Week 8 · Chapter

Chapter 8 — Midterm Review & Exam

Introduction to Philosophy Free sample edition

The module's primary reading · ~35–45 minutes · Objective 1 (explain what philosophy is, name its main branches, and describe the Socratic practice of examining beliefs through questioning and argument) to Objective 4 (compare positions on the mind-body problem, personal identity, and free will, and evaluate them with the thought experiments that test them) reviewed, with Pascal's wager reconstructed through Objective 2 (identify arguments, put them in standard form, judge whether they are valid, sound, or inductively strong, and test claims with counterexamples and thought experiments) · Read it early this week, before the practice set and the discussion and well before the midterm.

In plain language

This chapter helps you review the first seven weeks before the midterm. Instead of rereading everything, you ask each topic for the one distinction it asks you to keep (a line between two ideas that are easy to mix up, such as a valid argument and a true one). You rerun each distinction on cases you have already met, so the review adds no new arguments to them. Then you meet one new idea: Pascal's wager (an argument that believing in God is the wise bet, offered as advice about what to believe rather than as proof). Your goal is to state each view fairly and to keep each pair of ideas apart, not to pick a winner.

Why you already care about this

Picture four students at a library table the night before a big review session. Between them they have seven weeks of notes: a courtroom in Athens, a cave, a deceiver, a hiker and a trail sign, a room full of rule-books, a ship rebuilt plank by plank. One student says, "I can't memorize all of this." Another says, "Then don't. Ask each week what it keeps apart."

That second student has found the method of this chapter. Almost every wrong answer in an introductory philosophy course comes from blurring two ideas that a topic asks you to keep apart. People call a valid argument true. They call a determinist a fatalist. They put a famous line in the wrong book. Fix those few blurs, and most of the course comes into focus.

In Plato's Apology, Socrates, on trial in Athens in 399 BCE, says that "the unexamined life is not worth living" (Plato, Apology, trans. Benjamin Jowett; Dataset C, Q1). A review is a small version of that examination: you question what you think you know, one belief at a time, before a test does it for you.

By the end of this chapter you will be able to:

tell a valid argument from a sound one, and key Dataset B's arguments for validity without keying soundness;
tell a deductive argument from an inductive one, and say what Hume's problem of induction does and does not claim;
tell rationalism from empiricism, and place "I think, therefore I am" in its pinned source with its translator;
tell a priori knowledge from a posteriori knowledge, and keep that pair apart from rationalism and empiricism;
tell belief from knowledge, using Plato's cave and a Gettier-style case;
tell substance dualism from physicalism, and say what the Chinese room does and does not show;
tell determinism from fatalism, and read Dataset F row by row;
state Pascal's wager in its strongest form, put it in standard form, give its two strongest objections with replies, and say why it is not a proof.

Carry this line with you:

One topic, one distinction; a bet is not a proof.

Where we are

Already covered: Week 1, What Philosophy Is: Socrates and the Examined Life, gave you the counterexample test and the habit of reading a translation as its translator's words. Week 2, Arguments and Thought Experiments, gave you standard form, validity, soundness, and inductive strength. Week 3, Plato: Reality and the Forms, set appearance against reality. Week 4, Knowledge I: Doubt, Reason, and Experience, set reason against experience. Week 5, Knowledge II: What Knowledge Is, tested the definition of knowledge. Week 6, The Mind-Body Problem, asked what a mind is. Week 7, Personal Identity and Free Will, asked what keeps a self the same and whether its choices are free.
This week: a review of Weeks 1 to 7 by distinction, one light new topic (Pascal's wager), and then the midterm.
How they connect: every distinction you review is a tool you have used on an argument, and the wager is one more argument to put in standard form and test.
Where we're going next: Week 9, Philosophy of Religion, opens a new unit on God, asks whether reason can show that God exists or does not, and recalls the wager.

The midterm covers Objectives 1 to 4 as Weeks 1 to 7 taught them, and you take it without AI help. Pascal's wager is new this week and returns in Week 9. Every worked example below reruns a case from Datasets A to F: the thought-experiment roster, the argument set, the quotations, and the mind and free will positions. If a case surprises you, go back to the week that built it.

Two tools from Week 2 do most of the work. Standard form numbers each premise (P1, P2, and so on) and gives the conclusion last, marked C and introduced by "So". A premise the reconstruction supplies is marked "(added)". And Dataset B, the argument set, is illustrative: its premises were written for teaching, and they are not claims the course endorses.

1. Keep a valid argument apart from a sound one

Picture a juror listening to a closing argument. The lawyer's reasoning hangs together perfectly: if this, then that; this; so that. The juror nods. But a second question is still waiting. Are the lawyer's starting claims true? An argument can be put together well and still start from a false claim.

That gap is the first distinction of the review.

Distinction — a line between two ideas that are easy to mix up, such as valid and sound, that a topic asks you to keep straight before you judge an argument or state a position.
Valid — said of a deductive argument whose conclusion cannot be false if its premises are true; validity depends on the argument's form, not on whether its premises are true.
Sound — said of a deductive argument that is valid and whose premises are all in fact true.

Worked example — three arguments from Dataset B (illustrative). Key each one for validity, and say whether soundness is keyed.

Argument 7 in standard form:

P1 If Socrates is wise, he admits his ignorance.
P2 Socrates is wise.
C So he admits his ignorance.

It is valid, by modus ponens (if P then Q; P; so Q): if both premises are true, the conclusion cannot be false.

Argument 1 in standard form:

P1 If knowledge requires certainty, then I know very little.
P2 Knowledge requires certainty.
C So I know very little.

It is valid, by modus ponens, the same form as argument 7. Soundness is not keyed, because whether knowledge requires certainty is an open question.

Argument 8 in standard form:

P1 If a machine understands Chinese, it can answer questions in Chinese.
P2 This machine answers questions in Chinese.
C So it understands Chinese.

It is invalid, because it runs the conditional backward, from the consequent to the antecedent. Picture a help-desk chatbot that answers in Chinese by matching symbols. Both premises are true of it, and the conclusion is false. One such case is enough to show the form is invalid.

In words: arguments 7 and 1 share a valid form, so each is valid whatever its premises say, while argument 8's form lets true premises lead to a false conclusion.

Misconception check — valid does not mean true. Students often think "valid" means "has true premises" or "is correct". It is tempting because in everyday speech "a valid point" is a good point. The cure is argument 1. It is valid, yet the course never calls it sound, because its second premise is an open question. The reverse slip is equally common: an invalid argument does not thereby have a false conclusion. Argument 8's conclusion might be true of some machine; the form fails to guarantee it.

2. Tell deductive from inductive: guarantees versus probabilities

A weather forecaster looks at the barometer on a gray evening. It has fallen overnight. On every past morning in her records when that happened, rain followed. She predicts rain. She is not guessing, but she is not proving anything either.

That is the second distinction.

Deductive argument — an argument that aims to guarantee its conclusion, so that the conclusion cannot be false if the premises are true.
Inductive argument — an argument whose premises are offered to make its conclusion probable rather than to guarantee it.
Strength — the degree to which an inductive argument's premises make its conclusion probable without guaranteeing it; strength comes in degrees, while validity does not.

Worked example — the forecaster (illustrative). Put the reasoning in standard form and classify it.

P1 On every past morning in the records when the barometer fell overnight, rain followed.
C So rain will follow this time.

The premise makes the conclusion probable without guaranteeing it. Rain could still hold off. So the argument is inductive, and you judge it by its strength, not its validity. Now add the premise a philosopher would ask about:

P2 (added) The future will resemble the past.

David Hume's An Enquiry Concerning Human Understanding (1748) asks what supports P2. Any argument from experience for it would assume it, since it would reason from how the future has resembled the past so far. That would make it a circular argument (one that assumes, among its premises, the very conclusion it sets out to support).

In words: the forecaster's argument is inductive and can be strong, and Hume's question is what justifies the step from past to future, not whether to keep forecasting.

Misconception check — the problem of induction is not "science is useless". Students often hear Hume's problem as a claim that predictions are worthless. It is tempting because the problem seems to knock away the ground under every forecast. The cure is to read the question exactly. Hume asks what justifies a prediction. Reasoning from past patterns is still how a forecaster, a nurse, or a scientist learns from evidence; the problem asks what makes that reasoning good.

3. Trace knowledge to its source: rationalism versus empiricism

Think of two ways you might learn that a friend is lying. You might catch a contradiction in their story, reasoning it out with your eyes closed. Or you might see the receipt that shows where they really were. One route runs through reason, the other through experience. Philosophers built two rival views on that contrast.

Rationalism — the view that some substantive knowledge of the world comes from reason independent of experience.
Empiricism — the view that all knowledge of the world comes from experience, through the senses and through noticing the workings of one's own mind.

Worked example — from the deceiver to the cogito, and to white paper. Walk the rationalist case, then the empiricist answer.

The case: the evil deceiver (Dataset A, the Week 4 entry), from René Descartes' Meditations on First Philosophy (1641). Suppose a powerful deceiver is faking everything you perceive. The roster's question: what can I know if everything I perceive might be faked?
What survives: the Second Meditation concludes, said in words, that the proposition that he exists is necessarily true whenever he thinks it.
The famous wording: "I think, therefore I am (COGITO ERGO SUM)" (René Descartes, Discourse on the Method, Part IV, trans. John Veitch; Dataset C, Q2). The parenthetical Latin is Veitch's own insertion. The English words are Veitch's, not Descartes'.
The order of the books: the Discourse (1637) came out 1641 − 1637 = 4 years before the Meditations, so the famous wording is older than the Meditations and is not printed in them.
The empiricist answer: John Locke's An Essay Concerning Human Understanding (title page dated 1690) compares the mind at the start to white paper, with no innate ideas, and traces every idea to 2 sources, sensation and reflection.

In words: Descartes finds one belief that reason secures while every sense is in doubt, and Locke answers that even the ideas of thinking and existing must first come from experience.

Misconception check — the famous line is not from the Meditations. Students often say "I think, therefore I am" is "from the Meditations". It is tempting because the Meditations is where Descartes doubts everything and finds that he exists. The cure is the order of the books: the wording comes from the Discourse (1637), four years earlier, in Veitch's translation. A second slip rides along: Descartes' doubt is a method for testing beliefs, not a belief that nothing is real.

4. Sort how a claim is known: a priori versus a posteriori

Ask a friend how they know that every triangle has 3 sides. They will not go and count the sides of triangles. Now ask how they know the bus is late. They will point at the empty street and the clock. The two claims are known in two different ways.

A priori — knowable independently of experience, as in mathematics; it describes how a claim is known, not when a person first learned it.
A posteriori — knowable only through experience, such as what the senses report about the world.

Worked example — sorting two claims from Week 5. Sort each claim by how it is known.

"Every triangle has 3 sides." You can know it by understanding what a triangle is. A priori.
"The left trail leads to the lake." You can know it only by looking, walking, or trusting a report. A posteriori.

Now keep this pair apart from the last one. A priori and a posteriori sort how a single claim is known. Rationalism and empiricism are rival views about where knowledge of the world comes from. A rationalist and an empiricist can agree that the triangle claim is a priori; they disagree about whether a priori reasoning can tell you anything substantive about the world.

In words: the triangle claim is a priori and the trail claim is a posteriori, and that sorting is a different job from choosing between rationalism and empiricism.

Misconception check — a priori does not mean "learned first". Students often read "a priori" as "what you learned before anything else". It is tempting because prior means "before". The cure is the definition: a priori is about how a claim is known, not when. You may have learned that a triangle has 3 sides at age six, from a teacher's drawing, and it is still a priori, because the drawing is not what makes the claim known.

5. Separate belief from knowledge: the cave and the trail sign

You can believe your phone is in your bag and be wrong. You cannot know it is in your bag and be wrong. That small test, whether being wrong is possible, marks the next distinction. Two weeks of the course approached it from two sides.

Belief — a person's taking a claim to be true; a belief can be true or false, and can be held with good reason or with none.
Justified true belief — the traditional analysis of knowledge: a person knows a claim when the claim is true, the person believes it, and the person is justified in believing it.

Worked example — Plato's cave (Week 3). The allegory of the cave (Dataset A, the Week 3 entry) opens Book VII of Plato's Republic. Prisoners chained in an underground den take shadows on the wall for reality. 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. On that view, what the prisoners hold about the shadows is belief, not knowledge: they are confident, and they are looking at appearances.

Worked example — the trail sign (Week 5). Edmund Gettier's "Is Justified True Belief Knowledge?" (1963) described cases that test the traditional analysis. Rerun the variation written for this course on the shape of his cases. A storm has spun a trail sign around, but by chance it still points the right way, and a hiker follows it to the lake.

(1) True: the left trail does lead to the lake. That is 1.
(2) Believed: the hiker believes it. That makes 1 + 1 = 2.
(3) Justified: a posted trail sign is good evidence. That makes 1 + 1 + 1 = 3 of the 3 conditions.

Yet the belief is true only by luck: the spun sign would have pointed the same way whichever trail led to the lake. So the hiker seems not to know.

In words: Gettier's cases suggest that a belief can be justified and true by luck, so justified true belief may not be enough for knowledge.

Misconception check — justified true belief is not the settled definition. Students often memorize "knowledge is justified true belief" as the answer. It is tempting because it is the first definition the course teaches. The cure is the trail sign: one counterexample is enough to defeat a definition that claims every case. A second slip: knowledge does not require certainty. The analysis asks for justification, which can fall short of certainty, which is why defenders of the analysis reject the second premise of Dataset B's argument 1.

6. Place the mind: dualism versus physicalism

Stub your toe. Something happens in your foot, your nerves, and your brain. Something also happens that only you can feel: the sting. The mind-body problem asks how those two descriptions fit together.

Substance dualism — the view that mind and body are different kinds of thing, so that a mind is not a physical object and is not made of the matter that makes up a body.
Physicalism — the view that everything that exists is physical, so that minds, too, are made of nothing beyond the physical world.

Dataset E pins 3 standard positions.

Dataset E: three standard positions on the mind-body problem, with each one's central claim and what presses it
Position	Central claim	Pressed by
Substance dualism	Mind and body are different kinds of thing	The problem of how an immaterial mind moves a body
Identity theory	Mental states are brain states	Nagel's bat (1974); Jackson's Mary (1982)
Functionalism	Mental states are defined by their causal roles	Searle's Chinese room (1980); Jackson's Mary (1982)

The identity theory is a form of physicalism. Functionalism is a view about what defines a mental state, its causal role, rather than about what the state is made of.

Worked example — Dataset B's argument 2 (illustrative). Put it in standard form and key it.

P1 If the mind is the brain, then mental states have locations.
P2 Mental states have no locations.
C So the mind is not the brain.

It is valid, by denying the consequent (if P then Q; not Q; so not P). Soundness is not keyed: an identity theorist replies that P2 is false, because a pain is located where its brain state is.

Now recall the Chinese room, from John Searle's "Minds, Brains, and Programs" (1980). A person who knows no Chinese follows rule-books for matching Chinese symbols and passes out fluent answers. Its question: is following a program the same as understanding? It presses functionalism.

In words: argument 2 is a valid argument for a dualist conclusion whose second premise the physicalist rejects, and the Chinese room is a challenge to functionalism, not a verdict on the mind-body problem.

Misconception check — two slips about machines. Students often think the Chinese room shows that machines can never be intelligent. It is tempting because the person in the room is a stand-in for a computer. The cure is the roster's question: the case asks whether following a program is enough for understanding; it says nothing about every possible machine. A related slip reads functionalism as a claim about brains only. Functionalism defines a mental state by what it does, so a human, an octopus, or a well-built machine could each be in pain if something in it plays pain's role.

7. Tell determinism from fatalism, once more

Think of a line of dominoes again. Tip the first, and each one knocks over the next. Now imagine a different story: a fortune-teller tells a student that she will fail a test whether she studies or not. Both stories sound fixed. Only one of them leaves your choices doing any work.

Determinism — the view that every event is necessitated by prior events together with the laws of nature.
Fatalism — the view that what will happen will happen whatever anyone does; it differs from determinism, on which choices are among the causes of what happens.

Worked example — Dataset F and argument 4. Read the free will positions row by row, then key the argument.

Dataset F: three standard positions on free will, with each one's answer to three questions
Position	Is determinism true?	Does free will exist?	Are they compatible?
Hard determinism	yes	no	no
Libertarianism	no	yes	no
Compatibilism	takes no stand of its own	yes	yes

Hard determinism answers yes, no, no.
Libertarianism answers no, yes, no.
Compatibilism takes no stand of its own on determinism, and answers yes, yes.

Dataset B's argument 4 (illustrative), in standard form:

P1 Either free will is an illusion or determinism is false.
P2 Free will is not an illusion.
C So determinism is false.

It is valid, by disjunctive syllogism (P or Q; not P; so Q). Soundness is not keyed. The hard determinist rejects P2, the compatibilist rejects P1, and the libertarian accepts both.

Now tally the review's arguments. You have rerun five from Dataset B: arguments 1, 2, 4, and 7, which are valid, and argument 8, which is invalid, so 4 + 1 = 5.

In words: determinism makes your choices part of the chain of causes, while fatalism says the outcome arrives whatever you choose, so only fatalism makes deliberating pointless.

Misconception check — determinism is not fatalism, and compatibilism does not deny determinism. Students often hear "determinism" and think "nothing I do matters". It is tempting because both views say the future is fixed. The cure is the dominoes: take one out, and the last one does not fall. On determinism, your choices are among the causes of what happens. A second slip reads compatibilism as the view that determinism is false. Look at its row: it takes no stand of its own on determinism and says free will is compatible with it.

8. Meet Pascal's wager: a bet about belief

Picture a gardener on a cold evening in early spring. The forecast says a frost is unlikely. Covering the seedlings with old sheets takes a few minutes. A hard frost could kill the whole planting. Without knowing whether the frost will come, the gardener covers the seedlings, because the small cost is worth the protection if the worst happens. The gardener has not proved there will be a frost. The gardener has decided what to do without knowing.

That shape of reasoning is the week's one new topic.

The case is Pascal's wager (Dataset A, the Week 8 entry), from Blaise Pascal's Pensées, published after his death, in 1670. The roster's question: is it rational to bet on belief? It tests faith, reason, and expected value.

Pascal's wager — Blaise Pascal's argument, from his Pensées, that since the possible gain from believing in God is infinite and the possible loss finite, a prudent person should wager that God exists; it is an argument about what to believe, not a proof that God exists.
Pensées — the collection of Blaise Pascal's writings published after his death, in 1670, which contains the argument known as Pascal's wager.
Expected value — the worth of a choice found by weighing each of its possible outcomes by how likely that outcome is, so that a large but unlikely gain can still count for a lot.
Prudential argument — an argument that a choice, such as holding a belief, serves the chooser well given what they stand to gain or lose, rather than an argument that a claim is true.

Worked example — reading Dataset G's row and placing the book. Dataset G, the arguments about God, carries one row this week, the wager's.

Dataset G: the wager's row, with its source, its kind, and its direction
Argument	Source	Kind	Direction
The wager	Pascal, Pensées (1670)	prudential (about belief, not proof)	for belief

Kind: prudential. The wager gives a reason to believe, based on what is at stake, not evidence that the belief is true.
Direction: "for belief", not "for God's existence". It argues that believing is the prudent bet.
Placing the book: the Pensées (1670) appeared 1670 − 1641 = 29 years after Descartes' Meditations and 1690 − 1670 = 20 years before the title-page date of Locke's Essay, so 29 + 20 = 49 years, the same span as from the Meditations to the Essay.

In words: the wager belongs to the same century as Descartes and Locke, and it argues about what a prudent person should believe, not about whether the belief is true.

Misconception check — the wager is not a proof that God exists. Students often remember the wager as "Pascal's proof of God". It is tempting because it is about God and it ends with "God exists". Read the conclusion again: a prudent person should wager that God exists. The cure is Dataset G's kind column. The wager is prudential, about belief, not proof: it argues that believing is the wise bet, and it gives no evidence that the bet will pay.

9. Build the wager's table and its argument

Back to the gardener. You could lay out the choice in a small grid: cover the seedlings or not, frost or no frost. Pascal's argument has the same shape, with far higher stakes. Laying it out in a grid is the clearest way to see why it is a prudential argument and where it could be pressed.

Worked example — the wager's table (illustrative, written for this course). 2 choices, believing and not believing, meet 2 possibilities, that God exists and that God does not. That makes 2 × 2 = 4 outcomes.

The course's illustrative table for Pascal's wager: 2 choices against 2 possibilities, with the outcome in each cell said in words
Choice	If God exists	If God does not exist
Believing	an infinite gain	a finite loss
Not believing	the infinite gain is missed	at most a finite gain

The table only lays out the claim the wager makes: the possible gain from believing is infinite, and the possible loss finite. Nothing in it is a number you compute.

Worked example — the wager in standard form (the course's reconstruction, illustrative). Number the premises, mark the added one, and judge validity.

P1 Believing in God has a possible infinite gain and a possible loss that is only finite.
P2 Not believing has no possible infinite gain.
P3 (added) If one choice has a possible infinite gain at the risk of only a finite loss, and the other has no possible infinite gain, then a prudent person should make the first choice.
C So a prudent person should wager that God exists.

Is it valid? P1 and P2 together give the if-part of P3. P3 then says what follows. That is modus ponens, so as reconstructed the argument is valid: if the premises are true, C cannot be false. Its soundness is not keyed, because each premise can be questioned.

Now state the wager in its strongest form, as a defender would. Weigh each outcome by how likely it is. An infinite gain outweighs any finite loss as long as its chance is not zero. So the bet does not need God's existence to be likely, only possible. A person who thinks God's existence is unlikely still faces the same table.

In words: on the wager's reasoning, an infinite possible gain makes believing the prudent bet even under deep doubt, which is why the argument concerns expected value and belief rather than proof.

Misconception check — the wager is not only about money or gambling. Students often hear "wager" and picture a casino. It is tempting because the argument talks about gains, losses, and bets. The cure is the table: "wager" here names any choice made without knowing how things will turn out, like the gardener's sheets over the seedlings. The stakes in Pascal's table are a whole life's commitments, not chips on a table.

10. Press the wager: two objections and two replies

A strong argument deserves strong objections. Two objections press the wager hardest. Each has a reply from the wager's side. The course gives both sides their best form and keys no verdict.

Many-gods objection — the objection to Pascal's wager that more than one possible god might ask for a different belief, so the wager's table has more than two columns and the wager alone cannot say which belief to bet on.

Worked example — the many-gods objection and its reply. State the objection at full strength, then answer it.

The objection: the table has a column for "God exists" and a column for "God does not exist". But more than one possible god might ask for a different belief. Add those columns, and each one may promise an infinite gain to its own believers. Now every choice has a possible infinite gain, and the wager alone cannot say which belief to bet on.
The reply, from the wager's side: the wager compares the options a person is actually choosing between. Among those, it shows that the bet on belief beats the bet on no belief. Reason must then do further work among the options, but the wager has done its job: it has shown that the bet on no belief is the weaker one.

Worked example — the objection from choice and its reply. Do the same for the second objection.

The objection: a person cannot decide to believe something at will, any more than you can decide to believe it is raining when the sky is clear. If belief is not chosen, advice about which belief to choose seems to miss its target.
The reply, from the wager's side: a person can choose actions, such as study and practice, that may lead to belief over time. The wager gives advice about those choices, much as a person who wants to become kinder chooses habits that may make them kinder.

An honesty note: neither objection shows that the wager's conclusion is false, and neither reply shows that it is true. The objections press the premises, especially P2 and P3; the replies defend them. That is where the debate lives.

Pause and think. Choose one, and write two or three sentences.

(a) Which of the two objections presses the wager harder, and which premise of the standard form does it press?
(b) Describe a choice in your own life that has the wager's shape, where you acted without knowing how things would turn out, and say whether the wager's reasoning fits it.

In words: the many-gods objection and the objection from choice each press a premise of the wager, each has a reply from the wager's side, and the question stays open.

Misconception check — an objection is not a verdict. Students often think that once a strong objection is on the table, the argument is finished. It is tempting because objections can sound decisive. The cure is the reply that follows each one. An argument is weighed by its strongest objection and the best reply to it. A caveat in the other direction: a reply is not a proof either. Week 9 takes up the arguments that do aim to show whether God exists.

Key terms

Distinction — A line between two ideas that are easy to mix up, such as valid and sound, that a topic asks you to keep straight before you judge an argument or state a position. (first used: 1. Keep a valid argument apart from a sound one)
Pascal's wager — Blaise Pascal's argument, from his Pensées, that since the possible gain from believing in God is infinite and the possible loss finite, a prudent person should wager that God exists; it is an argument about what to believe, not a proof that God exists. (first used: 8. Meet Pascal's wager: a bet about belief)
Pensées — The collection of Blaise Pascal's writings published after his death, in 1670, which contains the argument known as Pascal's wager. (first used: 8. Meet Pascal's wager: a bet about belief)
Expected value — The worth of a choice found by weighing each of its possible outcomes by how likely that outcome is, so that a large but unlikely gain can still count for a lot. (first used: 8. Meet Pascal's wager: a bet about belief)
Prudential argument — An argument that a choice, such as holding a belief, serves the chooser well given what they stand to gain or lose, rather than an argument that a claim is true. (first used: 8. Meet Pascal's wager: a bet about belief)
Many-gods objection — The objection to Pascal's wager that more than one possible god might ask for a different belief, so the wager's table has more than two columns and the wager alone cannot say which belief to bet on. (first used: 10. Press the wager: two objections and two replies)

Summary

Review by distinction: ask each topic what two ideas it keeps apart.
Valid is about form; sound is valid with true premises; soundness is never keyed for contested premises.
Deductive arguments aim to guarantee; inductive arguments aim to make probable and are judged by strength.
Hume's problem asks what justifies a prediction, not whether science is useless.
Rationalism and empiricism disagree about where knowledge of the world comes from.
"I think, therefore I am" is from the Discourse (1637), in Veitch's translation, not the Meditations.
A priori and a posteriori sort how a claim is known, not when it was learned.
A belief can be false; knowledge cannot; Gettier's cases press justified true belief.
Substance dualism says mind and body are different kinds of thing; physicalism says everything is physical.
Determinism is not fatalism, because your choices are among the causes.
Pascal's wager is a prudential argument about what to believe, not a proof that God exists.
The many-gods objection and the objection from choice each have a reply; the course keys no verdict.

Check your understanding

Work these before looking at the answers — they are ungraded, and the answers (with reasoning) are at the bottom of the page.

A coworker reasons, "If the printer is out of paper, it shows a red light. It shows a red light. So it is out of paper." Put the argument in standard form, say whether it is valid, and describe a case that shows your answer.
Sort each claim as a priori or a posteriori: (a) "Every square has four equal sides." (b) "The library closes early in summer." Then explain why sorting these claims does not settle whether rationalism or empiricism is right.
A friend says, "If everything is determined, then whether I get the job is already settled, so there is no point preparing for the interview." Which view is the friend describing, and what would a determinist say back?
A classmate says, "Pascal proved that God exists by showing that believing pays off." Name two things wrong with that sentence, using Dataset G's row.

Answers (worked reasoning — read after attempting)

P1 If the printer is out of paper, it shows a red light. P2 It shows a red light. C So it is out of paper. The argument runs the conditional backward, from the consequent (the red light) to the antecedent (out of paper), so it is invalid. A case shows it: the printer could show a red light because of a paper jam while its tray is full. Then both premises are true and the conclusion is false, which is enough to show the form is invalid.
(a) A priori: you can know it by understanding what a square is, without measuring any square. (b) A posteriori: you can know it only through experience, such as reading the posted hours. Sorting single claims is one job; rationalism and empiricism are rival views about where knowledge of the world comes from. Both sides can agree that (a) is a priori and (b) is a posteriori and still disagree about whether reason alone can teach anything substantive about the world.
The friend is describing fatalism: the outcome comes whatever they do. A determinist would answer that the outcome is necessitated by prior events, and preparing, or not preparing, is among those events. So on determinism preparation is one of the causes of how the interview goes, and it is not pointless. That is why determinism does not imply fatalism.
First, the wager is not a proof: Dataset G's row sorts it as prudential, about belief, not proof, so it gives a reason to believe, not evidence that God exists. Second, its direction is "for belief", not "for God's existence": its conclusion is that a prudent person should wager that God exists. A third slip hides in "pays off": the wager says believing has a possible infinite gain, not that the gain is certain.

Next up in this module: the lecture, the slide deck, the Readings & Resources page, the practice set, the discussion, and the midterm; next week the philosophy of religion applies the same standard-form method to the question of whether reason can show that God exists.

Built with The Course Maker · samples.thecoursemaker.com