Logic Final Exam
(O) particular negative Some
F are not G
The conclusion to be false.
For an argument to be valid, it is impossible for the premises to be true and...
Conjunction
For any two statements on accessible lines, you may derive a new line showing their conjunction. Φ Ψ ∴ Φ • Ψ
Disjunction Introduction
Given any accessible line, you may derive a new line showing a disjunction such that: one disjunct is the statement from the accessible line, and the other is any statement you like (atomic or complex). Φ ∴Φ v Ψ
Any kind of line
Disjunction introduction may be used on what kind of line in a proof?
(A) universal affirmative
All F are G
The truth-value of any compound sentence is strictly determined by the truth-values of its component sentence(s)
Each of the five connectives in our formal notation is truth-functional. This means:
Is the Conditional's consequent.
Any atomic statement following 'only if'...
Deductive Arguments
Arguments that we expect the premises to provide conclusive, watertight support.
Inductive Arguments
Arguments that we expect the premises to provide strong, but not conclusive, support.
categorical syllogisms
Arguments with two premises and a conclusion - three terms, each appearing in two statements.
Two Simpler Statements
Conjunction, Disjunction, Conditional, and Biconditional always build a compound statement from...
If the conditional antecedent is false on every row, then it doesn't matter what the truth value of the consequent is: either way, the conditional comes out true. So, the conditional will be true of every row, and hence a tautology.
As long as we know that the antecedent of a conditional is a contradiction, the conditional itself will always be a tautology. Why?
The conditional will always be a tautology.
As long as we know that the antecedent of a conditional is a contradiction...
True when component is False; False when component is True (It Flips the truth-value of whatever it negates).
How is the truth-value of a Negation determined?
32
How many rows does a truth table have when the number of atomic sentences is 5? (Not counting the header.)
Appeal to ignorance
Identify the Fallacy of the following statement: Nobody has ever disproved Bigfoot's existence, so he's got to be out there somewhere.
Appeal to ignorance
Identify the Fallacy of the following statement: Nobody has ever proved Bigfoot's existence, so surely he doesn't exist.
Ad hominem circumstantial
Identify the Fallacy of the following statement: Of course Congress voted to draft 18 year-olds into the military. All the Representatives who voted are well beyond draft age.
straw man fallacy
Identify the Fallacy of the following statement: Of course I'm not a feminist! You think I'd support a movement that wants to subjugate men?
Ad populum bandwagoning
Identify the Fallacy of the following statement: Of course criminal penalties should be harsher—in polls, 80 to 90 percent of respondents are in favor of longer sentences for felonies, and harsher punishments for misdemeanors
No fallacy
Identify the Fallacy of the following statement: Of course people think criminal penalties should be harsher—in polls, 80 to 90 percent of respondents are in favor of longer sentences for felonies, and harsher punishments for misdemeanors.
Ad hominem circumstantial
Identify the Fallacy of the following statement: Of course she supports the war—her brother's deployed in Afghanistan!
Ad Hominem Abusive
Identify the Fallacy of the following statement: You think I should quit smoking, huh? Well you're ugly!
Genetic Fallacy
Identify the Fallacy of the following statement: You're not going to wear a wedding ring, are you? Don't you know that the wedding ring originally symbolized chains that prevented women from leaving their husbands? I can't believe you'd take part in such a sexist practice.
(R =) I'll give you a ride. (G =) You pay for gas. G ⊃ R
Identify the atomic statements and Translate the following statement into formal notation: I'll give you a ride if you pay for gas.
(B =) Beyonce will be there. (C =) Coldplay will headline the show. (K =) Katy Perry will headline the show. ∼B ⊃ (C ∨ K)
Identify the atomic statements and Translate the following statement into formal notation: If it's not the case that Beyonce will be there, then either Coldplay or Katy Perry will headline the show
(H =) The good homes are sold. (N =) The neighborhood will suffer. (S =) The schools close. (D =) The neighborhood will be devastated. (H ⊃ N) • (S ⊃ D)
Identify the atomic statements and Translate the following statement into formal notation: If the good homes are sold then the neighborhood will suffer, but if the schools close the neighborhood will be devastated.
(F =) You can (could) feel this fabric. (B =) You'd buy it (the fabric) right away. F ⊃ B
Identify the atomic statements and Translate the following statement into formal notation: If you could feel this fabric, you'd buy it right away.
(D =) I have a degree (Q =) I am qualified ∼∼D • ∼Q (or (∼(∼D ∨ Q); or D • ∼Q)
Identify the atomic statements and Translate the following statement into formal notation: It is neither false that I have a degree nor true that I am qualified.
(L =) You attend all the lectures. (H =) You do all the homework. (A =) You get an A. (P =) You get an A+. ∼{(L • H) ⊃ (A ∨ P)}
Identify the atomic statements and Translate the following statement into formal notation: It's false that if you attend all the lectures and do all the homework, then either you'll get an A or an A+.
(M =) I saw that movie with you ∼M
Identify the atomic statements and Translate the following statement into formal notation: It's not true that I saw that movie with you.
(E =) Samuel exercises. (D =) Samuel diets. E • ∼D
Identify the atomic statements and Translate the following statement into formal notation: Samuel exercises but doesn't diet.
(S =) Stocks are tanking. (H =) Home prices are falling. S • H
Identify the atomic statements and Translate the following statement into formal notation: Stocks are tanking and home prices are falling.
(P =) You are Penske material.
Identify the atomic statements in the following statement: You're not Penske material.
(Y =) y is the additive inverse of x; (A =) Adding x and y gives a sum of 0
Identify the atomic statements in the following statement: y is the additive inverse of x if and only if adding x and y gives a sum of 0.
(O =) The store is open until midnight.
Identify the atomic statements in the following statement: The store is open until midnight.
"But"; Conjunction
Identify the main connectives in the following statement: A large planet is large, but a large molecule is still small.
"Unless"; Disjunction
Identify the main connectives in the following statement: Both Sue and Cathy will change the oil in their cars unless you tell them not to.
"If"; Conditional
Identify the main connectives in the following statement: If Steve and Hakim want to go climbing, then either we need to buy some new rope or rent gear
"If"; Conditional
Identify the main connectives in the following statement: If you want a car then get a job or build one yourself.
Then the conditional is a tautology.
If a conditional consequent is a tautology...
The argument is valid
If the conclusion made true by the diagram...
There is no fallacy
If the premise is relevant...
Disjunctions (one disjunct of which is a disjunction) and Conjunctions (one conjunct of which is a conjunction), and not for any other types of statement.
Association only works on...
Begging the question
Assuming the conclusion you are trying to prove. This is formally valid, but rhetorically bad.
Then their truth tables must be the same.
S1 implies S2 and S2 implies S1, If S1 and S2 imply each other...
Justification (Be sure to write the correct justification!)
Every line that's not given as a premise needs...
Conjunct
The name of each component of a Conjunction
there is no rule that permits this derivation
What is the correct justification for line 3? 1. (P • ~Q) ⊃ ~R 2. ~R 3. (P • ~Q) ???
Universal affirmative
Which type of categorical statement is this? "Every good detective carries a magnifying glass"
Particular negative
Which type of categorical statement is this? "Some chocolates aren't worth tasting"
Affirming the Consequent Denying the Antecedent
Bad argument whose badness can be explained formally: it's invalid.
3
categorical syllogism venn diagrams have how many circles?
conjunction fallacy
Bronwyn reasons that she's more likely to eat old pizza and get sick than she is to get sick. Bronwyn is committing:
existence in either region (but we don't know which)
(1) a bar (in a categorical syllogism venn diagram) indicates...
Indirect proof (in outline)
1. Assume some statement (anything you want!) 2. Derive an explicit contradiction (i.e. Φ • ~Φ) 3. "Close off" the assumption and all its derived lines 4. Immediately derive the negation of your assumption
Conditional proof (in outline)
1. Assume some statement (anything you want!) 2. Derive some statement (also anything you want) 3. "Close off" the assumption and all its derived lines 4. Immediately derive a conditional such that: 4a. the antecedent is your assumption 4b. the consequent is the last line of the subproof
equivalence
A relation between two or more statements whose truth-columns match
Contingency
A statement whose truth-column has some T and F
When they negate the same statement
Double negation allows you to add or remove two tildes, but only...
Affirming the Consequent Denying the Antecedent
Identify the Fallacy of the following statement: 1. P ⊃ Q 2. ~P ∴~Q
Affirming the Consequent Denying the Antecedent
Identify the Fallacy of the following statement: All midwesterners are nice. But you're not a midwesterner, so you're not nice.
Affirming the Consequent Denying the Antecedent
Identify the Fallacy of the following statement: All the best athletes drink gatorade, and I drink gatorade, so I'm a great athlete.
Affirming the Consequent Denying the Antecedent
Identify the Fallacy of the following statement: All the really successful presentations have flashy slideshows, so I know mine's going to be great--I've got a slideshow, too.
Then each must be a tautology or a contingency.
If two statements are consistent...
appeal to pity
Is a fallacy committed here, and if so which one? Your honor, yes, I admit I was doing 100 in a 35mph zone. But if you find me guilty, my insurance rates will skyrocket, and I won't be able to pay for my daughter's education. Surely you can find me not guilty.
No fallacy
Is a fallacy committed here, and if so, which one? Mike is completely off base when he says that people don't like Obama. A recent opinion poll showed that 75% of people do like him.
Straw man fallacy
Is a fallacy committed here, and if so, which one? The student government wants to build a new recreation center near the bookstore. Why do the students only want to play and never study? They're here to learn, not play video games. Turning the university into an arcade is clearly a bad idea—we need to oppose the student government on this.
ad hominem tu quoque
Is a fallacy committed here, and if so, which one? Yeah, I'm aware of all those climate change arguments you're getting from your hero Al Gore. Do you have any idea how much energy Gore's gargantuan household consumes? And you still take what he says seriously?
Fallacies of weakness
Problems with inductive arguments, where the premises are relevant but don't provide enough support.
Disjunct
The name of each component of a Disjunction
Particular Negative
Think: "There is some S that are not P"
You Too
Tu Quoque = ???
There is at least one row where all the sentences are true
Two or more sentences are consistent when:
Conditional
Usually expressed in English by 'if ... then', or 'only if'.
Negation
Usually expressed in English by 'not' or the '-n't' suffix, but also 'it is not the case that'.
Disjunction
Usually expressed in English by 'or', 'either ... or', or 'unless'.
categories (expressed in English by plural nouns)
Variables must stand for...
False cause fallacy
What is the following an example of? Homer: Not a bear in sight. The Bear Patrol must be working like a charm. Lisa: That's specious reasoning, Dad. Homer: Thank you, dear. Lisa: By your logic I could claim that this rock keeps tigers away. Homer: Oh, how does it work? Lisa: It doesn't work. Homer: Uh-huh. Lisa: It's just a stupid rock. Homer: Uh-huh. Lisa: But I don't see any tigers around, do you? Homer: Lisa, I want to buy your rock.
Premises
What is the name for the statement(s) that do the supporting of an argument?
Line 3 should show 'B' instead of '~B'
What is wrong with this application of DS? 1. B v ~(A ⊃ B) 2. A ⊃ B 3. ~B 1, 2 DS
MP derives a conditional's consequent from the conditional and its antecedent; in this example the antecedent has been derived from the conditional and its consequent.
What is wrong with this application of Modus Ponens? 1. (P v Q) ⊃ Q 2. Q 3. P v Q 1, 2 MP
MP requires two lines to be applied
What is wrong with this application of Modus Ponens? 1. A ⊃ ~B 2. ~B 1, MP
Particular negative
What type of categorical statement is the following? "Some dogs aren't very smart"
when there is at least one row on which both statements are T.
When are two (or more) statements Consistent?
When their truth columns match (T for T, F for F).
When are two (or more) statements Equivalent?
Whenever you like
When are you permitted to close a conditional proof?
When you have derived an explicit contradiction
When are you permitted to close an indirect proof?
A row on which all premises are true but the conclusion is false
When assessing an argument's validity with a truth table, a counterexample row is:
Because they replace one statement with an equivalent statement
Why do replacement rules work in both directions?
Ad hominem association
Identify the Fallacy of the following: Political Attack Ads
(R =) I['ll] give you a ride. (G =) You pay for gas. R ∨ ∼G
Identify the atomic statements and Translate the following statement into formal notation: I'll give you a ride unless you don't pay for gas.
(S =) I'm going to starve to death. (M =) You give me the money you owe me. (H =) The hot dog stand is still open. S ∨ (M • H)
Identify the atomic statements and Translate the following statement into formal notation: I'm going to starve to death unless you give me the money you owe me and the hot dog stand is still open.
Convert it to a noun phrase. (Often 'things' helps, e.g. things that run late, poisonous things)
If an English sentence has a verb phrase (runs late) or an adjectival phrase (poisonous)...
Then the conjunction is a contradiction.
If one conjunct of a conjunction is a contradiction...
Whenever the first is true, so is the second
If one statement implies another, then:
Whenever the first is true, so is the second.
If one statement implies another, then:
The conditional's consequent on a new line.
Modus Ponens produces:
A conditional on one accessible line and its antecedent on another accessible line.
Modus Ponens requires:
The conditional's negated antecedent on a new line.
Modus Tollens produces:
A conditional on one accessible line and its negated consequent on another accessible line.
Modus Tollens requires:
One Simpler Statement
Negation builds a compound statement from...
Biconditional
Not common in conversational English, but expressed by 'if and only if' or 'just in case'.
Bias Blind Spot
People tend to think they are less biased than others! (You are biased; I am thinking clearly and rationally.)
(I) particular affirmative
Some F are G
Slippery slope argument
Someone claims that if P occurs, then a cascade of consequences will follow: P leads to Q, Q leads to R, etc., and the last one is a very bad consequence. Therefore we should prevent or avoid P. This is formally valid, but is fallacious when one or more of the links are dubious.
It wouldn't matter what the second disjunct is, the entire disjunction would be true.
Suppose you have a disjunction, one disjunct of which is a tautology. What, if anything, do you know about the disjunction?
S1 implies S2 if and only if: Wherever S1 is True, S2 is also True; There is no row where S1 is True and S2 is False; or The conditional S1 ⊃ S2 is a Tautology.
Suppose you have two sentences, S1 and S2. You know that S1 implies S2. On the basis of that information, do you also know whether S2 implies S1?
Main Connectives
The connective responsible for putting together the whole expression.
Antecedent
The left component of a Conditional
Consequent
The right component of a Conditional
False Dichotomy
This is another formally valid inference, but the issue is the truth of the disjunction
Association
This rule allows us to change the grouping of a disjunction, one disjunct of which is a disjunction; and likewise for conjunctions. (Φ v Ψ) v Χ :: Φ v (Ψ v Χ) Or (Φ • Ψ) • Χ :: Φ • (Ψ • Χ)
Cognitive Reflection Test
This test pits a fast, automatic cognitive system ("System 1") against a slow, effortful cognitive system ("System 2").
Conjunction
Usually expressed in English by 'and', 'but', or 'both ... and'.
Roman Capital Letters
What always indicate atomic statements?
P, Q, R, Q ⊃ R, ~(Q ⊃ R), P v ~(Q ⊃ R), and ~(P v ~(Q ⊃ R))
What are all the statements used to construct this compound statement? ~(P v ~(Q ⊃ R)) (Draw a tree diagram if you're having difficulty!)
The argument's pattern or structure, independent of what the argument happens to be about
What is the logical form of an argument?
The main connective of this compound statement is V, because V is connecting (P•Q) and (R ⊃ Q) v P
What is the main connective of (P•Q) v {(R ⊃ Q) v P} and why?
When the statement is atomic, and when a connective working on one or two atomic sentences.
When DON'T we need parentheses?
Sound
When an argument is not just valid, but also has true premises
use the conclusion as a line in your proof. (You must rely on assumptions + things that follow from your assumptions.)
When proving a tautology, you may not...
Universal affirmative
Which type of categorical sentence is this? "Only statues are made of marble"
Because replacement rules express equivalence, whereas inference rules express implication.
Why can replacement rules apply to parts of lines, but inference rules must apply to whole lines only?
Because if a conjunction is true, then both of its conjuncts are true
Why is the rule of Conjunction truth-preserving?
No
Yes or No? Is this a correct application of DN? 1. ~(~A • ~B) 2. A • ~B 1, DN
Ad Hominem Association
You associate the speaker with an unpopular group, belief, etc. and use that against their claims.
Ad Hominem tu Quoque
You counter an individual's claims due to their hypocrisy.
Atomic Statement (Sentence)
a type of declarative sentence which is either true or false, and cannot be broken down into other simpler sentences.
categorical logic
a.k.a. "traditional logic," "syllogistic logic," "term logic," "Aristotelian logic"
straw man fallacy
involves appearing to argue against one claim, but really arguing against a different, weaker claim.
genetic fallacy
involves treating the (perhaps questionable) origin of some claim as reason to reject the claim.
Appeal to pity
involves trying to convince someone by appealing to their sense of pity, instead of on the merits of the claim.
Conjunction
• (dot)
Disjunction
∨ (vee/wedge)
Biconditional
≡ (triple bar)
Conditional
⊃ (hook/horseshoe)
The Conditional's antecedent.
(Usually) The Atomic Statement that follows 'if' is...
The Conditional's consequent.
(Usually) The atomic statement that follows 'then'...
A conditional such that the antecedent is what you assumed to begin the Conditional Proof, and the consequent is the last line of the Conditional Proof.
A conditional proof may close on any line you like, but the next line must be...
The truth-values of the components (inputs) strictly determine the truth-value of the whole (output).
A connective is truth-functional if and only if...
Informal Fallacy
A mistake in reasoning that's not due to formal features of the argument, but instead is due to what the particular statements mean.
counterexample row
A row which shows that an argument is invalid, or that an implication fails to hold
On any row where each member of the set is true, the statement is also true, or Valid arguments can have false premises.
A set of statements jointly implies a single statement if and only if:
Contradiction
A statement whose truth-column is all F
Tautology
A statement whose truth-column is all T
Can't possibly have true premises and a false conclusion; Must have a true conclusion, if the premises are true.
A valid argument is one which:
Can't possibly have true premises and a false conclusion; and It must have a true conclusion, if the premises are true.
A valid argument is one which:
Generally, facts about a person are irrelevant to the truth of their claims
Ad hominem fallacies are considered fallacies of relevance because:
to the people
Ad populam = ???
The premises jointly imply the conclusion. (If its premises are true its conclusion must be true; It is impossible for the premises to be true and the conclusion to be false.)
An argument is valid if and only if:
Appeal to ignorance
An attempt to show that P from the premise that we don't know that ~P.
Framing Effect
An example of cognitive bias, in which people react to a particular choice in different ways depending on how it is presented (such as a loss or as a gain).
The negation of the assumption that began the Indirect Proof.
An indirect proof may close on an explicit contradiction only, and the next line must be...
valid
Diagram the following argument and determine whether it's valid: "Some ostriches are not fast. All ostriches are beautiful. So, some beautiful things are not fast."
The other disjunct (unchanged!) on a new line.
Disjunctive Syllogism produces:
A disjunction on one accessible line and the negation of one disjunct on another accessible line
Disjunctive Syllogism requires:
Composition/Division
Fallacies in which one mistakenly infers that a whole has a property that its parts have, or that the parts have a property that the whole has.
The premise is irrelevant to the conclusion.
Fallacies of relevance are fallacious because...
Whether the premise(s) give enough support for the conclusion, or whether they're true in the first place.
Fallacies of weakness depend on...
Its conclusion must be true.
For an argument to be valid, if its premises are true, then...
It is determined by the placement of the commas within the (written) statement.
How do we determine where to place the parentheses in a (symbolic) statement?
2 ^ the number of atomic statements
How do you figure out how many columns (not including the heading) to put into a Truth table?
Use a bar for the particular premise or Diagram the universal premise first
How do you map out a particular affirmative statement if the x could be in either of two places?
True when both sides are True or both sides are False; False otherwise (it demands that both components match in truth-value).
How is the truth-value of a Biconditional determined?
False when antecedent is true and consequent is false, True otherwise.
How is the truth-value of a Conditional determined?
True when both conjuncts are true, and False otherwise (it demands truth from both of its components).
How is the truth-value of a Conjunction determined?
False when both disjuncts are false, and True otherwise. (it permits everything but double-falsehood).
How is the truth-value of a Disjunction determined?
No Fallacy, because the sample in this case is reasonably representative of the population.
Identify the Fallacy of the following statement and why: The spaghetti is done cooking—I know since I chewed on a noodle and it was just right.
composition/division
Identify the Fallacy of the following statement: Berkeley: Sure, blood looks red to the naked eye, but when you see the parts under a microscope, they look yellow. But blood can't be both red and yellow, so it must not be colored.
No fallacy
Identify the Fallacy of the following statement: Captain Beefheart fans are an exclusive club—only 10,000 people worldwide own Trout Mask Replica.
Ad hominem circumstantial
Identify the Fallacy of the following statement: Carter claims that clean coal will solve our emissions problems, but all those studies he did were funded by the coal industry.
Ad Hominem Association (or Ad Hominem Abusive)
Identify the Fallacy of the following statement: Come on, only fringe right-wing lunatics believe we're going to ration health care!
False cause fallacy
Identify the Fallacy of the following statement: Everyone knows that facial expressions are a barometer of the emotions, and recently researchers at Wayne State linked happiness to longevity. I'm trying to smile more sincerely these days, because I want to do everything I can to promote my longevity.
Ad populum bandwagoning
Identify the Fallacy of the following statement: How can you say that Coldplay isn't a talented band when they've sold more than 50 million records?
Composition/Division
Identify the Fallacy of the following statement: I don't care what you say, I'm gonna eat it. I mean, the ingredients are harmless, so how bad can the whole thing be?
Hasty Generalization
Identify the Fallacy of the following statement: I don't think anyone will vote for Johnson—I asked all my friends, and none of them are going to.
composition/division
Identify the Fallacy of the following statement: I know the Sheldon gang is going to come after me this afternoon, but I've beat up each of them before, so I'm not worried.
Appeal to pity
Identify the Fallacy of the following statement: I know the Toros weren't the best, but they tried so hard---shouldn't they win the contest?
Hasty Generalization
Identify the Fallacy of the following statement: I saw a crow burying food outside my window this morning. I guess crows bury their food
Composition/Division
Identify the Fallacy of the following statement: I should be able to read this book in a sitting--after all, I can read each page in a sitting.
straw man fallacy
Identify the Fallacy of the following statement: I'll never vote Republican—are you kidding me? There's no way I'd ever support foreign occupation, domestic surveillance, or corporate rule!
No fallacy
Identify the Fallacy of the following statement: I'm feeling super down; one of my cats died yesterday and then this morning I got a flat tire.
Appeal to pity
Identify the Fallacy of the following statement: I'm sorry, officer, but I just had a bad breakup and I'm still upset and I just couldn't handle getting a ticket!
Affirming the Consequent Denying the Antecedent
Identify the Fallacy of the following statement: If it's Wednesday, then we've got class. We've got class today, so it's Wednesday.
Affirming the Consequent Denying the Antecedent
Identify the Fallacy of the following statement: If my cats are hungry, then they'll whine at me. My cats aren't hungry, so they won't whine at me.
Slippery slope argument
Identify the Fallacy of the following statement: If we allow physician-assisted suicide to become legal, then soon we'll be killing off anyone who's inconvenient, and then the non productive members of society, until we're a full-blown fascist state! So we need to keep euthanasia illegal.
No fallacy
Identify the Fallacy of the following statement: In his capacity as legal advisor, Garrett claims to be free of any conflicts of interest, but he's on the payroll of his advisees' competitors!
straw man fallacy
Identify the Fallacy of the following statement: Isn't it just obvious that Darwin was wrong? I don't know about you, but no one in my family is a monkey.
Composition/Division
Identify the Fallacy of the following statement: It can't be that hard to make mole; every step is pretty simple.
Begging the question
Identify the Fallacy of the following statement: Killing a human being is murder, and abortion kills human beings. So abortion is murder.
False Dichotomy
Identify the Fallacy of the following statement: Look, either I keep smoking or I gain weight. I don't want to gain weight, so I need to keep smoking.
False Dichotomy
Identify the Fallacy of the following statement: Look, we can either give the communists free run of our government, or we can criminalize communist speech. You don't want the commies running our country, do you?
ad hominem circumstantial
Identify the Fallacy of the following statement: Michael Crichton says secondhand smoke is harmless, but he only thinks that because he smokes .
ad hominem tu quoque
Identify the Fallacy of the following statement: My dad's always telling me not to text while driving, but I know he sends me texts when he's behind the wheel all the time!
Ad hominem circumstantial
Identify the Fallacy of the following statement: Of course you oppose student input on hiring decisions, Dean Barrett—you'd oppose any changes that dilute your power.
Ad populum bandwagoning
Identify the Fallacy of the following statement: Oh, I don't drink Budweiser—those big corporate breweries that everyone loves don't know what they're doing.
Appeal to pity
Identify the Fallacy of the following statement: Ok so I didn't technically get enough points, but I need to pass this class to graduate!
straw man fallacy
Identify the Fallacy of the following statement: People say global warming is happening, but during the last three winters our state reached record low temperatures and had record high snowfalls. Obviously the planet is getting colder, not warmer—we'll be just fine.
Begging the question
Identify the Fallacy of the following statement: People should have free choice to do what they want. Abortion is a choice, so people should be free to choose it.
Ad hominem association
Identify the Fallacy of the following statement: Pollitt thinks we need another economic stimulus, but what do you expect from someone who writes for The Nation?
Ad Hominem tu Quoque
Identify the Fallacy of the following statement: President Bush was compared to Hitler at protests in Pelosi's own San Francisco district. But when Mr. Obama is compared to similar imagery, Ms. Pelosi becomes offended all of a sudden? How about cleaning up your own backyard first, Madam Speaker?
composition/division
Identify the Fallacy of the following statement: Proposition 13 will reduce Michigan's budget by 30% —could your household withstand that kind of belt tightening?
genetic fallacy
Identify the Fallacy of the following statement: There's no such thing as god—religions are just cultural systems that evolved to keep human groups cohesive.
Appeal to authority
Identify the Fallacy of the following statement: There's no way I'm buying another Windows machine after Jon Hodgman explained how bad they are.
False Dichotomy
Identify the Fallacy of the following statement: Unless we raise taxes, we can't afford social programs. But we need those social programs, so we have to raise taxes.
No fallacy (although not decisive against Venkman)
Identify the Fallacy of the following statement: Venkman says he should be the next Dean of Students—but he didn't even go to college!
Ad hominem abusive (or Ad Hominem association)
Identify the Fallacy of the following statement: Venkman says the best policy for Detroit is extending and improving public transit—but he didn't even go to college!
begging the question
Identify the Fallacy of the following statement: Violence is never permissible, and war is violent, so waging war is never permissible.
Appeal to authority
Identify the Fallacy of the following statement: Why waste time studying philosophy? Stephen Hawking says it's dead!
ad hominem tu quoque
Identify the Fallacy of the following statement: You Europeans criticize us for racism. But it's not like your countries don't have race problems!
Ad Hominem Abusive
Identify the Fallacy of the following statement: You can disregard Ferguson's view on the health plan—what can someone who didn't even go to college know about health policy?
straw man fallacy
Identify the Fallacy of the following statement: You say that students' evaluations of their professors should be included in promotion decisions; but I certainly don't think promotion decisions should be made by students!
Affirming the Consequent Denying the Antecedent
Identify the Fallacy of the following: Allison: If Tim finished his last paper, then he went to the movies. Eric: Oh, Evan saw him at the movies with Joy, so he must have finished his paper.
Ad Hominem tu Quoque
Identify the Fallacy of the following: Dale: it's wrong to buy luxuries—we should use extra money to help people in need. Me: but you just bought a new car!
(D =) I'm dreaming. (N =) These are the right numbers. D ∨ R
Identify the atomic statements and Translate the following statement into formal notation: Either I'm dreaming or these are the right numbers.
(M =) Mark will be quarterback. (J =) Javier will be receiver. (C =) The coach is crazy. ∼C ⊃ (M ∨ J)
Identify the atomic statements and Translate the following statement into formal notation: Either Mark will be quarterback or Javier will be receiver, if the coach isn't crazy.
(B =) Biology satisfies the requirement. (M =) You are a major. (C =) Chemistry satisfies the requirement. (M =) You took the math class before the new requirements took effect. (W =) You have to worry about it. {(M ⊃ B) • (∼M ⊃ C)} ∨ (M ⊃ ∼W)
Identify the atomic statements and Translate the following statement into formal notation: Either both biology satisfies the requirement if you are a major and chemistry satisfies the requirement if you are not, or if you took the math class before the new requirements took effect then you don't have to worry about it.
(G =) You need to graduate. (M =) You need to maintain a certain GPA for any administrative reason. (W =) You make sure you stay on top of the work. (E =) You make sure you can do well on the exams. (R =) You risk a bad situation. (G ∨ M) ⊃ {(W • E) ∨ R}
Identify the atomic statements and Translate the following statement into formal notation: If either you need to graduate or you need to maintain a certain GPA for any administrative reason, then either you make sure you stay on top of the work and can do well on the exams or you risk a bad situation.
(S =) It's strange to be calling yourself. (M =) Maybe I'm here. S • ∼M
Identify the atomic statements and Translate the following statement into formal notation: It's strange to be calling yourself, but maybe I'm not there.
(E =) Samuel exercises. (Y =) Samuel does yoga. (D =) Samuel diets. (S =) Samuel smokes like a chimney. (E • Y ) • (∼D • S)
Identify the atomic statements and Translate the following statement into formal notation: Samuel exercises and does yoga, but he doesn't diet and he smokes like a chimney.
(S =) Stocks are tanking. (H =) Home prices will [would] fall. (I =) Inflation is (was) lower. S • (I ⊃ ∼H)
Identify the atomic statements and Translate the following statement into formal notation: Stocks are tanking, but home prices wouldn't fall if inflation was lower.
(H =) That sandwich has horseradish. (T =) That sandwich has tomatoes. H • T
Identify the atomic statements and Translate the following statement into formal notation: That sandwich has horseradish and tomatoes.
(H =) That sandwich has horseradish. (W =) That sandwich has wasabi. ∼H • ∼W or ∼(H ∨ W)
Identify the atomic statements and Translate the following statement into formal notation: That sandwich has neither horseradish nor wasabi.
(P =) The patient will survive. (T =) She (the patient) gets a transfusion. (C =) Her (the patient's) condition is as bad as it looks. P ≡ (T ∨ ∼C)
Identify the atomic statements and Translate the following statement into formal notation: The patient will survive if and only if either she gets a transfusion or her condition isn't as bad as it looks.
(O =) They do it over there. (H =) They do it here. O • ∼H
Identify the atomic statements and Translate the following statement into formal notation: They do it over there, but they don't do it here.
(L =) You('ll) get your license. (W =) You pass the written test. (D =) You pass the driving test. L ≡ (W • D)
Identify the atomic statements and Translate the following statement into formal notation: You'll get your license if and only if you pass both the written test and driving test.
(L =) You['ll] get your license. (P =) You pass the written test. L ⊃ P
Identify the atomic statements and Translate the following statement into formal notation: You'll get your license only if you pass the written test.
(W =) Whitney can be in the experiment. (D =) Derrick can be in the experiment. (C =) Coffee has caffeine. (H =) Chocolate has caffeine. (C • H) ⊃ (∼W • ∼D) (or C • H) ⊃ ∼(W ∨ D))
Identify the atomic statements and Translate the following statement into formal notation: Neither Whitney nor Derrick can be in the experiment if both coffee and chocolate have caffeine.
(G =) I'll have another glass of water; (J =) it's (water is) nature's fruit juice.
Identify the atomic statements in the following statement: I'll have another glass of water; it's nature's fruit juice.
(F =) Food was at the party; (I =) I'd be fine; (S =) I'm starving.
Identify the atomic statements in the following statement: If food had been at the party, I'd be fine, but there wasn't and I'm starving.
(S =) There is enough sugar in the bag; (H =) Honey can be used as a substitute.
Identify the atomic statements in the following statement: If there isn't enough sugar in the bag, honey can be used as a substitute.
(S =) Mike is asleep; (A =) Mike is awake.
Identify the atomic statements in the following statement: Mike is either asleep or awake.
(K =) Kevin likes beer; (M =) Matt likes beer.
Identify the atomic statements in the following statement: Neither Kevin nor Matt likes beer.
(P =) Paris likes foreign accents.
Identify the atomic statements in the following statement: Paris likes foreign accents.
(C =) You're saying there's a chance.
Identify the atomic statements in the following statement: So you're saying there's a chance.
(C =) The cat is on the mat.
Identify the atomic statements in the following statement: The cat isn't on the mat.
(O =) The store is open until midnight; (C =) The store is closed on Mondays.
Identify the atomic statements in the following statement: The store is open until midnight, but is closed on Mondays.
(T =) You should try the pizza.
Identify the atomic statements in the following statement: You should try the pizza.
(T =) You should try the pizza.
Identify the atomic statements in the following statement: You shouldn't try the pizza.
"It's not..."; Negation
Identify the main connectives in the following statement: It's not true that if you attend all the lectures you are guaranteed to pass the class.
Invalid; rows 1, 3, and 5 are counterexample rows
Is the following argument valid? Use a truth table to find out and then explain why or why not: 1. ~Q ⊃ P 2. (P • ~R) v R ∴ ~R
Tautology
Is the following statement a contingency, tautology, or contradiction? Q ⊃ (P ⊃ Q)
Contradiction
Is the following statement a tautology, contingency, or contradiction? Use a truth table to find out: ~{P ⊃ (Q ⊃ P)}
availability heuristic
Judging how likely something is by how many instances you can easily call to mind
(E) universal negative
No F are G
inaccessible
Once a subproof is closed, its lines become...
Fallacies of Relevance vs. Weakness
Premises can be irrelevant to establishing conclusion, or they can be relevant but don't provide enough evidence or support.
Entire lines only!
Remember that inference rules (as opposed to replacement rules) may be applied to...
S2 is equivalent to S1, S1 implies S2, and S2 implies S1
Suppose a statement (call it S1) is equivalent to some other statement (call it S2). On the basis of that information, what else do you know about these statements?
The other component is a contingency - it matches
Suppose you have a biconditional which you know is a tautology, and one component is a contingency, What, if anything, do you know about the other component?
There is not enough information to determine whether it is a contingency, tautology, or contradiction.
Suppose you have a conditional, and you know that its antecedent is a tautology. What do you know about the conditional?
It is a tautology
Suppose you have a disjunction, and one disjunct is a tautology. On the basis of this information, what do you know about the disjunction?
Daniel Kahneman & Amos Tversky
These two did groundbreaking work in 1960s and 70s showing that people rely on "heuristics and biases"—mental shortcuts—in reasoning, especially under conditions of uncertainty or incomplete information
Replacement Rules
They may be used in both directions, They express equivalence, They are truth-preserving, and They are falsity-preserving.
Universal Negative
Think: Shading = "There is no S that is P" or "There is no P that is S"
Universal Affirmative
Think: Shading = "There is no S that is not P"
Particular Affirmative
Think: x = "There is some S that are P"
Distribution
This rule allows us to distribute disjunction across a conjunction, and conjunction across a disjunction (and vice versa). Φ v (Ψ • Χ) :: (Φ v Ψ) • (Φ v Χ) Or Φ • (Ψ v Χ) :: (Φ • Ψ) v (Φ • Χ)
DeMorgan's
This rule allows us to exchange a negated disjunction for a conjunction of its negated disjuncts, and a negated conjunction for a disjunction of its negated conjuncts. ~(Φ v Ψ) :: ~Φ • ~Ψ Or ~(Φ • Ψ) :: ~Φ v ~Ψ
Biconditional Exchange
This rule allows us to replace a biconditional with the conjunction of two conditionals, which have complementary antecedent and consequent. We can also do the reverse. (Φ ≡ Ψ) :: (Φ ⊃ Ψ) • (Ψ ⊃ Φ)
Exportation
This rule allows us to replace a conditional, whose antecedent is a conjunction, with a conditional whose antecedent is the former first conjunct, and whose consequent is also a conditional whose antecedent is the former second conjunct and whose consequent is the original consequent. We can also do the reverse. {(Φ • Ψ) ⊃Χ} :: {Φ ⊃ (Ψ ⊃ Χ)} Or {Φ ⊃ (Ψ ⊃ Χ)} :: {(Φ • Ψ) ⊃Χ}
Double Negation
This rule allows us to replace a statement with its double negation, or to take a double-negated statement and remove two tildes. ~Φ ∷ ~~Φ
Duplication
This rule allows us to replace any statement with: a disjunction with itself, or a conjunction with itself. We can also do the reverse. Φ :: Φ v Φ Or Φ :: Φ • Φ
Contraposition
This rule allows us to swap a conditional's antecedent and consequent, provided we negate them both. (Φ ⊃ Ψ) :: (~Ψ ⊃ ~Φ)
Commutation
This rule allows us to swap the order of conjuncts in a conjunction of disjuncts in a disjunction. (Φ v Ψ) :: (Ψ v Φ) Or (Φ • Ψ) :: (Ψ • Φ)
Conditional Exchange
This tells us that we can derive a disjunction from a conditional, where the first disjunct is the negation of the conditional's antecedent. We can also derive a conditional from a disjunction by negating the first disjunct. (Φ ⊃ Ψ) :: (~Φ v Ψ) Or (Φ v Ψ) :: (~Φ ⊃ Ψ)
(Logical) Connectors
Transitional Phrases that are used to connect two or more statements to indicate their particular relationship.
True
True or False? The following is a correct application of disjunction introduction: 1.) P ⊃ Q 2.) R v (P ⊃ Q) 1, DI
False
True or False? The following is a correct application of disjunctive syllogism: 1.) ~F v K 2.) ~K 3.) F 1, 2 DS
False
True or False? The rule of simplification may be used on the following line: (A • B) ⊃ B
True
True or false: the lines of a subproof are available to use until the subproof is closed, when they become unavailable.
True
True or false? The following is a compound sentence: "It's not raining today"
Confirmation Bias
We are biased toward confirming (rather than falsifying) our existing beliefs
Availability Heuristic
We estimate how likely or frequent something is by how easily it comes to mind (how "available" it is to us)
Conjunction Fallacy/Effect
We sometimes judge the conjunction of two things to be more likely than either alone
"white rabbits" and "things that run late"
What are the categories in this categorical sentence? "A white rabbit always runs late"
"good books" and "things you just recommend to someone"
What are the categories in this statement? "A good book isn't something you just recommend to someone"
"icebergs" and "things that sank the Titanic"
What are the categories in this statement? "An iceberg sank the Titanic"
Any kind of statement (atomic or compound)
What do kind of statements do Greek Capital Letters indicate?
The snow melts and nobody intervenes
What is the antecedent of this conditional? "If the snow melts and nobody intervenes, then we'll have good drinking water this summer"
The tomatoes will get tall
What is the antecedent of this conditional? "Only if the sun comes out will the tomatoes get tall"
~C ⊃ (M v J)
What is the best translation of the following sentence? "Either Mark will be Quarterback or Javier will be Reciever, if the coach isn't crazy." Use the following translation key: M = Mark will be Quarterback J = Javier will be Reciever C = The coach isn't crazy
S v L
What is the best translation of the following sentence? "Either this soup needs more salt, or it needs a splash of lemon juice" Use the following translation key: S = This soup needs more salt L = It needs a splash of lemon juice
~(T v H)
What is the best translation of the following sentence? "I had neither Tacos nor Hotdogs for breakfast." Use the following translation key: T = I had Tacos for Breakfast H = I had Hotdogs for Breakfast
(S v C) ⊃ H
What is the best translation of the following sentence? "If tomatoes are in season or we can get them canned, then we can make huevos rancheros." S = Tomatoes are in season C = We can get them canned H = We can make huevos rancheros
A ⊃ T
What is the best translation of the following sentence? "It is necessary for you to legally consume alcohol that you are at least 21 years old." A = You legally consume alcohol T = You are at least 21 years old
(W • R) ⊃ D
What is the best translation of the following sentence? "To get a driver's license it is sufficient that you both pass the written test and the road test." D = you get a driver's license W = you pass the written test R = you pass the road test
1. B v (~B ⊃ F) 2. ~B 3. ∴ F
What is the best translation of the following: 1. Either cats eat birds or if they don't eat birds then they eat fish. 2. Cats don't eat birds. 3. So cats eat fish. Use the following translation key: B = Cats eat birds F = Cats eat fish
~(B ⊃ M)
What is the best translation of the following? "It's not the case that only if music has the right to children will I find a beautiful place out in the country." M = Music has the right to children B = I will find a beautiful place out in the country
(C • Y) ⊃ S
What is the best translation of the following? "It is sufficient for drawing a sun that you draw a circle and color it yellow." S = you draw a sun C = you draw a circle Y = you color it yellow
A person making a claim is a source of the claim, so ad hominem fallacies are one kind of genetic fallacy. For our purposes, if an example fits one of our ad hominem types (abusive, association, circumstantial, tu quoque), we'll call it ad hominem. If it fits the genetic fallacy but not any of the ad hominem types, we'll call it genetic.
What is the difference between genetic and ad hominem fallacies?
A row on which all premises are true but the conclusion is false.
When assessing an argument's validity with a truth table, a counterexample row is:
When its antecedent is false or its consequent is true
When is a conditional statement true?
When (and only when) both conjuncts are true.
When is a conjunction true?
Any statement you like
When making an assumption for indirect proof, what are you allowed to assume?
False cause fallacy
When the arguer claims that one thing causes another, but the two things are merely correlated.
Appeal to authority
When the person in being appealed to isn't an authority on the subject.
A conditional, such that the antecedent is the assumption that began the subproof and the consequent is the last line of the subproof.
When you close a conditional proof, what must you write on the next line of the proof?
The negation of whatever statement was assumed at the beginning of the indirect proof
When you close off an indirect proof, what must you write on the next line of the proof?
Modus Ponens
When you have a conditional on an accessible line, and its antecedent on another accessible line, then you may derive a new line showing the consequent. Φ ⊃ Ψ Φ ∴ Ψ
Modus Tollens
When you have a conditional on an accessible line, and the negation of its consequent on another accessible line, then you may derive a new line showing the negation of the antecedent. Φ ⊃ Ψ ~Ψ ∴ ~Φ
Simplification
When you have a conjunction on an accessible line, you may derive a new line showing either conjunct on its own. Φ • Ψ ∴Φ ∴ Ψ
Disjunctive Syllogism
When you have a disjunction on an accessible line, and the negation of one of its disjuncts on another, then you may derive a new line showing the other disjunct. Φ v Ψ ~Φ ∴Ψ Or Φ v Ψ ~Ψ ∴Φ
Dilemma
When you have two accessible lines showing conditionals and a third line showing the disjunction of their antecedents, then you may derive a new line showing the disjunction of their consequences. Φ ⊃ Ψ Χ ⊃ Γ Φ v Χ ∴ Ψ v Γ
Hypothetical Syllogism
When you have two accessible lines showing conditionals, and the antecedent of one is the consequent of the other, then you may derive a new line showing a conditional with unshared antecedent and consequent. Φ ⊃ Ψ Ψ ⊃ Χ ∴ Φ ⊃ Χ
One counterexample row will suffice
When you've built a truth table for an argument, how many counterexample rows are sufficient to show that an argument is invalid?
affirming the consequent
Which fallacy is committed here, if any? "If the universe had been created by a supernatural being, then we would see order and organization everywhere, instead of randomness. And we do see order, not randomness, so it's clear that the universe was created by a supernatural being."
1, 2, and 5
Which of the following lines may Simplification be legitimately applied to? 1. ~P • Q 2. (P v Q) • R 3. ~A ⊃ B 4. C ≣ (A • ~B) 5. {B ⊃ (A • ~C)} • ~(B v C) 6. ~(P • Q)
Judging how likely or frequent something is by how easy it is to think of instances of that thing
Which of these descriptions best defines the availability heuristic?
Double Negation
Which rule permits this derivation? 1. (P v ~~Q) • ~(P v ~Q) 2. (P v Q) • ~(P v ~Q) 1, ???
DeMorgan's
Which rule permits this derivation? 1. P v ~Q 2. ~(~P • Q) 1, ???
CE (Conditional Exchange)
Which rule permits this derivation? 1. ~{P ⊃ (~Q v ~P)} 2. ~{P ⊃ (Q ⊃ ~P)} 1, ???
There is no rule permitting this derivation
Which rule permits this derivation? 1.) (P v R) ⊃ Q 2.) ~(P v R) 3.) ~Q 1, 2 [???]
DeMorgan's
Which rule permits this derivation? 1.) A v ~(B v C) 2.) ~[~A ∙ (B v C)] 1 [???]
Universal affirmative
Which type of categorical sentence is this? "A game is something you play with people you like"
Particular affirmative
Which type of categorical sentence is this? "A record I like is on sale at the flea market"
We put the parentheses around S v C because the comma is placed after the atomic sentence: "We can get them canned" which has turned the atomic sentence after it: "We can make huevos rancheros" into a single antecedent.
Why do we put parentheses around S v C in the following statement: "If tomatoes are in season or we can get them canned, then we can make huevos rancheros." (S v C) ⊃ H
Because there is a connective component between the Atomic Statements: "This is" and "My beautiful house".
Why is "This is not my beautiful house" a compound statement?
Because the third line is not ~F; In Disjunctive Syllogism, if one of the disjuncts are negated, the new line derived from that should be the other disjunct (without any changes).
Why is the following is a NOT a correct application of disjunctive syllogism: 1.) ~F v K 2.) ~K 3.) F 1, 2 DS
The word 'so' does not indicate a connective, but does often indicate that a conclusion of an argument is being drawn, in which case it's not part of the atomic sentence.
Why is the following not an atomic statement: "So you're saying there's a chance."
Ad Hominem Abusive
You disregard the opposing party's views and respond to their views with irrelevant insults.
It means that both of its conjuncts are true. Because, in order for a conjunction to be true, both conjuncts must be true.
You have a conjunction, and you know that's it's true. What, if anything, do you know about its conjuncts?
So a tautology means that sentence Φ's truth column is completely true. In a negation, the statement is True when its component is false; and false when component is true. Therefore, ~Φ's components must be false!
You have a sentence Φ, and you know it's a tautology. (You don't know what its main connective is.) What do you know about ~Φ?
Ad hominem circumstantial
You ignore an individual's reasons to support a claim and assume their views and opinions based on their circumstance.
Compound Statement (Sentence)
a sentence that consists of two or more statements separated by connectors.
Argument
a set of statements in which one statement is supported by the other(s).
Ad populam snobbery
trying to argue for/ against a claim by appealing to its lack of popularity
Ad populum bandwagoning
trying to argue for/ against a claim by appealing to its popularity
representativeness heuristic
we estimate the likelihood of an event by comparing it to an existing prototype that already exists in our minds. Our prototype is what we think is the most relevant or typical example of a particular event or object.
Hasty Generalization
when one predicates a property of a whole set of things based on one sample, a small sample, or a biased sample.
Negation
~ (tilde)
