Lecture: Midterm Review & Exam
Lecture script · about 15–20 minutes spoken · Week 8
Opening
Picture four students at a library table, the night before a review session. They have seven weeks of notes between them, and one of them says, "I can't memorize all of this." Another answers, "Then don't. Ask each week what it keeps apart." That second student has found the method of this lecture.
A nursing student sorting what a chart shows from what it only suggests uses that habit. So does a juror keeping a tidy argument apart from a true one. In this lecture we'll ask each topic for its distinction. A distinction is a line between two ideas that are easy to mix up, such as valid and sound. A topic asks you to keep it straight before you judge an argument or state a position.
You've built a lot. Week 1 gave you the counterexample test, Week 2 gave you standard form and validity, and Weeks 3 to 7 took you through reality, knowledge, mind, and the self. I'll rerun seven distinctions on cases you already know. Then I'll add one light new topic, Pascal's wager. The midterm covers Objectives 1 to 4, and you sit it without AI help. Next week, in Week 9, a new unit on God begins.
1. Valid versus sound
Think of a juror hearing a closing argument that hangs together perfectly. The juror still has a second question: are the starting claims true? Good structure and true starting points are two different things.
That's the first distinction. An argument is valid when its conclusion cannot be false if its premises are true; validity depends on form. It's sound when it's valid and its premises are all in fact true.
Take argument 7 from the argument set, which was written for teaching. If Socrates is wise, he admits his ignorance. Socrates is wise. So he admits his ignorance. That's modus ponens, so it's valid. Argument 1 has the same form: if knowledge requires certainty, then I know very little; knowledge requires certainty; so I know very little. It's valid too. But whether knowledge requires certainty is an open question, so the course never calls it sound.
Pause and try this. Argument 8 says that if a machine understands Chinese, it can answer in Chinese; this machine answers in Chinese; so it understands Chinese. Valid or invalid?
Picture a help-desk chatbot before you decide.
Here's the answer. It's invalid, because it runs the conditional backward: a chatbot matching symbols could make both premises true and the conclusion false.
2. Deductive versus inductive
A forecaster looks at a barometer that fell overnight. On every past morning in her records when that happened, rain followed. She predicts rain. She isn't guessing, and she isn't proving anything either.
A deductive argument aims to guarantee its conclusion. An inductive argument offers premises to make its conclusion probable rather than to guarantee it, and you judge it by its strength, which comes in degrees.
The forecaster's reasoning is inductive. Now add the premise a philosopher would ask about: the future will resemble the past. David Hume's Enquiry, from 1748, asks what supports that premise. Any argument from experience for it would assume it, so it would be circular.
Pause and try this. A classmate says Hume proved that weather forecasts are useless. What's the slip?
Think about what Hume actually asks.
Here's the answer. Hume asks what justifies a prediction, not whether to keep predicting, so the problem of induction doesn't say forecasts are useless.
3. Rationalism versus empiricism
You might catch a friend's lie by noticing their story contradicts itself, or by seeing the receipt. One route runs through reason, the other through experience.
Rationalism is the view that some substantive knowledge of the world comes from reason independent of experience. Empiricism is the view that all knowledge of the world comes from experience.
Recall the evil deceiver from René Descartes' Meditations on First Philosophy, from 1641. Suppose a powerful deceiver fakes everything you perceive. What survives? Put in words, the Second Meditation concludes that the proposition that he exists is necessarily true whenever he thinks it. The famous wording comes from an older book, the Discourse on the Method, from 1637. In John Veitch's translation it reads, "I think, therefore I am (COGITO ERGO SUM)". Those English words, and the Latin in brackets, are Veitch's. On the other side, John Locke's Essay, with a title page dated 1690, compares the mind at the start to white paper.
Pause and try this. Someone writes that "I think, therefore I am" comes from the Meditations. What needs fixing?
Think about the order of the two books.
Here's the answer. The wording comes from the Discourse, four years before the Meditations, in Veitch's translation, so the source needs changing.
4. A priori versus a posteriori
How do you know every triangle has 3 sides? You don't go and count them. How do you know the bus is late? You look at the empty street.
A priori means knowable independently of experience, as in mathematics; it describes how a claim is known, not when a person first learned it. A posteriori means knowable only through experience.
So "every triangle has 3 sides" is a priori, and "the left trail leads to the lake" is a posteriori. Here's the trap. This pair sorts how a single claim is known. Rationalism and empiricism are rival views about where knowledge of the world comes from. Both sides can agree the triangle claim is a priori.
Pause and try this. You learned that a triangle has 3 sides at age six, from a drawing. Does that make the claim a posteriori?
Remember what the term is about.
Here's the answer. No, because a priori is about how the claim is known, not when or how you first heard it.
5. Belief versus knowledge
You can believe your phone is in your bag and be wrong. You can't know it's there and be wrong. A belief can be false; knowledge can't.
Plato's theory of Forms holds that beyond the changing things we perceive there are unchanging, perfect Forms that are the true objects of knowledge. So the prisoners in the cave, taking shadows for reality, have beliefs about shadows, not knowledge.
Week 5 gave you justified true belief: you know a claim when it's true, you believe it, and you're justified in believing it. Edmund Gettier's paper from 1963 pressed it. In the trail-sign variation, a storm spins a sign around, but it still points the right way by chance. The hiker's belief is true, believed, and justified, 3 of 3 conditions, yet true only by luck.
Pause and try this. Does the trail-sign case show that the hiker's belief is false?
Check the first condition again.
Here's the answer. No, because the belief is true; the case suggests that justified true belief may not be enough for knowledge.
6. Dualism versus physicalism
Stub your toe. Something happens in your foot and brain, and something happens that only you can feel: the sting.
Substance dualism is the view that mind and body are different kinds of thing. Physicalism is the view that everything that exists is physical. The identity theory, a form of physicalism, holds that mental states are brain states. Functionalism says a mental state is defined by its causal role, by what it does.
Argument 2 runs: if the mind is the brain, then mental states have locations; mental states have no locations; so the mind is not the brain. It's valid, by denying the consequent. An identity theorist rejects the second premise. And John Searle's Chinese room, from 1980, asks whether following a program is the same as understanding.
Pause and try this. A friend says the Chinese room proves machines can never be intelligent. Is that what it shows?
Look at the question the case asks.
Here's the answer. No, because it asks whether following a program is enough for understanding, which presses functionalism without ruling on every machine.
7. Determinism versus fatalism
Picture a line of dominoes: tip the first, and each knocks over the next. Now picture a fortune-teller telling a student she'll fail a test whether she studies or not. Both sound fixed, but only one leaves your choices doing work.
Determinism is the view that every event is necessitated by prior events together with the laws of nature. Fatalism is the view that what will happen will happen whatever anyone does.
On determinism, your choices are among the causes, so take out one domino and the last one stands. Hard determinism says determinism is true and free will doesn't exist. Libertarianism says free will exists and determinism is false. Compatibilism takes no stand of its own on determinism and says free will is compatible with it. Argument 4, either free will is an illusion or determinism is false, is valid by disjunctive syllogism.
Pause and try this. A friend says, "If everything is determined, studying is pointless." Which view is the friend describing?
Ask whether studying is one of the causes.
Here's the answer. That's fatalism, because on determinism studying is one of the causes of the result.
8. Meet Pascal's wager
Now the new topic. Picture a gardener on a cold evening. A frost seems unlikely, but a hard one could kill the whole planting, and covering the seedlings takes a few minutes. The gardener covers them without proving anything about frost.
The case is Pascal's wager, from Blaise Pascal's Pensées, published after his death, in 1670. Its question: is it rational to bet on belief? The argument, in words: since the possible gain from believing in God is infinite and the possible loss finite, a prudent person should wager that God exists. It's an argument about what to believe, not a proof that God exists. That makes it a prudential argument, one that says a choice serves the chooser well, rather than one that says a claim is true. It leans on expected value: weigh each outcome by how likely it is.
Pause and try this. Dataset G lists the wager's direction as "for belief". Why not "for God's existence"?
Think about what the conclusion recommends.
Here's the answer. It concludes that believing is the prudent bet, without giving evidence that God exists, so its direction is belief.
9. The wager's table and its argument
Lay out the choice like a grid. Two choices, believing and not believing, meet two possibilities, that God exists and that God doesn't. That's four outcomes. Believing, if God exists: an infinite gain. Believing, if not: a finite loss. Not believing, if God exists: the infinite gain is missed. Not believing, if not: at most a finite gain.
Here's the course's reconstruction in standard form. The first premise says believing has a possible infinite gain at only a finite risk. The second says not believing has no possible infinite gain. An added third premise says a prudent person should make the first kind of choice. So a prudent person should wager. As reconstructed, it's valid by modus ponens. Its strongest form: the bet doesn't need God's existence to be likely, only possible.
Pause and try this. A classmate says the wager is about gambling money. What's the slip?
Recall the gardener and the seedlings.
Here's the answer. "Wager" names any choice made without knowing how things will turn out, so the stakes are a life's commitments, not money.
10. Two objections and two replies
The many-gods objection says more than one possible god might ask for a different belief, so the table has more than two columns, and the wager alone can't say which belief to bet on. The reply, from the wager's side: among the options a person is actually choosing between, the bet on belief beats the bet on no belief, and reason must then do more work.
The second objection: you can't decide to believe something at will, any more than you can decide to believe it's raining. The reply: you can choose actions, like study and practice, that may lead to belief over time.
Neither objection proves the conclusion false, and neither reply proves it true. The course keys no verdict.
Pause and try this. Which premise does the many-gods objection press: the one about believing, or the one saying not believing has no infinite gain?
Think about what the extra columns add.
Here's the answer. It presses the second, because other possible gods give other choices their own possible infinite gains.
Closing
Let me pull it together. Valid is about form; sound adds true premises. Deductive arguments aim to guarantee, and inductive ones aim to make probable. Rationalism and empiricism disagree about where knowledge comes from, and "I think, therefore I am" belongs to the Discourse, in Veitch's translation. A priori is about how a claim is known. A belief can be false; knowledge can't. Dualism and physicalism disagree about what a mind is. Determinism isn't fatalism. And Pascal's wager is a prudential argument about belief, pressed by two objections that each have a reply.
Next in this module come the slide deck, the Readings & Resources page, the practice set, the discussion, and then the midterm. Next week, in Week 9, Philosophy of Religion asks whether reason can show that God exists or does not.
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