CNM: Phil 1156-301,302: Logic & Critical Thinking (Salbato) Fall, 2013

Syllabus: Philosophy 1156: Critical Thinking & Logic (3 units)

Instructor: Jeff Salbato E-mail: jsalbato@cnm.edu Website: www.jeffsreadings.comOffice hours: MJG 201-14, M-R 1:30-3:00 Voicemail: 224-4000-ext.50166

Days, times, location, final exam:TR 9:00-10:15 in WS-MJG-215 Final exam: R 12/12 7:30-9:30TR 12:00-1:15 in WS-MJG-209 Final exam: T 12/10 11:30-1:30

Course Description (official): This course provides the tools of reasoning necessary for everyday decision-making and problem solving. Skills for argument, argument analysis, argument construction, and critical thinking are introduced. Informal fallacies, inductive and deductive systems of logic will be discussed and analyzed. The course will also take a critical thinking approach to the reasoning process.

What this course is REALLY about: Unlike most classes in college that, in part, aim to show you how much you don’t know, this course will try to help you become more literate in what you already know. We will be investigating how everyday reasoning works. You use reasons every day, but you have never been asked to articulate how you do it. The bulk of this class will be learning how to conceptualize and practice the good reasoning that we already know how to do. This will, then, provide us the vocabulary and competence to remedy faulty reasoning. As a bi-product you will become more articulate thinkers and writers, and, more importantly, you will be able to thoroughly annoy those around you as you dismantle their idiotic attempts to justify their ideas and lives (I cannot officially endorse applying these techniques to mass society and politics, but I have this “friend” that says it’s fun).

Course Text: All readings and handouts are available online: http://www.jeffsreadings.com These are Word documents that can be opened with the following password: _________

Evaluation: Final grade is out of 100pts. (90s = A, 80s = B, 70s = C, 60s = D, 0-59 = F) 7pts. Weekly Exercises: Due Thur: mid-week practice exercises (½ pt. each)14pts. Daily Reading Quizzes: Start of class; should be easy if you’ve read (½ pt. each)90pts. Weekly Big Quizzes: 20 minute quiz on that week’s material (6 pts. each)10pts. Final Exam: A cumulative set of questions, like a few large Weekly Quizzes

(Note: Total points possible: 121)

The Pep Talk: I will try my best to make this stuff interesting and lively. If you get involved in the issues, keep up with the reading, and put in a solid effort, you will do fine in here. There are so many points, so, if you are not lazy and attend regularly, there is no need to worry about your grade. This stuff can be pretty complex, so never hesitate to ask the most basic questions. It is my job to explain things clearly, and it is your job to make sure that I am being clear. So, if I start mumbling like Ozzy, you would be doing the whole class a favor by raising your hand and asking, “What are you talking about, you spastic, unshaven, bookworm?” There is no competition nor curve in here, so please see this as a collective endeavor. This is a specific challenge to you shy students. I was desperately shy in college, so I know that the class is tired of listening to those annoying, outgoing students and is missing out on your thoughtful insights.

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Course Policies Page:

Student ID Number: I will make up a student number for each of you. Please put this number on the back, at the very, very top, of all of your work in here.

Daily Tiny Quiz: These will occur at the beginning of class (when you are typically just walking in and are particularly disoriented...insert cackling laughter). These will be based on the concepts and examples in the readings and previous classes.

Weekly Readings & Exercises: I will assign readings at the end of every week by simply announcing the “letters” that distinguish each reading on the course website. I will assign a portion of the italicized exercises from the following pages of this syllabus at the end of every Tuesday that will be due Thursday. These are worth ½ point, based on accurately applying the techniques from the readings and class discussions. You must be in class when we go over them to earn the credit. These exercises will be like the ones we’ve been covering in class and will be similar to what will appear on the Weekly Quiz.

Weekly Big Quiz: These will be given the last 20 minutes of each week. There will be no surprises on these quizzes; they will be very similar to the examples we covered in class and in the exercises. Be careful to explain things clearly and write clearly.

Attendance/make-ups/tardiness: Every day is a chance to earn points, so absences are costly. The daily tiny quizzes and weekly exercises cannot be made up if you are absent or tardy (my sneaky way of getting you to class on time). The weekly big quizzes cannot be made up, but an extra five points will be added to the weight of your final exam for every missed quiz (and this way I don’t have to try to determine if, “I had to work to pay for my ipod, twirly rims, and cigs” is a valid excuse…zing!).

Playa’ hata’ rule: I am not disrespecting your urgent need to buy drugs, send pictures of your latest tattoo, or get directions to a rave (or whatever you little grasshoppers are into these days), but you have to silence your cell phones and not allow them to distract us. If you can be discrete, you can do brief texting, but handle them quickly so you can get back to learning. I’ve found that the avid texters keep failing my classes and annoy my favorite students. If you annoy the nerds, you have to bring snacks for everyone.

Warning to overachievers and grade-mongers: My past overachievers and grade-mongers have told me to write a special warning to you. I am supposed to tell you to be ready to feel alarmingly insecure, especially if you are used to cruising along in your memorization-based classes. This class is not about information; it is about everyday reasoning that is usually unconscious. Thus, you are not being asked to simply give the right answer but articulate how you arrived at it. Here’s an analogy: you know how to tie your shoes, but it would be surprisingly hard for you to explain and defend the particular technique you use. Don’t get me wrong, you will do fine in here and receive a good grade, but be prepared to feel intellectually insecure for the first time in a class.

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B: Claims: Spheres of Discourse: Truth, Values, and Tastes

Truth (factual) claims: Statements or ideas that make a judgment about reality.

Rational Standard: Does it agree with reality?

Important! Every truth claim must be either true or false, not both!

Are these examples of truth claims? It is raining. There’s life on Mars. I have a headache. God exists.

Values: Judgments about the quality or meaning of an action or thing.

Rational Standard: Does it fit reasonably with our other beliefs?

Two Tangents: Pimp-slapping normative relativism! Is vs. ought/ legal vs. moral

Are these examples of values? The Bible is sexist. This is a good watch. Hitler was a bad man. Rape is wrong.

Tastes/Preferences: Personal ideas about what we think or feel.

Rational Standard: Does it make sense? Is the person a reliable source?

Are these examples of preferences? I hate mustard. Federico’s is better than Taco Bell.

“A” Exercises:1. How do we access the readings?2. What do we do with our 4 digit student ID numbers?3. Are late exercises accepted?4. Can missed daily reading quizzes or weekly major quizzes be made up?

“B” Exercises: 1. Answer the following questions in plain language:

a. How do you tell if you are dealing with a truth claim (a factual issue), as opposed to a value or taste claim (nonfactual issue)?

b. Are all opinions about facts equal? Are all opinions about values equal?2. Explain whether the following are truth-claims, value-claims, or tastes (or both):

a. I think Jeff has a tattoo that says, “Rage Against the Machine” on his back.b. Monet is a much better artist than Pollack.c. The hills in western New Mexico are the most beautiful shade of red. The

landscape becomes more pale and beige as you head into Arizona.d. TV programs have too much violence and immoral behavior. Hundreds of

killings are portrayed every month.

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C: Concepts & Credibility

G.U.S. =General Understanding of Stuff: background knowledge & competence:G - Pre-judices:

Credibility: Can we trust a claim because of its author?Tangent: Media bias: no research, advertisers, couch potatoes, & fear…Tangent: Advertising: The lesson of Herbert, the American, middle class dog…

Analyzing Credibility:

A. Initial Plausibility (GUS) ?

B. Source Credibility :1. Expertise (access) ?

- Tangent: The paradox of American’s cynicism and scientific idolatry:

2. Sincerity : a. Presentation ?

b. Character ?

c. Coercion ?

“C” Exercises: Analyze the credibility of the following: 1. The President says, “We are promoting democracy in (fill in latest country).”2. A politician says, “The best way to create jobs is a tax cut for the wealthy.”3. A politician says, “We have the greatest health care in the world.”4. A TV news host says, “The death tax is unfair to the middle class.”5. A TV news host says, “We spend more on welfare than defense in this country.”6. An auto mechanic says, “Your exhaust manifold is cracked; it’ll cost $600 to fix.”7. A radio ad says, “We can cut your mortgage payment in half.”8. Your buddy says, “A thermostat is not complicated at all.”9. A citizen says, “We have poured money into education, and it hasn’t helped.”10.A citizen says, “The United States has the highest taxes in the world.”

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D&E: Reading: Paraphrasing and Analyzing for Structure

Headlines: Not to entice but to give the reader the right prejudice. This is an exercise to help you locate the Main Point (MP).

One Sentence Paraphrases: Give the key ideas of passage in one, complex (yet grammatically correct) sentence, and make a note of what you leave out.

Analyzing for Structure: Lay out the structure of a passage to reveal its connections and reasoning. We are so competent in using language that we naturally supply clues to our reasoning, or lack thereof, when we speak and write. We are not judging the truth or rationality of what is said; we are just analyzing what is intended.

MP (main point), SP (secondary point), and TP (tertiary point or tributary argument)

Format: A random example:MP: The key claim of the passage

SP: A claim that directly supports or follows from the MPTP: A claim that supports or follows from the above SP.

SP: Additional SP (should be indented to align with other SPs).SP: Additional SP

TP: (align with other TPs).TP:

Padding: What to leave out: Location, helpful background information, definitions of terms, restatements of previous points, illustrations, and friendly jokes or asides. The degree of detail that is left out as padding will depend on the degree of detail called for in your paraphrase.

“D” Exercises: Provide a 4-word, informative headline and a clear, one sentence paraphrase for the following passages on pages 8-9 below: US Budget, It’s a Vagina, War on Terror, Gas, Drug Scandal, and Israel.

“E” Exercises: Provide a structure analysis into MP, SP, TP (no subordination categories yet) for the following passages on pages 8-9 below: Hell, Iraq, Alienation, Monogamy, and Cro-Magnon.

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F: Reading: Subordination Categories: Understanding Nascar 1

Backward-looking reasons (“because”):Support: MP is supported by SP; MP is justified by the reason supplied in SP.

- I am certain that Nascar fans are morons, because (for the reason that) studies show they would be utterly confused if the cars turned any direction but left.

Explanation: MP was caused by SP; MP is explained by the motive SP.- Cause: Dale Earnhardt died because (due to the event that) 2,000 pounds of

corporate logos crushed his car.- Motive: Gus waves his confederate flag, because (due to his regard for) he

wishes the redneck racists had won the war.

Forward-looking reasons (“so”):Inference: MP allows us to infer SP; MP gives us a reason to believe SP.

- Nascar is the fastest growing sport, so (which allows us to infer that) all those couch potato yoo hoo addicts must be getting bored of wrestling.

Result: MP results in SP; MP produces SP; MP helps one bring about SP.- Cause: Several Nascar drivers crash, burn, or die every weekend, so (thus, as

a result) thousands of bored, impotent losers tune into watch.- Motive: Gus needs to be drunk so that (in order to bring it about that) he’ll

forget how stupid he looks in his mullet and tank top.

Other:Qualification: MP is refined by SP; MP has the tangent SP.

- Nascar fans chew their weight in tobacco, but they think it’s a vegetable.- Nascar fans are typically sunburned, and they also tend to be fat and toothless.

Three Part Question-and-Answer Technique:

1. Try to translate direct connections between points into “because” or “so”.If clearly “because”, then support or explanation.If clearly “so”, then inference or result.If “but” or “and” are clearly the better connector, then qualification.

2. Look for indirection (simple flags, normativity, predictions, psychological).If “because” with indirection, then support.If “so” with indirection, then inference.

3. Look for physical or psychological causation: one event causes another.If “because” with causation, then explanation.If “so” with causation, then result.

1 My apologies to all of you intelligent, health-conscious, sober, non-racist, self-actualized, sunscreen-using, fully toothed, fit, mullet-less, and non-tank top wearing Nascar fans….yeah, right! No such thing!

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“F” Exercises: For the following passages, write out the “Three Part Question-and-Answer Technique” (on previous page) to label each of the following with the proper subordination category that best explains the reasoning connection from the first sentence to the second sentence:

1. UCLA almost didn’t beat Stanford. They’ll never get past Washington.

2. NASCAR fans hate the new points system.It requires them to use math.

3. That cat is used to dogs.Probably fluffy won’t be upset if you bring home a new pet dog.

4. Marcus will never make it into the state police.He’s over their weight limit.

5. I guess he doesn’t have a thing to do.Why else would he waste his time watching daytime TV?

6. You can be sure that Ryan will marry Beth.After all, he told me he would.

7. Those clothes look like you slept in them and you look like you just came off a bender.

If I were you, I’d change and shave before you teach today.8. There was no fire on impact.

The plane must have been out of fuel.9. The plane was out of fuel.

There was no fire on impact.10. You failed the quiz.

You got it wrong.11. Jeff must be delusional.

He enjoys this stuff.12. Jeff has really bad breath.

He likely forgot to brush again.13. But I have to have those jeans.

I have to look like everyone else.14. I’m getting plastic surgery.

I’m trying to attract more shallow men.15. I dyed my hair purple.

I hate my parents.16. You should buy a gun.

You should make sure your kids are safe.17. But, wifey, it’s cheaper in bulk.

We should definitely buy the 8 gallon salsa.

“G”(NO READING) Exercises: Provide a full structure analysis, with subordination categories, for the following passages on pages 8-9 below: Jeff’s Truck, Tax, Alienation, and Cro-Magnon.

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D-G: Reading: Passages for Analysis:

THE U.S. BUDGET: Why are so few people actually informed about the budget when it is a public document? In 2006, for example, Bush is requesting that 54% of our discretionary budget go to defense. That means, of the tax dollars that the President can choose what to do with, he is choosing that 54% will go toward the military. Here’s a fun example, when you combine defense, homeland security, veterans affairs, and NASA, we’ll spend $494 billion. Compare that to the budgets for health & social services ($69 b) or education ($56 b). To make matters worse, these two budgets will decrease in the future, whereas since “W” took office, the defense budgets have gone up $138 billion. I guess killing Iraqi civilians is more important than your health care or education. And if you think this makes sense in our dangerous world, take note of the fact that our military budget is greater than the rest of the world, combined.

IT’S A VAGINA, NOT A CLOWN CAR!: All of these cases of quintuplets and septuplets get so much touchy-feely treatment from the media that most of the public are failing to see the significance of this medical practice. In-Vitro Fertilization is standardly done by fertilizing several eggs in the lab and injecting anywhere from 3-8 embryos into the prospective mother. Since the odds are very bad that any single egg will actually make it through to produce a live birth, most clinics play the odds and “hope” that only one of the multiple embryos will make it to full term. Yes, this is a procedure that hopes that most of these fetuses will miscarry. Even worse is the fact that a women’s body is not made to carry so many fetuses. Most of these children, if a few of them, or seven, make it to term, will be born with serious disabilities. Shouldn’t IVF be rightfully considered child endangerment?

WAR ON TERROR: Is the “War on Terror” a good idea? I can see how our former wars on concepts like poverty and drugs have been such successes that those things don’t exist anymore. But what if this war on a concept actually increases terror? Every other country in the world said it would, and these other countries are far more familiar with terror than we are.

HELL: It’s obvious why we hate coming to this class. The material always confuses us. It is just too hard for anyone that is not a damn nerd. And the last straw is the sucky teacher. He is way too hyper for such a retarded subject, and he has the sense of humor of a four-year-old. I wouldn’t be surprised if he started calling us doody-heads or something.

IRAQ: We needed to attack Iraq in order to send a message to the world’s terrorists. We also needed to oust that monster Saddam for using U.S.-made chemical weapons on his own people. It was also just a matter of time before he obtained WMDs to use against us.

GAS: The American Family Association called on its members to boycott gas from CITGO gas stations because it is a subsidiary of Venezuela’s national oil company. They did not want to support a democratic-socialist government. They prefer sending money to dictatorships and human rights abusers like Saudi Arabia, Algeria, Chad, Angola, etc.

JEFF’S TRUCK: Jeff should buy a better truck. The one he’s driving is just embarrassing for a guy with that many degrees, and he just got a new job, so he can certainly afford one now.

TAX: A cut in the capital gains tax will benefit wealthy people. Marietta says her family would be much better off if capital gains taxes were cut, so I’m sure her family is wealthy.

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ALIENATION: CNM students seem to be alienated from their true needs, because they spend every free moment on their cell phones in order to keep themselves from self-reflection. Self-reflection allows people to analyze their goals and values. They show a penchant for alcohol and violence, so they must be deeply bored. Jeff says, “beer and tattoos are like a religion out here in Alburtucky.” They spend inordinate amounts of money on cars and technology because these represent status to simple-minded people.

MONOGAMY: Why do you come down so hard on married men who cheat? Do you believe monogamy is the only “right” way when it comes to marriage? If monogamy works so well, how come so many men cheat? Many other cultures openly accept polygamy. And in many countries, adultery is shrugged off as nothing to get excited about. The wife gets the financial support and social position, and the mistress gets the sex. The truth is, there’s not a woman on the planet who can fully satisfy the needs of a powerful male.

DRUG SCANDAL: Just when you thought the use of performance-enhancing drugs couldn’t get worse, the world of figure skating is being rocked by doping allegations. Three top-ranking male figure skaters tested positive for estrogen levels 10 times those of 13 year-old girls at the height of puberty. Jess Folbota, the leader of the activist group Ethicists Against Athletes, read a statement to the media: “Though estrogen is not known to increase agility or strength, it showed dramatic rises in what is known in the industry as ‘General Fabulousness’. As such, this would give them an unfair advantage in key skills like twirling, hand-waving, and the all-important sequins-to-tassels category. It is clear that these athletes used a foreign, performance-enhancing substance and should be punished.”

FACEBOOK: In a cost saving move, congress and the CIA have agreed to replace most of their information gathering programs with Facebook, the CIA’s massive online surveillance program. Director Salbsky defended the move, “After years of secretly monitoring the public, we were astounded so many people would willingly publicize their religious and political views, lists of their friends, email addresses, personal photos, and even status updates about where they were moment to moment. They are even freely mapping every place in the world they’ve visited! That kind of information would have taken months of going through hotel and airline receipts.”

ISRAEL: It’s so cute how Israel tells the rest of the world what to think. They convince everyone to feel sorry for them, but they kill three times as many Palestinians and a much greater percentage of civilians and children. Peacemakers from Tutu to Chomsky have equated their laws in Palestine to Apartheid, and they wouldn’t let Bishop Tutu into the country to investigate a possible human rights crime. My favorite was when they would only allow the UN to send investigators to another incident if they promised, and I quote, “Not to make any observations.” I make observations all day long. Does that make me anti-semitic? Or how about how they secretly have nukes and vote against nuclear disarmament yet scream for disarming Iran?

CRO-MAGNON: Jeff looks like a living Cro-Magnon man. Cro-Magnon is a rare pre-human primate. Jeff is a dead ringer for one. He has freakishly long arms. He is able to grab his wallet by reaching over his shoulder. His head must be twice the size of a normal person. This is a particular feature of pre-humans. Just the other day one of his students mistook his hat for a car cover. Finally, he has grotesquely short legs and a protruding butt. These last two traits give him the distinct gait of some kind of primate. All that is missing is the uni-brow and a club. I’m thinking of bringing a giant net to class and nabbing the guy to see if the Smithsonian could use him for their Stone Age exhibit.

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H&I: Arguments: Induction Versus Deduction:

An Argument versus “an argument”:

Issues, premises, & conclusions:

Induction: An argument that compiles evidence to increase the likelihood of a generalization or prediction. The conclusion can never be more than likely.

- Strong = The evidence in the premises is relevant, truthful, and extensive enough to make the conclusion highly likely.

Deduction: A structured argument that relies on a valid argument form to provide conclusive proof for a stated conclusion.

- Valid = The structure of the (deductive) argument makes it so that if the premises are true, the conclusion has to be true. The conclusion follows with such logical precision from the premises that if they are true, the conclusion must also be true.

- Sound = A valid (deductive) argument with true premises, which, by definition, amounts to the conclusion being necessarily true.

So, for every argument, the assessment process looks like this:

1. Deductive or Inductive?D2. If deductive, is it valid?D3. If valid, is it sound?

I2. If inductive, is it strong?

“H” Exercises: Present the premises and conclusion (some of these are only implied). Are these people arguing about the same things?

1. Jeff: I need to find a way to get some free time soon. I haven’t had any truly free time in weeks. I’ve used every free second prepping my future classes.

2. Wifey: Oh, do you think I’ve had a ton of free time? Do you think I’m out there shopping for myself?

3. Jeff: You people need to learn to pay more attention to your children and put the cell phone down when it isn’t absolutely necessary.

4. Americans: But I need my cell phone for emergencies. If my kids get hurt at school or I’m running late, I need a phone handy.

“I” Exercises: 1. How do you tell the difference between an inductive and a deductive argument?

Give a couple of examples to illustrate your technique. 2. Explain how strong or weak the Mary, rainfall, and GRE examples are on page

11 below.

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I. Arguments: Examples:

1. There is a strong stench in class today.2. The pungency increases when Jeff walks

near my row.Thus, Jeff’s BO or halitosis is the cause of the caustic odor.

1. Those disgusting pigeons (sky rats) are in the family columbidae.

2. Doves are in the family columbidaeThus, pigeons and doves are in the same family (ie. They’re alike and deserve equal treatment).

1. The sun has risen every morning in recorded history.

Thus, the sun will rise tomorrow morning.

1. All snarfblats are whatsits.2. All whatsits are really thingamabobs.Thus, a snarfblat is a thingamabob.

1. Everyone named Mary I’ve ever had in my classes has received an A.

2. There are two students named Mary in my class this semester.

Thus, they will get A’s.

1. No one is parked in that spot over there.2. The sign on the parking meter says, “Out

of Order.”Thus, the meter must be broken.

1. My teacher is a tree frog.2. Tree frogs have sticky feet.Thus, my teacher has sticky feet.

1. All boy bands suck.2. Britney Spears is not a boy band.Thus, Britney Spears does not suck.

1. If Doug is drunk again, then he will be stumbling around campus.

2. Doug is stumbling around campus.Thus, Doug is drunk again.

1. It is either raining today or it is not.2. If it is raining, then the grass is wet.3. The grass behind Watkins is wet.Thus, it is raining.

1. The annual rainfall in California’s North Valley is 23 inches.

2. Last year, the rainfall was 23 inches.Thus, the rainfall this year will be about 23 inches.

1. All Nascar fans either have mullet haircuts or wear tank tops.

2. Jethro (of course, a Nascar fan), doesn't wear tank tops.

Thus, Jethro has a mullet haircut.

1. A hot shot architect would not have six kids sharing one bathroom (getting more bladder infections than a brothel).

2. Mr. Brady had six kids sharing one bathroom.

Thus, Mr. Brady was not a hot shot architect.

1. The graduates of Stanford generally score in the 90th percentiles on the GRE.

2. Students from Tumbleweed Tech generally score well below this mark.

Thus, Stanford does more toward educating their students than Tumbleweed Tech does.

1. If your buddy has a receding hair line, then he is a grown man.

2. If you take baths with a grown man, or are offered Jesus Juice from a grown man, and that man is not your Dad, then you are being targeted by a pedophile.

3. Your buddy (Bert) has a receding hair line.Thus, You (Ernie) are being targeted by a pedophile.

1. If you are standing in front of class, then you are the most handsome and intelligent man in the world.

2. Jeff is standing in front of the class.Thus, Jeff is the most handsome and intelligent man in the world.

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J: Arguments: Rhetorical Fallacies

Rhetorical Fallacies: These attempt to persuade the audience to accept a conclusion by means of emotion instead of good reasoning. It is important to note that not every use of emotional persuasion is fallacious. Sometimes an appeal to emotion can be relevant evidence for a conclusion.

1. Appeal to Fear or Force - Scares the audience into believing their claim, instead of giving relevant evidence.

2. Appeal to Pity and Flattery - Gains sympathy from audience to get them to accept a claim, instead of giving reasons.

3. Appeal to Popularity or People or Bandwagon - Evokes your desire to impress your simple little friends, instead of giving relevant evidence for the claim.

4. Ad Hominem (Argument against the Person) - Attacks the person instead of using reasons to attack their claim or position.

5. Straw Man - Presenting a ridiculously weak or exaggerated version of the rival position to make it easier to refute.

6. Red Herring - The reasons given actually support a different claim than the one at issue.7. Appeal to Unqualified Authority - Relies on the testimony of someone who has no expertise

on the particular issue in question.8. Appeal to Ignorance - Relies on a lack of knowledge as evidence, instead of providing

evidence.9. Hasty Generalization - Makes a general conclusion from an inadequate sample of evidence.10. False Cause - Uses a clearly coincidental occurrence to explain an event. 11. Slippery Slope - Invokes an unreasonable chain reaction of future events where such a

consequence is highly unlikely because the causes are vastly different.12. Weak Analogy - Argument rests on a tenuous set of similarities between two things.13. Begging the Question or Arguing in a Circle - The evidence for the claim either relies on the

very claim it is trying to prove or else is just a restatement of the original claim.14. Black & White Fallacy or False Dichotomy - Reduces an issue to a choice between two

options when, in reality, there are more than two possible options.15. Suppressed Evidence and Proof Surrogate - Overlooking key evidence and/or using

an expression that makes it sound as if evidence is unnecessary, when, in fact, it is needed.

16. Equivocation – Argument relies on a single word or expression being used in two different ways.

17.a. Euphemism (or dysphemism) - Makes a bad thing sound better than it is.17.b. Innuendo - Makes a derogatory remark indirectly.17.c. Hyperbole - Overstated exaggeration to the point of being practically impossible.

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“J” Exercises: 1. For the examples below, explain the type of fallacy each might be. If you cannot pin-

point a certain fallacy simply explain, in plain English, the techniques the author is using to persuade the audience. a. Everyone should support the death penalty. Either you kill the murderers or tell

them to go and kill some more.b. What, now I can’t smoke in restaurants? This is going too far. Pretty soon

smokers are going to be liable for damaging the health of their own kids with second-hand smoke in the privacy of their own homes.

c. I won’t try that supplement; two guys took that and their junk shriveled.d. The death penalty is morally fine, because murderers deserve to be killed.e. The animal rights people shouldn’t pick on rodeos. If they’d come out and see the

way the clowns put smiles on the kids’ faces and the determination it takes to ride the broncos or rope the hogs, they’d change their minds.

f. Women definitely hate this shirt. Just the other day I was wearing this shirt while I was trying to pick up on this hottie at a Gynecologist’s office, and she wouldn’t give me the time of day.

g. Gus, I am not going to take your advice on my philosophy assignment, you failed the class 7 times. And yes, that was 10 bucks on pump 4, please.

h. I have never seen God, so He must not exist.i. Everyone has the right to life, liberty, and the pursuit of happiness. Because we

take these truths to be self-evident. (U.S. Declaration of Independence)j. Jim Caviezel, star of The Passion of Christ, supports the U.S.’s unflinching pro-

Israel stance, and that guy knows more than anyone else what Jesus would do in the Middle East today.

k. Jeff wants us to stop focusing our life goals around money, so he wants us all to be homeless beggars.

l. During WWII, the U.S. government resettled many people of Japanese ancestry in internment camps. We sure have a generous government.

m. You are such a stud. So you should definitely test drive one of our power trucks.n. We should get some ice cream from Jack’s Parlor, because that old guy is very

friendly and rarely gets any business now that those three Starbucks moved in down the street.

o. The tax system in this country is unfair! Just ask anyone!p. You should get a health exam or you may die of cancer that could be treatable.

2. Go back through the above examples and explain whether the author’s strategy, no matter how emotion-driven, is still partially relevant as support for the conclusion.

3. Rewrite the following biographical sketch of your favorite teacher (yes, me!) by using rhetorical language, especially dysphemisms, innuendo, and hyperbole, to state the same information but in such a way that Jeff would appear to be (even) dumber, uglier, and more neurotic than he actually is: “Jeff is a rather short and broadly built teacher. He tends to have a five o-clock shadow as his normal day-to-day look. This earthy look is the only thing that makes him seem old enough to teach college, because he has the style, height, enthusiasm, and sense of humor of a younger person. He can also be a bit eccentric in his cynicism and political opinions.”

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K: Arguments: Analogies

Analogy: Object/event X is like Y in these ways, so X must be like Y in this way too.

X = sampleY = target

Q = feature in questiona,b,c,... = properties

Analysis of an argument by analogy (paraphrase author):

1. X has properties a, b, c, … and property Q.2. Y has properties a, b, c, …------------------------------------Thus: Y must have property Q as well.

Critique of an argument by analogy (Apply GUS):

1. What are the key properties that result in something having property Q?2. Does Y have those key properties?3. Does Y have any special properties that may restrict the presence of property Q?

“K” Exercises: Analyze and critique the following analogies:1. I have short brown hair, a boyish sense of humor, two eyes, two legs, I’m a biped, and

many other features just like George Clooney, so why aren’t I a heartthrob?2. My friend’s paper received an A, so why didn’t mine receive an A? My paper fit the

prompt, was painstakingly proofread, was well-researched just like hers. In fact, I turned in the same exact paper.

3. If Gus didn’t treat you well on the first date, then if this date tonight is also with Gus, then you should cancel it.

4. I am as pretty as Brittany Spears, I can sing as good as her, I have a body like hers, and I just got a nice boob job like hers, so I am likely to become rich and famous like her any day now.

5. Tiger Woods began playing golf at the age of two, and he is a superstar. I’m going to get Micah started by a year and a half.

6. Cigarettes and alcohol are addictive, harmful, and threaten the well-being of innocent bystanders, just like many narcotics, so cigs and alcohol should be illegal, too.

7. A pigeon is in the same family as a dove, so they should be respected equally.8. Weapons of mass destruction are illegal for civilian ownership, so automatic and

semi-automatic weapons should be as well.9. Don Marquis: Killing a fetus is wrong for the same reason killing you or me is

wrong, the loss of a potentially valuable future.

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L-O: Explanations: Diagnostic Explanations as Arguments

Diagnostic arguments: Explaining the occurrence of trace data. (crime scenes)Effect-to-cause reasoning …. “Inference to the best explanation”:

Rival Conclusions (Explanations): stories that explain the presence of the TD

TD (Trace Data): pieces of evidence that need explaining: “Why is it the case that…?”

CTD (Central Trace Data): Pieces of TD that are most in need of explaining; any rival conclusion that does not explain the CTD is not a serious rival explanation.

PTD (Peripheral Trace Data): Those pieces of TD that are not essential to explain, but a rival gains strength if it can account for the PTD as well as the CTD.

- Correlations: explain why these two events are occurring together

NTD (Non-Trace Data): help for the rivals and/or help for our GUS- Trace-signalers:- MO:

Ranking the Rivals: the rankings are based on whether that conclusion (explanation) best explains the CTD (and, hopefully, the PTD as well).

- Articulating Relevance: impact on the ranking of the rivals:

“L” Exercises: State the question and provide the author’s rival explanation, then suggest two stronger rivals of your own:1. I got into so much trouble as a kid because my father became a heavy drinker.2. I’ll tell you what caused all these cases of kids shooting up their schools. Every

single one of those kids liked to play violent video games.3. So many Americans buy luxury items, whether they can afford them or not. They see

that top executives wear expensive clothes and drive nice cars. They do the same, thinking that projecting an image of success is a key to being successful.

4. Women with boob jobs tend to die younger than women without boob jobs. This must be because the implants cause deadly infections.

“M” Exercises: Specify the Trace Data (TD), Non-Trace Data (NTD), and provide 2 serious rivals for the following examples on pages 16-17: Waldo & Potter.

“N” Exercises: State the question, specify the CTD and PTD, give 2 rivals of your own, and explain which rival is the strongest for the following examples on pages 16-17: Fire & Lawn Sculptures.

“O”(no reading) Exercises: State the question, specify the CTD and PTD, give 3 serious rivals, articulate the relevance of 2 pieces of NTD, rank the rivals, and fully articulate your ranking for the following examples on pages 16-17: Puddle & Magic

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L-O: Explanations: Examples

WALDO (true): Waldo the turtle is missing. He must have gotten out of the garden’s fence, because he always tries to dig under it or climb over it. We have found him after he escaped before. Turtles like Waldo do bury themselves in the ground when they sleep, including when they hibernate. Kelly dug all around in the garden and didn’t find him buried in any of his usual sleeping spots.

ABORTION RATES (true): It seems that the abortion voters have an alarming impact on abortion rates. The abortion stance of the president we vote for correlates with the abortion ratio (abortions to 1,000 births). It correlates backwards. The pro-life presidents Carter, Reagan, and Bush Sr. had abortion ratio averages of 356, 354, and 337, respectively. Clinton, our only clearly pro-choice candidate in the last 35 years, averaged 283 and saw the ratio drop steadily from 321 in his first year to 246 in his last year. What could explain this?

MAGIC: The famous magician David Copperfield has undergone a major image change over the last decade. Early on in his career he wore the standard-issue costumes that clearly identifies one as either an ice skater, boy band member, or magician. Now he wears guy clothes. He has even gotten rid of his Las Vegas mullet and Dallas Cowboys Cheerleaders make-up in favor of short hair and no make-up. This change seems to have occurred rather rapidly, right about the same time he started dating Claudia Schiffer, a supermodel that is an accomplished amateur magician. It is clear that Claudia used a magical spell to make David’s sexual preference disappear.

HESPERIA (true): The skull and one foot of a woman were discovered in her home by her nephew, authorities said. "We dug everywhere (in the yard), but with the rain and everything, it's hard to locate anything,” said Hammock, a San Bernardino county deputy coroner. Hammock said he believes Mary Hessey, a 61-year-old cancer patient, died naturally and her body later was eaten by the dogs. "There is no visible trauma to the skull, and no indication of what caused her death." San Bernardino County sheriff's deputies believe the woman died inside her home and was dragged outside by the dogs when they became hungry. The woman had been dead between three and four weeks before the remains were discovered Tuesday by her nephew. He said the dogs, described as medium-sized mongrels, "looked in pretty good shape to me—not like they were starving or any thing.”

FIRE: Through the rain of embers and flying ash from a nearby brush fire, Herman scrambled up a ladder onto his roof carrying a hose. He must be trying to keep his house from catching fire.

PUDDLE: I woke up in a puddle this morning. I didn’t do anything unusual last night. I went to bed pretty early after snacking on some watermelon. I did have a slightly unusual dream, though. I dreamt about surfing in Kauai. This was a little weird, because I haven’t been to Hawaii since I was 16, and all of my more recent surfing dreams are about my favorite cold water break in Baja.

WHY WE FIGHT (true): The U.S. spends more on its military than the rest of the world combined. We have bases all over the world. I hear that we fight for freedom, yet none of our 59 military interventions since 1945 have resulted in clear victories for democracy or human rights? What am I missing?

LAP DESK: An emphatically highlighted and make-uped female sitting near the back of the room is staring into her lap. She is raising her eyebrows one moment and then grinning the next, but these facial expressions in no way correspond with my fascinating insights or hilarious jokes. Maybe she has Tourette’s? Epilepsy? Then a student behind her yells, “Snacks!”

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CRIME (true): Crime rates in nearly every category were going up at alarming rates in the late 80s and early 90s (hmmm, once again, the Reagan and Bush years… coincidence?) Then, while the experts were predicting the crime rates would continue to skyrocket and cities were implementing all sorts of drastic and drastically diverse crime programs, crime rates suddenly reversed and have continued to decline every year since 1992 (although it has started climbing since 2004). Again, the presidential rhetoric seems backwards, because Reagan and Bush ran on “tough on crime” platforms.

THE QE2 (true): The Queen Elizabeth II suffered a series of gashes, cracks and dents extending along 400 feet of the hull. The NOAA, which has been surveying the accident area, has found a “number of uncharted rocks out there.” One rock, 34 ½ feet deep, attracted the most attention. “Vegetation is not on the rock the way it is on surrounding rocks, and it has this substance that appears to be red paint.” The QE2’s hull, which is painted red, goes 32 feet below the water line. In Boston, the local pilot told investigators he wasn’t worried when he altered their usual course slightly. Charts showed sufficient depth. But the British Ministry of Defense said these charts use information from surveys done in 1939 and that it was possible for the hull to dip below 32 feet because of certain oceanic conditions.

POTTER (true): Ivan Potter died last night in a car accident. On his way home from work, Mr. Potter’s car crashed through a freeway guardrail and rolled down a soft embankment into a shallow stream. Examination of the corpse at the crash site by a qualified physician revealed no broken bones or external injuries. There was also no sign of skidding or swerving on the road leading up to the guardrail.

LAWN SCULPTURES (true): While working in my office at UC-Riverside, Wifie called me with the news that someone had taken a large duke on the lawn in front of our duplex in the family housing on campus. After cleaning it up that night, to my horror, the same thing happened the next day, and the next. The pile was even in the same spot. The only difference was that the toilet paper with the specimen was different colors. I racked my brain, but, unlike at CNM, I couldn’t think of a single one of my UCR students that hated me.

CARLSBAD (true): A hiker, Raffi Kodikian, 26, of Boston, was rescued from the desert back country of Carlsbad Caverns National Park says he killed his companion to put him out of his misery when the pair became lost and were dying of thirst. An autopsy Tuesday showed 26-year-old David Coughlin of Millis, Mass., had been stabbed twice in the chest. Park rangers on Sunday found Kodikian camped next to Coughlin’s shallow grave. Kodikian was suffering from dehydration and exposure when rangers found him about a mile from the nearest road and about two miles from the park’s visitors center. Rangers launched a search two days after the pair were supposed to return.

SUICIDE? (true) Police investigators were called to the scene of an attempted suicide. Bystanders saw a man leap from the roof of a six story apartment building. They said the man’s fall was broken by two awnings on the way down and came to rest on top of a rather large pile of trash. The fall transpired so slow that the witnesses were shocked to find that the young man was dead among the trash cans and bags. Their perceptions were warranted, however, for the investigators found that none of the injuries associated with the fall led to his death. Instead, it was a gunshot wound through the chest that killed the man. No gun was found on the scene or on the roof, but the man did have a suicide note in his coat pocket which read, “I cannot take your fighting anymore. For years I have wished that you would just kill each other and leave me in peace.”

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P-R: Formal Logic: The Symbolic Language SL

4 methods for Proving Invalidity (An advertisement for formal logic):1. Imagine a situation in which the premises would be true and the conclusion false.2. Crude Venn diagrams/ Check basic form.3. Construct an obviously invalid counterexample using same basic form.4. Formal logic

Our new language: “SL”...Its Sentences and Connectives:Sentence Letters: A, B, C, etc. represent simple sentences (“simple” depends on context)Connectives: Negation (~) represents “not” (our only one-place connective)

Conjunction (&) represents “and”Disjunction (v) represents “or”Conditional (→) represents “if, then” (if-antecedent, then-consequent)Biconditional (↔) represents “if and only if”

One-place connective (~), Two-place connectives: (&,v,→,↔)

A word on well-formed formulas: The rules:1. Any basic sentence is a well-formed formula.2. A negated well-formed formula is a well-formed formula.3. Any two well-formed formulas joined by a two-place connective, is a well-

formed formula (parentheses should be used to group two-place connectives in complex statements to preserve truth and meaning).

4. Any statement is well-formed if it is constructed from 1-3 above.

Properties of Connectives:- Scope: the range of terms connected by that connective.- Main connective: the connective whose scope is the whole sentence; this determines the truth-value of the whole statement.

Translation technique (for those anal, err, I mean, “A” students):1. In each step, start with the conclusion (if it is an argument).2. Underline all the possible connectives, put an arrow over the main connective. (Hint:

Look for hints in punctuation).3. Determine the basic sentences you will need, and use this to create your dictionary of

sentence letters. (Hint: Use full sentences and “positive” phrases).4. Fill in the main connective, leaving room on either side for rearranging content, then

translate the content on either side of the main connective.

Translations: Some tricky English idioms:Exclusive OR: (AvB)&~(A&B) Neither-nor: ~(AvB) (or) (~A&~B)A if B: B→A A only if B: A→BA unless B: ~B→A (or) ~A→B Not A unless B: (~B→~A) (or) (A→B)

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“P” Exercises: Finish labeling the deductive arguments on page 11 above as valid or invalid and, if valid, sound or unsound. Explain your decision in any case that wasn’t obvious to you…meaning, if you get one wrong and you didn’t explain your decision, you’ll miss points.

“Q: Exercises: 1. Label the following sentences as either well-formed or ill-formed. For those that

are ill-formed, make the necessary corrections to make them well-formed:a. (A → B) & ~Cb. ~ ~ C v Bc. (A ~ B) → Cd. ~ ((A & B) → ~ (B v C))e. (~ (A v B) → C) & B → C

2. Symbolize the following statements using the variables G, P and S (G = Gus has herpes; P = Peggy is in rehab; S = Speedy has herpes):a. Gus has herpes and Speedy does not have herpes.b. Peggy is in drug rehab if Speedy has herpes.c. Gus doesn’t have herpes if Speedy doesn’t have them or Peggy is in rehab.d. If Peggy’s in rehab, Gus has herpes, and if Speedy has them, so does Gus.e. Speedy does not have herpes if and only if Peggy is in drug rehab.

“R”(NO READING) Exercises: Translate the following arguments: (Jeff will announce)

1.) Translate the following arguments using the provided dictionaries:

A: Most of the students are getting A’sC: Jeff is a Comic genius.D: Jeff’s quizzes are too Difficult

E: Logic is very ExcitingF: Jeff’s Nascar jokes are Fresh.H: Jeff is Hyperactive

1. Jeff’s quizzes are too difficult, and his Nascar jokes are tired.2. Either Jeff’s quizzes are too difficult or most of the students are getting A’s.3. If Jeff’s quizzes were not too difficult, then most of the students have A’s.4. Either Jeff’s quizzes are not too difficult or logic is boring.-----------------------------------------------------------------------------------------

Therefore: Logic is boring if and only if most of the students are not getting A’s.

1. If Jeff’s Nascar jokes were fresh, then logic would be exciting.2. Jeff is a comic genius if and only if his Nascar jokes are fresh.3. If Jeff were hyperactive as well as a comic genius, then logic would not be so

boring and most of us would be getting A’s:-------------------------------------------------------------------------------------------

Therefore: Logic is exciting and most students have A’s.

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2.) Translate the following arguments, providing your own dictionary of basic sentences:Dictionary:

1. If Jeff takes the time to shave, he doesn’t use deodorant.2. Today Jeff is not clean-shaven. ----------------------------------------------------------------------Therefore, he must have used deodorant.

1. Jeff either has forgotten to brush his teeth or he forgot to use deodorant or shave.2. Jeff didn’t brush his hair.3. If he didn’t brush his hair, then he is probably not clean-shaven either.4. If he’s not clean-shaven, then he must have used deodorant.------------------------------------------------------------------------------Therefore, Jeff either shaved or used deodorant.

1. If Jeff doesn’t have minty fresh breath, then he is clean-shaven and smells flowery.2. Either Jeff used some “French shower in a can” or else he didn’t brush his hair and is rudely unshaven, but, if he is unshaven, then he must have BO.3. Jeff’s hair must look like a nest, if he didn’t take the time to shave.-------------------------------------------------------------------------------Therefore, Jeff must have BO if he has brushed his teeth.

1. If Jeff didn’t leave his hair unbrushed, then if he used deodorant or shaved, he would have remembered to brush his teeth.2. Jeff must have brushed his teeth, used deodorant, and shaved, unless Jeff, as usual, forgot to brush his hair, but if he forgot to brush his teeth, then he likely also forgot to use deodorant or forgot to shave.-------------------------------------------------------------------------------Therefore, Jeff remembered to shave only if he remembered to do the other three.

3.) Translate the following argument, providing your own dictionary of basic sentences:Dictionary:

1. If you have narcolepsy, then you will be passing out.2. You will be fidgety or passing out if you attended last night’s rave.3. You do not have narcolepsy, but you are passing out and fidgety.-------------------------------------------------------------------------------------Therefore: You attended last night’s rave unless you have narcolepsy.

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S-U: Formal Logic: Truth Values & Truth Tables

Determining the truth-values of the connectives:~ A A & B A v B A → B A ↔ BF T T T T T T T T T T T T TT F T F F T T F T F F T F F

F F T F T T F T T F F TF F F F F F F T F F T F

In other words, in English:~: Reverses the truth-value of the statement.&: Is only true when both sides are true.v: Is only false when both sides are false.→: Is only false when order of antecedent-to-consequent is true-false.↔: Is true whenever both sides have the same truth-value.

Constructing Full Truth Tables to Test the Validity of Arguments:1. Write all statements on same line, separating premises with “/” marks and conclusion

with “//” marks.2. Draw an arrow over the main connective for each premise and conclusion.3. If n is the number of different sentence letters in the statement, 2n is the number of

rows in the table. (Or: 2 sentence letters = 4 lines; 3 letters = 8 lines; 4 = 16, etc.)4. Go in reverse alphabetical order when representing every possible situation: the

column under the last alphabetical letter will alternate true, false every row, the next alphabetical letter will alternate true, true, false, false, every two rows, the third alphabetical letter will alternate every four rows, and so on.

5. Starting with the inmost parentheses, work your way down columns, filling in the truth values for one connective at a time.

6. Once you solve the truth-values under the main connective of each premise and the conclusion, circle these main connective truth-values: this is the truth-value of each statement.

7. If any row has True premises and a False conclusion, the argument is invalid.

“S” Exercises: Determine the truth-values of the following sentences by plugging in the following values and solving each connective until you arrive at the truth value of the main connective: A = true B = false C = true1. A → B 2. (A v ~B) & C 3. (~A & C) v (B → C)4. (B ↔ C) → ~C 5. ((A → B) → C) → B 6. ~ (A & C) & (~A → ~B)

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Abbreviated Truth Tables: 1. Do steps 1 and 2 from above.2. Fill in the specific truth values of the variables in the conclusion that would make the

conclusion false. There may be a few combinations that work (Ex. “&” statements can be false in at least 3 different ways, which means an “&” will require at least 3 rows).

3. Apply these values to the variables consistently across that row in the premises. In other words, if, in making your conclusion false, a certain sentence letter is false, that letter must be given the value of false wherever it appears on that line in the premises.

4. If it is possible to fill in the remaining variables in such a way that each premise comes out true, then the argument is invalid; if not, the argument is valid.

“T” Exercises: Use a full truth table to determine whether the following arguments are valid or invalid. Be sure to label your table to demonstrate where it establishes its validity or invalidity:

1.)1. B → S2. ~B=> ~S

2.) 1. D → S2. S=> D

3.) 1. ~ ~ F → ~ ~ G2. ~ G → ~ F=> G → F

4.) 1. N → (M v T)2. N3. ~ T=> M

5.) 1. R v ~R2. R → W3. W=> R

6.) 1. (D ↔ ~ G) & G2. (G v ((A → D) & A)) → ~ D=> G → ~ D

“U” Exercises: Determine whether the following, are valid or invalid by using abbreviated truth tables. Be sure to label and explain your results: 1.) 1. A → B2. ~ (B & C) → (A v D)=> (A & D) → ~ B

2.)1. (C & D) → E2. C ↔ E3. ~ C4. D=> (C ↔ D) & ~ D

3.)1. R → M2. (M & (B & R)) → H3. (R & G) → P4. R5. R & M=> H v P

4.) 1. A & (B → (A v B))2. C → B=> C

5.) 1. (A→B) & (B→C)2. (B v D) → (C→B)3. A & E=> B ↔ C

6.)1. (A & B) v (C & D)2. A → E3. D → E=> E

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V-W: Formal Logic: Deductions (Logical Proofs)

The Rules: The Five Elimination Rules: Taking Connectives ApartEach Rule Explained Each Rule in Action(&E)(1): If I know that Jeff is immature and short, then I can deduce that Jeff is immature [I can also deduce that he's short]If “A & B” is true...Then I know “A” is true, because an “&” is only true if both sides are true.

1. A & B [a previous line in my proof]2. A 1,&E [the justification for line 2: “A” is justified by the line that contains the original “&” sentence that I took apart, line 1 in this case, and the “&E” rule]

(VE)(5): I know that Jeff is either a nerd or a Trekky. If I assume he is a nerd, then I know he is pathetic. If I assume he is a Trekky, then I know he is pathetic. So, either way, Jeff is pathetic.If “A v B” is true...Then if I can show that some third claim is true from both sides of the “v” sentence, then that third claim is true, because if an “v” is true that means at least one side of it is true.

1. A v B [a previous line in my proof]2. A as.* [assume the left side of the “v”]3. C [derive “C” using previous lines]4. B as.* [assume the right side of the “v”]5. C [derive “C” again]6. C 1,2,3,4,5,vE* [justification for line 6: “C” is justified by the line that contains the original “v” sentence, the lines where I assumed each side of the “v”, the lines where I derived the third claim from each side, and the “vE” rule ...assumptions are now justified]

(→E)(2): If Jeff talks about rednecks, then he is a comic genius. Jeff does talk about rednecks. Therefore, Jeff is a comic genius.If “A→B” is true...Then if I can show that “A” is true, “B” has to be true, because if an “→” is true, if the left side is true, the right side has to be true.

1. A→B [a previous line in my proof]2. A [a previous line in my proof]3. B 1,2,→E [the justification for line 3: “B” is justified by the line that contains the original “→” sentence that I took apart, the line where I proved the left side is true, and the “→E” rule]

(~E)(1): I know that Jeff is not beardless. So Jeff has a beard (a glorious one, by the way).If “~ ~A” is true...Then I know “A” is true, because “~ ~A” has the same value as “A”.

1. ~ ~A [a previous line in my proof]2. A 1,~E [the justification for line 2: “A” is justified by the line that contains the original “~ ~” sentence that I took apart and the “~E” rule]

(↔ E)(1): You’re a redneck if and only if you’re a hick. Therefore, if you’re a redneck, you’re hick, and if you’re a hick, you’re a redneck.If “A↔B” is true...Then I know “(A→B)&(B→A)” is true because a “↔” means the same thing as two mirror-image conditionals.

1. A↔B [a previous line in my proof]2. (A→B)&(B→A) 1,↔E [the justification for line 2: “(A→B)&(B→A)” is justified by the line that contains the original “↔” sentence that I took apart and the “↔E” rule]

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V-W: Formal Logic: Deductions (Logical Proofs)

The Rules: The Five Introduction Rules: Creating New ConnectivesEach Rule Explained Each Rule in Action(&I)(2): If I know Jeff is hyperactive, and if I know Jeff has a fat head. Then, I can deduce that Jeff is a hyperactive fat-head.If “A” and “B” are true...Then I know “A&B” is true because an “&” is true if both sides are true.

1. A [a previous line in my proof]2. B [a previous line in my proof]3. A&B 1,2,&I [the justification for line 3: “A&B” is justified by the lines that contain the “A” and “B” that I am putting together and the “&I” rule]

(VI)(1): If I know that Jeff is a nerd, then I know that Jeff is a nerd or my baby-daddy.If “A” is true...Then I know that I can create a new “v” that will be true so long as “A” is on one side, because an “v” is true if one side is true.

1. A [a previous line in my proof]2. AvX 1,vI [the justification for line 2: “AvX” is justified by the line that contains the original “A” that became one side of the new “v” I created and the “vI” rule]

(→I)(2): Let’s assume that I make fun of Jeff's looks. That will lead to the class finding me hilarious. So, I know that if I make fun of Jeff's looks, then the class will find me hilarious.If I assume “A” is true...Then if I can derive “B” from that assumption, then I can create a new “→” because I have shown that “A” leads to “B”.

1. A as.* [assume the left of the new “→”]2. B [derive “B” using previous lines]3. A→B 1,2,→I* [the justification for line 3: “A→B” is justified by the line where I assumed the left side of the new “→” I'm creating, the line where I derived the right side of the new “→” I'm creating, and the “→I” rule ...and my assumption is now justified]

(~I)(2): Let’s assume that Jeff is handsome. That will lead to the impossible situation of Jeff being both attractive and ugly. Therefore, Jeff must not be handsome.If I assume “A”...Then if I can derive a contradiction from this assumption, then this means my assumption must be false, so “~A” must be true.

1. A as.* [assume the opposite of what I want]2. B&~B [derive a contradiction]3. ~A 1,2,~I* [the justification for line 3: “~A” is justified by the line where I assumed the opposite, the line where I derived a contradiction, and the “~I” rule … and my assumption is now justified]

(↔I)(1): If I'm a couch potato, then I'm lazy. And if I'm lazy, then I'm a couch potato. Therefore, I’m a couch potato if and only if I’m lazy.If “(A→B)&(B→A)” is true...Then I know “A↔B” is true because two mirror-image conditionals mean the same thing as a “↔”.

1.(A→B)&(B→A) [previous line in my proof]2. A↔B 1,↔I [the justification for line 2: “A↔B” is justified by the line that contained the two mirror-image conditionals and the “↔I” rule]

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“V” Exercises: (Jeff will announce)

1. Fill in the right-hand justifications for the following deductions:a) Goal: C v D b) Goal: (A → B) & (C → D)(1) A & B premise (1) A ↔ B premise(2) B → C premise (2) C → D premise(3) B __________ (3) (A → B) & (B → A) __________(4) C __________ (4) A → B __________(5) C v D __________ (5) (A → B) & (C → D) __________

c) Goal: D d) Goal: B ↔ C(1) A → B premise (1) (A → B) & (B → C) premise(2) B → (C ↔ D) premise (2) (B v D) → (C → B) premise(3) C & A premise (3) A & E premise(4) A __________ (4) B → C __________(5) B __________ (5) A → B __________(6) C ↔ D __________ (6) A __________(7) C __________ (7) B __________(8) (C → D) & (D → C) __________ (8) B v D __________(9) C → D __________ (9) C → B __________(10) D __________ (10) (B → C) & (C → B) __________

(11) B ↔ C __________

2. Complete the following deduction with full (right-hand) justifications:

e) Goal: C f) Goal: (A & B) v C(1) (A & B) → (C & D) premise (1) D & ~~A premise(2) B & E premise (2) D → (A → ~~B) premise(3) A & E premise (3) _______(4) __________ (4) _______(5) __________ (5) _______(6) __________ (6) _______(7) __________ (7) _______(8) __________ (8) _______

(9) _______(10) _______

“W” Exercises: Complete the following deductions with full (right-hand) justifications on page 25 below: 5, 6, 7, and 8.

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V-W: Formal Logic: Deductions (Logical Proofs): Examples:

1.) Goal: A 2.) Goal: D 3.) Goal: A & E1) A ↔ B 1) A → (B → (C → D)) 1) (~B & C) & D2) ~ ~B 2) A & C 2) ~B → E

3) ~ ~B 3) D → A

4.) Goal: A & B 5.) Goal: K 6.) Goal: P ↔ Q1) A ↔ B 1) (A v L) → (H & K) 1) ~S & (P → Q)2) ~ ~B & (~ C & ~ ~ A) 2) A & C 2) ~S → R

3) R → (Q & (Q → P))

7.) Goal: C & ~D 8.) Goal: ~A 9.) Goal: A → D1) B 1) A → B 1) A → (B & C)2) ~D 2) A → ~B 2) B → D3) (A v B) → ~~C

10.) Goal: D 11.) Goal: E 12.) Goal: ~A1) B & C 1) (A & B) v (C & D) 1) A → B2) B → ~A 2) A → E 2) (A & B) ↔ C3) (~A & C) ↔ D 3) D → E 3) ~C

13.) Goal: (A & B) → (A v B) 14.) Goal: A → ~D 15.) Goal: B ↔ C[no premises] 1) A → (B v C) 1) (A → B) & (B → C) 2) B → ~D 2) (B v D) → (C → B) 3) C → ~D 3) A & E

16.) Goal: A & (B v C) 17) Goal: A → ~B **18.) Goal: A ↔ B 1) (C ↔ D) → (D & ~~A) 1) A ↔ (C & D) 1) (A & B) v (~A & ~B)2) (C → E) & (D → C) 2) C → E [at least 28 lines!]3) (D → C) → (C → D) 3) B → ~E

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