Use the traditional square of opposition along with conversion, obversion, and contraposition to determine the truth value of the second sentence is each pair. (6)

I) (This Section pertains to chapter 4– These are NOT categorical syllogisms.) Put the argument into standard form and then identify the INFORMAL fallacies that are committed (if any).  Make sure to both defineand explain how the INFORMAL fallacies are committed. (9)

Example: In his History of the America Civil War, Jeffry Noland argues that the war had little to do with slavery.  However, as a historian from Alabama, Noland could not possibly present an accurate account.  Therefore, his arguments should be discounted.

Answer:

P: In his History of the America Civil War, Jeffry Noland argues that the war had little to do with slavery.

P: As a historian from Alabama, Noland could not possibly present an accurate account.

C: His arguments should be discounted.

Fallacy: Ad Hominem – an attack against a, generally irrelevant, characteristic of the person.

Explanation: Whether Noland is from the South or not should not automatically undermine his expertise in the area in which he’s studied.

A crust of bread is better than nothing.  Nothing is better is than true love.  So a crust of bread is better than true love.

We’ve all heard that millions of Americans are without adequate health care.  But America’s doctors, nurses, and hospitals are among the best in the world.  Thousands of people come from abroad every year to be treated here.  Clearly there is nothing wrong with our health care system.

On Friday, I took Jeff out to dinner.  He told me that if I wasn’t interested in a serious relationship, I should forget about dating him.  On Saturday I took Dave to a film.  When we discussed it afterward over a drink, he could understand why I wasn’t interested in babies.  Men are all alike.  All they want is a secure marriage.

 

II) Use the traditional square of opposition along with conversion, obversion, and contraposition to determine the truth value of the second sentence is each pair. (6)

Example: All people who disagree with religion are saints. (T)

Some sinners agree with religion.

Answer: The terms don’t match up in two ways: they aren’t in the right spots (the subject and predicate terms are different in each sentence) and they are complements (i.e. sinners are non-saints.) So I need to get the right terms in the right spots and I can do that using contraposition on the first sentence. That gives me “All sinners are people who agree with religion.”

So now my two sentences are

All sinners are people who agree with religion. (T)

Some sinners agree with religion.

The top sentence is an A proposition and the bottom sentence is an I proposition. I know from the relationship of subalternation that if an A position is true and I proposition must also be true.

Final Answer: The second sentence must be true.

Some integers which are even numbers are not prime. (T)

All non-prime numbers are odd integers.

All inflammable substances are high in carbon isotopes. (T)

No incombustible substances are low in carbon isotopes.

 

III) Translate the following into standard form categorical propositions.  If there are multiple translation options list all of them. (8)

Example: Only the smartest will succeed.

Answer: All people who will succeed are people who are the smartest.

Everyone who races will get a medal except those who didn’t finish.

Not all ghosts are friendly.

Cara is cool.

Kaitlyn is never not on time.

IV) Restate the following in standard categorical syllogism form – make every attempt to have it in a valid mood and figure if possible. If it’s invalid, list the relevant rules and fallacies. (Have a look a Chapter 6, part E and F.) (9).

Example: Not any dandelion is a feline, for every dandelion is a plant and no cat is a plant.

Answer: No felines are plants.

All dandelions are plants.

No dandelions are felines.

EAE 2: Valid

Since each and every pachyderm is a vertebrate, we may conclude that only some arthropods such as shrimp, crabs, and lobsters are elephantine animals, for there is an invertebrate that is a crustacean.

There are handsome men, but only man is vile, so it is false that nothing is both vile and handsome.

All schools that are driven by careerism are schools that do not emphasize liberal arts.  It follows that some some universities are not institutions that emphasize liberal arts, for some schools that are not driven by careerism are universities.

 

BONUS!!

For any 2 of the following, indicate what categorical proposition will yield a valid syllogism. If no proposition will, indicate that the argument is invalid. (You may use a Venn Diagram as well as the rules for enthymemes) (1.5 each.  Answer ONLY two.  If you answer more than two I’ll only grade the first two.)

Encouraging toy-gun play gives children a clear message that the best way to  deal with frustration and conflict is with a gun.  Is this message that we want to be sending to our kids?

If you did your homework, which you did, then you should be able to identify the form of this syllogism.

Since no popular political candidates are people who were alive in 1901, and Hillary Clinton is not a person who was alive in 1901, you know what follows!

Some cats are not polecats, so some polecats are malodorous beasts.

 

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