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Home , Modus ponens

IN CLASS EXERCISES Instructions: Diagram the following In view of the fact that . First number each Instructions: Determine whether the , then use plus signs and Conclusion Indicators following are . If some arrows to designate the are not propositions, see if they can structure as either a joint inference Therefore be rewritten as propositions. or an independent inference. Thus Hence (1) I have superpowers. (7) Joe has no friends since the only So (2) Not here, Bob! people he knows are on social Accordingly (3) I think I’m going to sell little media, and those aren’t real For this reason Joey into slavery. friends. Consequently (8) Bob was voted most popular It follows that Instructions: Identify the premises student in class, and Bob is and conclusions in the following always seen with lots of Argument Diagrams arguments, and identify any premise people around him. Thus, Bob and conclusion indicators. has many friends. Joint inference: (9) Joe and Bob aren’t friends 1+2 |→ 3 (4) English is the best language because each says that he can’t Independent inference: since it’s the only one that I stand the other, and each 1 |→ 3 and 2 |→ 3 speak. angrily insults the other when (5) Bob likes to argue all the time, they pass in the hall. and for that reason he would make a good lawyer. Premise Indicators (6) In view of the fact that Joe cheated on his taxes, we Since consequently cannot appoint For him to the ethics committee. Because Given that For the reason that FALLACIES OF RELEVANCE Instructions: Identify the informal OTHER COMMON FALLACIES fallacy in each of the following. Argument against the Person (argumentum ad hominem): False Cause (post hoc ergo (10) “The Dead Milkmen” is a rock attacking a person’s character procter hoc): inferring a causal band. Most people who were instead of the content of that connection based on mere once milkmen in the U.S. are person’s argument. correlation. now dead. Yikes! That’s one Argument from Ignorance Circular Reasoning: implicitly big rock band! (argumentum ad ignorantiam): using your conclusion as a premise. (11) Hey, forget about Beth, she’s concluding that something is true Equivocation: an argument nothing special. Is there since you can’t prove it is false. which is based on two definitions of anything special about her Appeal to Pity (argumentum one word. kidneys, tonsils, or small ad misericordiam): appealing to a Composition: assuming that intestine? She’s only a person’s unfortunate circumstance the whole must have the properties collection of those things. as a way of getting someone to of its parts. (12) Of course the Major thinks that accept a conclusion. Division: assuming that the the Army offers good career Appeal to the Masses parts of a whole must have the opportunities. He’s an Army (argumentum ad populum): going properties of the whole. man himself. along with the crowd in support of a Red Herring: introducing an (13) I think Beth will go out with conclusion. irrelevant or secondary subject and you. I haven’t heard anything Appeal to Authority thereby diverting attention from the which suggests that she (argumentum ad verecundiam): main subject. wouldn’t. appealing to a popular figure who is Straw Man: distorting an (14) We have a good faculty here at not an authority in that area opposing view so that it is easy to Preppy State University. Irrelevant Conclusion (non refute. Therefore, Dr. Joseph sequitur): drawing a conclusion Drunkard, who teaches here, is which does not follow from the a good faculty member. evidence.

Conditional: if P then Q Instructions: In each of the : not P following identify the being used and translate Conjunction Clue Words (“And”) the into standard form. P, but Q (15) Father Joe’s marriage to Beth P, although Q implies that he first leaves the P; Q priesthood. P, besides Q (16) I was accepted at Yale P, however Q University, but I’d much P, whereas Q rather attend Thrift Community College. Conditional Clue Words (“If- (17) Bob’s name does not appear on Then”) Santa’s “nice” list. If P, it follows that Q Instructions: Determine which of P implies Q the following are well-formed P entails Q nested propositions. Whenever P, Q P, therefore Q (18) if P then (Q or R) Q follows from P (19) (P and Q) not Q, since P (20) not (P or Q) (21) P and (if Q then R)

Logical Connectives

Conjunction: P and Q Disjunction: P or Q Instructions: Translate the following proposition to make your premises premise (2) not P premises and conclusions into complete. concl. (3) therefore, Q standard form and decide which valid argument form or fallacious (25) Joe will fail his exam. (modus Hypothetical argument form is being used. ponens) (26) Polly wants a cracker. premise (1) if P then Q (22) If the band “Satan’s Pitchfork” () premise (2) if Q then R performs in town, they will (27) If you insult Beth’s mother, concl. (3) Therefore, if P play “Hell, Sweet Hell.” If you will go to the hospital. then R they perform “Hell, Sweet () Hell” then dudes will stage (28) Thrift Community College is dive. Therefore, if they not a good school. (modus perform, dudes will stage dive. tollens) (23) Either Bob will go bankrupt, or I will. Bob will go bankrupt. Modus Ponens Therefore, I will not. (24) If Joe flunks out of college, premise (1) If P then Q then his brother Bob will premise (2) P inherit the family business. Joe concl. (3) Therefore, Q will not flunk out of college. Therefore, Bob will not inherit the family business. premise (1) If P then Q Instructions: Make up a valid premise (2) Not Q argument that leads to the concl. (3) Therefore, not P conclusion given. Use the rule indicated in parentheses. You will Disjunctive Syllogism (two versions) need to invent some simple premise (1) P or Q Instructions: Are the following Modus Ponens arguments valid, invalid, sound, or unsound? premise (1) If P then Q premise (2) P (29) If Fido is a Dalmatian, then concl. (3) Therefore, Q Fido would have lots of spots It is not the case that Fido is a Modus Tollens Dalmatian Therefore, it is not the case premise (1) If P then Q that Fido has lots of spots premise (2) Not Q concl. (3) Therefore, not P (30) If Joseph Stalin had U.S. citizenship, then he would Disjunctive Syllogism (two versions) have been born in the U.S. It is not the case that Joseph premise (1) P or Q Stalin was born in the U.S. premise (2) not P Therefore, it is not the case concl. (3) therefore, Q that Joseph Stalin had U.S. citizenship. Hypothetical Syllogism

Instructions: The following test your premise (1) if P then Q understanding of . premise (2) if Q then R concl. (3) Therefore, if P (31) Can a valid argument have a then R false conclusion? (32) Can a sound argument have a false conclusion?

Instructions: What is the inductive Inductive Probability strength of each of the following (that is, very strong, strong, weak, Inductively very strong: very weak)? probability is close to certain. (33) Some notable guitarist have Inductively strong: probability died in their 20s. Joe is a is high. notable guitarist. Therefore, Inductively weak: probability Joe will probably die in his is low. 20s. Inductively very weak: (34) College dropouts make $1 probability is close to million less during their non-existent. careers than college graduates. Joe is a college dropout. Therefore, Joe will probably make around $1 million less during his career than an average college graduate. (35) 45% of Americans go to church at least once a month. Joe is an American. Therefore Joe will probably go to church this month.

Instructions: For each of the concl. (3) Therefore, there is following, indicate the inductive premise (1) n percent of a an n percent probability argument form that is followed, and sample has attribute A. that x has A. whether it commits any inductive concl. (2) Therefore, n fallacy. percent of a population Fallacy of small proportion: a probably has attribute A. conclusion is too strong (36) Joe and Bob live in the same to be supported by the town, listen to the same music, Fallacy of small sample: a small population and like the same sports teams. conclusion is too strong proportion with the Joe is Presbyterian. Therefore, to be supported by a attribute. Bob is probably also small sample number. Presbyterian. Argument from Analogy: drawing a (37) 60% of college students in the Fallacy of biased sample: a conclusion about one item based on U.S. are women. Preppy State conclusion is too strong its similarities with another item. University is a U.S. College. to be supported by a Therefore, there is a very high nonrandom sampling premise (1) Objects x and y probability that the next technique. each have attributes A, B student who walks out of and C. Preppy State’s student center Statistical syllogism: drawing a premise (2) Object x has an will be a woman. conclusion about an item based on additional attribute D. (38) 100% of 20 randomly surveyed statistics about the population as a concl. (3) Therefore, object adults in the small town of whole. y probably also has Hornbeak, Tennessee shop at attribute D. Walmart. Therefore, 100% of premise (1) n percentage of a Fallacy of false analogy: Americans shop at Walmart. population has attribute comparing two items that A. have trivial points in Statistical induction: drawing a premise (2) x is a member of common, but differ from conclusion about a population based that population. each other in more on a statistically acceptable sample. significant ways.