Lecture: Midterm Review & Exam
Lecture script · about 15–20 minutes spoken · Week 8
Opening
Picture the week before a midterm. You have seven weeks of notes open: 6 argument forms, 6 syllogisms, and 12 fallacy passages. Every page looks equally important, and you don't know where to start.
Here's the way in I want to give you. Every topic so far asks for one test or one distinction. If you can say which test a passage calls for, you've done most of the work. A business major told to either cut a product line or close a store needs that habit. So does a nursing student reading a form that asks, "Have you stopped skipping safety checks?"
Here's where we are. Week 1 taught you to find an argument. Week 2 gave you standard form and maps. Week 3 gave you validity, soundness, strength, and cogency. Week 4 taught the conditional forms, and Week 5 the Venn test. Week 6 watched words shift meaning, and Week 7 named the fallacies of relevance.
In this lecture I'll walk through those weeks one test at a time. Then you'll meet the one new family of the week, the fallacies of presumption. We'll finish with how to meet the midterm. After that, Week 9 turns to Inductive Generalization and Analogy.
1. Find it and write it out
Let's start with two texts from a teammate. The first says, "The game was canceled because the field flooded." Everyone already knows the game is off, so the teammate is telling you why. The second says, "The game will be canceled, because the field is flooding." Nobody knows yet, so the teammate is giving you a reason to believe it.
That's the distinction from Week 1. An argument is a set of claims in which one or more, the premises, are offered as reasons to accept another, the conclusion. An explanation is a set of claims that gives reasons why something already accepted is so, rather than reasons to believe something still in question. The test is one question about the audience: is the claim in doubt for them? Notice that both texts use "because", so the word can't settle it alone.
Week 2 taught you to write an argument out. Each premise gets its own numbered line. A line that says "So" comes next, and then the conclusion. A premise you add, because the arguer left it unsaid, is marked "supplied".
Take the running question, whether the campus library should stay open around the clock during finals week. The newsletter states 3 premises: students need a quiet, safe place late at night, the library is the only such space, and the overnight cost is about 1,600 dollars. You supply one more, P3: the campus should provide study space students need during finals when it can do so at modest cost. That's 4 premises and 1 conclusion, so 5 lines.
Pause and try this. In the running question, which premise did the newsletter never say out loud?
Think about which line carries the word "supplied".
Here's the answer. It's P3, the premise about providing study space at modest cost. The newsletter needed it to reach its conclusion but never stated it.
In doubt, it argues; accepted, it explains.
2. Judge the link
Now the Week 3 question: how good is the link? Think of two friends. One says, "Every bus on this route stops at the library, and this is one of them, so it stops at the library." The other says, "The app says rain is likely, so I'm bringing an umbrella." The first promises the conclusion can't miss. The second promises only that it probably won't.
An argument is valid when it is impossible for all its premises to be true and its conclusion false. It is sound when it is valid and every premise is true. An inductive argument is strong when its premises, if true, make its conclusion likely. It is cogent when it is strong and every premise is true.
Here's how that played out on the running question. P1, P2, and P3 lead to the conclusion validly, once the cost is granted to be modest. But is 1,600 dollars modest? That figure comes from 2 staff, 8 hours a night, 5 nights, and 20 dollars an hour. A campus that has spent its whole study-space budget might not call it modest. So the step from P4 to "modest" is inductive. One deductive link plus one inductive link makes 2 support links.
Pause and try this. Given those two links, can the running question as a whole be valid?
Ask what kind of link the weaker one is.
Here's the answer. No. Because one link is inductive, the argument as a whole can be no better than cogent.
And remember the trap here. Valid doesn't mean true. A valid argument can have a false conclusion when a premise is false. Valid is the link; sound is the link plus the facts.
3. Read the conditional
Week 4 was about "if" sentences. Picture a sign at a student-services desk: you can register for a course only if you passed the prerequisite. A classmate who passed says, "Great, I'm registered." Then the course turns out to be full.
A conditional says "if P, then Q", where P and Q stand for whole claims. It's false in exactly one situation, when P is true and Q is false. You can turn it around in three ways. The converse swaps the parts: "if Q, then P". The inverse denies both parts. The contrapositive swaps and denies both parts, "if not Q, then not P", and it's the only one that says the same thing as the original.
Take the soccer field. "If it rained overnight, the soccer field is wet." The contrapositive is, "If the soccer field is not wet, it did not rain overnight." That's equivalent. The converse is, "If the soccer field is wet, it rained overnight." That's not. The sprinklers ran overnight and it didn't rain. On that morning, the field is wet without any rain, and that one morning refutes both affirming the consequent and denying the antecedent. So the set holds 4 valid forms and 2 invalid ones, 6 in all. The truth table backs this up: 4 rows, and only 1 of them is false.
The same sentence also tells you about conditions. In "if P, then Q", P is sufficient for Q, and Q is a necessary condition for P. Passing the prerequisite is necessary for registering, but it isn't sufficient. You also need an open seat.
Pause and try this. Is "if the soccer field is wet, it rained overnight" safe to use in place of the original?
Picture the sprinklers.
Here's the answer. No, it isn't. That's the converse, and the sprinkler morning makes it false while the original stays true.
Swap and deny both, or you changed the claim.
4. Check the regions
Week 5 gave you a picture test, and I'll describe it in words. Imagine a flyer at a dog park that says every poodle there is a dog and every beagle there is a dog. Someone concludes that every poodle there must be a beagle.
A Venn diagram is a drawing of overlapping circles, one for each term, used to test a categorical syllogism: a shaded region is empty, and an X sits in a region that holds at least one thing. You shade what the premises say is empty first. Then you place any X. Then you check the conclusion's region.
Here's the poodle case. Draw three circles, one each for poodles, beagles, and dogs. The first premise lets you shade the part of the poodle circle outside the dog circle. The second lets you shade the part of the beagle circle outside the dog circle. Now look at the conclusion. "All poodles are beagles" needs every poodle that isn't a beagle to be gone. But the region of poodles that are not beagles, inside the dog circle, is left unshaded. Across the whole set, 3 syllogisms are valid and 3 are invalid.
Pause and try this. Both premises are true. Does that make the poodle syllogism valid?
Remember what validity asks about the link.
Here's the answer. No. The premises leave open a region that could hold a poodle that isn't a beagle, so the syllogism is invalid even with true premises.
Shade first, then the X, then look at the conclusion's region.
5. Watch the words and the link
Weeks 6 and 7 gave you two more pairs. Picture a driver reading a curb sign: "Fine for parking here." The driver parks and gets a ticket anyway.
A vague term has fuzzy edges, like "late at night". An ambiguous term has two or more distinct meanings that both fit its context, such as "fine" read as a penalty or as "all right". The parking sign uses "fine" as a penalty, and the driver reads it as "all right". One word with two meanings across the steps is equivocation.
Week 7's pair was the fallacy and the false premise. A fallacy is a flaw in the reasoning. A false premise is a premise that is not true, a flaw in an argument's content rather than in its reasoning; an argument can have a false premise and still be valid. The treasurer passage is the model fallacy: "We can ignore the treasurer's budget proposal; she failed a math class in high school." That grade wouldn't bear on the budget even if it were true. That's the attack on the person.
Now suppose P2 in the running question turned out false, because the campus had another big, quiet, safe space. Then the argument would have a false premise. Its reasoning would still hold together; its facts would fail. By the end of Week 7 you'd keyed 12 fallacy passages, 3 from Week 6 and 9 from Week 7.
Pause and try this. If P2 turned out false, would the running question commit a fallacy?
Decide whether the link failed or the facts failed.
Here's the answer. No. It would have a false premise, a flaw in the facts, while its reasoning still connects.
A fallacy breaks the reasoning; a false premise breaks the facts.
6. Find the hidden assumption
Here's the new material. Picture a campus forum. A speaker says, "Either we raise student parking fees or the library closes on weekends." The room splits into two camps. Nobody asks whether those are the only choices.
A fallacy of presumption is a fallacy in which an argument quietly assumes, without support, the very thing it should be supporting, so the conclusion rests on an assumption the audience was never asked to accept. This week you meet three.
A false dilemma, also called a false dichotomy, is the fallacy of presenting two options as the only ones when others exist, so that rejecting one seems to force the other. The parking-fee passage is one. Other options exist, like shorter weekend hours or savings elsewhere.
Begging the question, also called circular reasoning, is the fallacy of assuming in a premise what the conclusion is meant to show. Here's the passage: "The new class schedule is the best schedule because no other schedule is better." The premise says what the conclusion says, in other words. It's valid, oddly enough, but a doubter gets no reason at all.
A loaded question, also called a complex question, builds a disputed claim into its wording, so that any direct yes or no answer concedes the claim. The passage is, "Have you stopped wasting time on your phone during lectures?" A yes admits you used to. A no admits you still do.
The cure for all three comes from Week 2. Write the hidden assumption out as a supplied premise, and ask what holds it up. With these three, the tally reaches 15 keyed passages, and 5 are still to come.
Pause and try this. Write the hidden premise of the parking-fee passage as a supplied premise.
Ask what the speaker never said but needed.
Here's the answer. It's "these are the only two options." Once it's written down, you can see that nothing supports it.
Write the hidden assumption down, then ask what holds it up.
7. Name the test first
Every fallacy in this course has had a neighbor that isn't a fallacy. These three do too. Two options are fine when they really are the only two. A claim is either true or false, and there's no third choice. Saying "that raises the question" isn't begging the question. It asks for more reasons. And the fair response to a loaded question is to challenge it, not answer it. You might say, "I don't accept that I was wasting time."
Now the habit for the midterm. Before you test any passage, name the test it calls for. An "if" sentence calls for the conditional test. "All" sentences about groups call for the Venn test. A reason that may not bear on the conclusion calls for the relevance test. An either-or offered as the whole menu calls for the hidden-assumption check. Then run the test, and say the verdict in one plain sentence.
The midterm covers Objectives 1 to 4 as taught in Weeks 1 to 7. You practice the three fallacies of presumption in this week's discussion and practice set, and they are not on the midterm. You take it on your own, with no AI help, because it confirms that you can run these tests yourself.
Pause and try this. A friend says a claim is either true or false. Is that a false dilemma?
Ask whether a third option really exists.
Here's the answer. No. Two options are fine when they really are the only two, and a claim has no third choice.
Name the test first; then run it.
Closing
Let me pull it together. An argument supports a claim in doubt, and an explanation accounts for one already accepted. Standard form numbers each premise and marks the supplied one. Valid is the link, and sound adds true premises; strong and cogent split the same way. Only the contrapositive says the same thing as a conditional, and a necessary condition isn't always sufficient. A Venn verdict comes from the regions. Vagueness is fuzzy edges, ambiguity is two meanings, and a fallacy breaks the reasoning while a false premise breaks the facts. The false dilemma, begging the question, and the loaded question each hide an assumption, so write it down and ask what holds it up.
Next in this module come the slide deck, the Readings and Resources page, the practice set, the discussion, and the midterm. Then, in Week 9, Inductive Generalization and Analogy turns the tests from the passage on the page to the evidence in the world.
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