most of the time conditional statements are obvious. What is not always so obvious is exactly how the statement works, the information it imparts, what role it plays in an argument. [Noticing that the panic is no longer vague as Hatch raises his cup] But, you will come to understand all of this later on [TBD]. For now, it will suffice to know of them.
Hatch: [Smoking] I sure hope so. So, what’s the last statement?
SocX: The final kind of statement is one of the most abused. It is called a categorical statement.
Hatch: Categorical? You mean, like, categories? Or groups?
SocX: Yes. When we talk about groups or categories or types or classes, we have to be very careful. We have to remember that these are merely convenient tools for discussion, and not necessarily perfectly concordant with reality.
Hatch: [Hesitantly, as he raises his cigarette for its final breath] What?
SocX: [As Hatch finishes his beer, smiling] Well, we will come back to that later [TBD]. For now, we need to be able to identify categorical statements. They have indicator words, just like the “if” and “then” in conditional statements, but there are a lot more of them. The words most often used are: all, every, none, some, many, few, most; but, there are others.
Hatch: Oh, okay. Like, All cats meow. Or, Some beers make me sick.
SocX: [Chuckling] Yes, both are categorical statements. [Lifting his empty cup] Are you ready for another?
Hatch: I can’t. The dogs have to eat, rain or not.
SocX: [As they both rise] Undoubtedly. Until next time, take care.
Hatch: You bet, SocX! [With more voluminous effort, and a quickly returned wave] See ya, Phil!
Chorus: As Hatch exits the P‘s & Q‘s, a clap of thunder greets him; nobody notices. Socrates X offers a hand, and Philonius accepts. As the storm thins throughout the evening, so do the patrons. With help, the pub is slowly restored, calmed and cleaned. After bidding farewell to its proprietor, Socrates X steps out of the pub into a cool, rainless night. A crisp, gibbous moon hangs in a clear sky, its light shimmering off nearly every water-soaked surface, and outlining the tremendous storm clouds passing to the East. Socrates X marvels for many moments, and then turns West.
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Next: Day 4: For Arguments’ Sake [TBA]