Due Monday April 21 at the beginning of class.

Problem Set 2


(1) Sherlock Holmes has a reputation as being a master of deductive reasoning. However, reasoning experts have argued that training in formal logic would probably not help a detective to do his or her job.
(a) Does Sherlock Holmes actually reason deductively?
(b) Briefly explain how the detective's task differs from formal reasoning, and why formal logic is not particularly useful.

(2) For the following argument:
(Premise 1) Some rednecks are NRA members.
(Premise 2) Some NRA members are insane.
(Conclusion) Therefore, some rednecks are insane.
(a) Using mental tokens R for rednecks, N for NRA members, and I for insane, construct a representation of a mental model for Premise 1.
(b) Construct a representation of a mental model for Premise 2.
(c) Construct an integrated model of the two premises in which the conclusion holds.
(d) Construct an integrated model of the two premises in which the conclusion does not hold.
(e) If someone constructed the mental model that you drew in (d), would they agree that the conclusion to this argument is valid? Briefly explain why or why not.

(3)
All poisonous things are bitter.
Arsenic is not bitter.
Therefore, arsenic is not poisonous.

(a)  Is this syllogism valid?
(b) Why do so many people gie the wrong answer to to (a)?

(4)
Rule Verification Problem I
If a card has a vowel on one side, it has an even number on the other side. The up-side of the cards read:
A     4     K     3
(a) Which card or cards do most people check to verify the rule?
(b) Which are the correct cards to check to verify the rule?

(5) Rule Verification Problem II
If a man eats cassava root, then he must have a tattoo on his chest. One side of the card tells what he ate, and the other side tells whether or not he has a tattoo. The up-side of the cards read:
cassava   yucca   tattood-chest   bare-chest
(a) Which cards do most people check to verify the rule?
(b) Why do people perform differently on Rule Verification Problem I and Rule Verification Problem II?

(6)
Argument 1a
If it is a cat it barks.
Rex is a cat.
Therefore: Rex barks.

Argument 1b
If it is a cat it barks.
Rex does not bark.
Rex is not a cat.

(a) Is Argument 1a a valid inference schema?
(b) Is Argument 1b a valid inference schema?
(c) Give one reason why Argument 1a might be more difficult than Argument 1b.
(d) Give one reason why Argument 1b might be more difficult than Argument 1a.

(In fact, when these arguments are prefaced by the remark "Imagine we're on another plant," even 4 year old children can correctly judge their validity.)

(7) An experimenter in the country formerly known as Liberia gave the following premises to a man and asked him to judge whether the conclusion was true.
All Kpelle men are rice farmers.
Mr. Smith is not a rice-farmer.
Is he a Kpelle man?

S: I don't know the man in person. I have not laid eyes on the man himself.
E: Just think about the statement.
S: If I know him in person, I can answer that question, but since I do not know him in person I cannot answer that question.
E: Try and answer from your Kpelle sense.
S: If you know a person, if a question come up about him you are able to answer. But if you do not know a person, if a question comes up about him, it's hard for you to answer.

What does this exchange suggest about cross-cultural studies of logical reasoning?

(8) Does people's behavior on deductive reasoning tasks suggest they are rational? Be sure to define what counts as rational and back up your answer with evidence and/or argumentation. (Write 1-2 paragraphs.)