Introductory Logic
Test #1
September 26, 2005
 
Name: ________________________
R. Hammack
Score: _________

1. Identify each of the following passages as an argument or a non-argument. If the passage is an argument, underline the conclusion.

(a)
 The prophecies of Nostradamus are so vague that no one knows what they mean until after the "predicted" event. Consequently, they are not really predictions.
ARGUMENT

(b)
 Water is a good solvent for many different substances, and it picks them up as it moves through the environment. For example, rain water flowing over and under the ground disolves minerals such as limestone.
NOT AN ARGUMENT (example)

(c)
 The plane was late because a thunder storm in Chicago caused it to be diverted to Kansas City.
NOT AN ARGUMENT (report or explanation)

(d)
 If it walks like a duck and swims like a duck and quacks like a duck, then it's a duck.
NOT AN ARGUMENT (conditional statement)

(e)
 For every action, there is an equal and opposite reaction.
NOT AN ARGUMENT (simple statement)



2. Each of the following passages is an argument. Underline the conclusion. Say if the argument is deductive, inductive, valid, invalid, weak, strong, and (if possible) sound, unsound, cogent, or uncogent.

(a)
 Since George Bush was elected president twice, he will probably be elected a third time.
INDUCTIVE, WEAK, UNCOGENT

(b)
 Since Randolph-Macon is not an urban university, then it follows with certainty that it is a private college.
DEDUCTIVE, INVALID, UNSOUND

(c)
 Randolph-Macon College is either in Virginia or North Carolina. So it's in North Carolina, since it's not in Virginia.
DEDUCTIVE, VALID, UNSOUND

(d)
 Randolph-Macon has had about 1100 students for the past 10 years, so we can expect that it will have about 1100 students next year.
INDUCTIVE, SRTONG, COGENT

(e)
 Randolph-Macon is in Ashland, and there are no large universities in Ashland, so Randolph-Macon is not a large university.
DEDUCIVE, VALID, SOUND

(f)
 Randolph-Macon is an Ivy League college because it's in Ashland, and every college in Ashland is an Ivy League college.
DEDUCTIVE, VALID, UNSOUND




3. Use the counterexample method to prove each of the following arguments is invalid.

(a)
 If human rights are recognized, then civilization flourishes. But it's not true that human rights are recognized, so it's not true that civilization flourishes.


If H then C
It's not true that H
Thus it's not true that C


If George Washington was assassinated then George Washington died
It's not true that George Washington was assassinated
Thus it's not true that George Washington died


True premises, false conclusion, INVALID ARGUMENT




(b)
 No Republicans are Democrats, so some Democrats are wealthy stockbrokers, since some wealthy stock-brokers are not Republicans.


No R are D
Some W are not R
Some D are W


No german sheppards are cats
Some dogs are not german sheppards
Some cats are dogs


True premises, false conclusion, INVALID ARGUMENT



(c)
 Some plants are edible, and some mushrooms are plants, so some mushrooms are edible.

 

Some P are E
Some M are P
Thus some M are E

Some pets are dogs
Some cats are pets
Thus some cats are dogs


True premises, false conclusion, INVALID ARGUMENT


4. Diagram the following extended argument

  (1) America's farm policy desperately needs revamping. (2) Seventy-three cents of every farm program dollar ends up in the pockets of the nation's super-farmers. As a result, (3) the mid-sized family farms are being squeezed out of existence. Also, (4) our farm policy courts environmental disaster. (5) Federal subsidies encourage farmers to use enormous amounts of fertilizer and pesticides. (6) These chemicals percolate down through the soil and pollute limited groundwater. 




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     1

5. Decide if the following immediate inferences are valid or invalid. Use either Venn diagrams or the Modern Square of Opposition.

(a)
 It is false that all dry martinis are dangerous concoctions. Therefore it is false that some dry martinis are not dangerous concoctions.

Suppose premise is true. Then A statement "All dry martinis are dangerous concoctions" if false. Thefore, by Modern Square, the O statement "some dry martinis are not dangerous concoctions" is true. But then the conclusion "it is false that some dry martinis are not dangerous concoctions" is false. Therefore the argument is INVALID.





(b)
 All dry martinis are dangerous concoctions. Therefore it is false that no dry martinis are dangerous concoctions.

Suppose premise is true. Then A statement "All dry martinis are dangerous concoctions" if true. Thefore, by Modern Square, the E statement "no dry martinis are dangerous concoctions" could be true or false. But then the conclusion "it is false that no dry martinis are dangerous concoctions" is either true or false. Therefore the argument is INVALID.


6. Translate the following sentences into standard-form categorical propositions.

(a)
 Not all tests are difficult.

Some tests are tests that are not difficult

OR

Some tests are not difficult things


(b)
 If it quacks like a duck, then it's a duck.


All things that quack like a duck are ducks




 

(c)
 Rome wasn't built in a day.

All cities identical to Rome are things not built in a day

OR


No cities identical to Rome are things built in a day