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

(a) Hypertension is sometimes called a silent killer because it may not be detected until a stroke or a heart attack occurs. Therefore it is important to have regular blood pressure checks and to adopt a life-style that protects against the development of hypertension.

ARGUMENT; conclusion is highlighted.

(b) The Titanic sank on its maiden voyage in 1912 because it collided with an iceberg. Four of the ship's sixteen watertight compartments could have been flooded without the ship sinking. However, the iceberg tore gashes in the hull, flooding five of the compartments.

NOT AN ARGUMENT; expository passage.

(c) Acid rain is a threat that must be taken seriously. Acid rain has killed the fish in thousands of lakes, and has caused billions of dollars in damage to crops. Moreover, acid rain poses a serious risk to our forests.

ARGUMENT; conclusion is highlighted.

(d) Bismarck, chancellor of Prussia, harnessed the conservative agenda of keeping the aristocracy in power while promoting the liberal nationalist aim of German unification. He also proved successful at diplomacy with the other great powers. Through three quick wars against Denmark, Austria, and France, he united Germany in 1871 under Prussian leadership.

NOT AN ARGUMENT; report.

(e) Chemical reactions and physical processes on early Earth created an environment that made life possible. And life, one it began, transformed the planet's chemistry. Biological and geological history are inseparable.

ARGUMENT; conclusion is highlighted.

(f) Capitalist society is responsible for technological power on an unprecedented scale, progressing at an unprecedented rate. This is because the competitive position of its industrial decision makers compels them the productivity of production processes.

NOT AN ARGUMENT; explanation.

2. Each of the following passages is an argument. For each argument, say if it is deductive, inductive, valid, invalid, weak, strong, and (if possible) sound, unsound, cogent, or uncogent.

(a) The headline of today's New York Times says a hurricane struck Indonesia. Therefore it must be the case that a hurricane struck Indonesia.

Inductive; strong.

(b) All gargoyles are monsters. Some gargoyles are water spouts. Therefore, some monsters are water spouts.

Deductive; valid; unsound.

(c) Either Hemingway wrote Plato's Republic or he wrote the Bible. Hemingway did not write Plato's Republic. Therefore Hemingway wrote the Bible.

Deductive; valid; unsound.

(d) A day is exactly 10 hours long. An hour is exactly 50 seconds long. Therefore there are 500 seconds in a day.

Deductive; valid; unsound.

(e) This year one presidential candidate won the popular vote and another won the electoral college. Therefore the same thing is likely to happen in the year 2004.

Inductive; weak; uncogent.

(f) All Democrats are members of a political party, and all Republicans are members of a political party. Therefore all Democrats are Republicans.

Decuctive; invalid; unsound.

(g) Since Shakespeare wrote many plays, and anyone who can write a play is literate, then it follows that Shakespeare was literate.

Deductive; valid; sound.

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

(a) Some existentialist poets are geniuses, for some madmen are existentialist poets, and all geniuses are madmen.

Letting E=fish, G=mammals, and M=animals, we get true premises and a false conclusion. Thus the argument is invalid.

(b) If the prime rate is lowered, then stock prices will increase. If the rich get richer, then stock prices will increase. Therefore if the rich get richer, then the prime rate will be lowered.

Letting P = my car is red, R = my car is blue, and C = my car is not white, we get true premises and a false conclusion. Therefore the argument is invalid.

(c) All diabetes victims are either insulin-takers or glucose eliminators. Some diabetes victims are insulin-takers. Therefore some diabetes victims are glucose eliminators.

4. Diagram the following extended argument.

(1) Flesh food is not a necessity in the human diet, as (2) nutritionally adequate alternatives are readily available. (3) Many people in the world thrive on a nonmeat diet. (4) Indeed, vegetarian Seventh-Day Adventists in this country live an average of six years longer than their counterparts. (5) The National Academy of Science warns that our fat-laden diet is directly responsible for much of the heart disease and cancer that afflict so many. (6) At a time when people are starving in certain parts of the world, it should be noted that a steer must consume sixteen pounds of grain and soy to produce one pound of meat. (7) The grain and soy beans we feed our meat-producing animals would feed every hungry mouth in the world many times over. (8) Cattle are competing with humans for food. (9) Clearly a reassessment of raising animals for food is in order.

       4       6
       |       |
       |       |
       |       |
    2  3   5   7
    \  |  /    |
     \ | /     |
      \|/      |
       1       8
        \     /
         \   /
          \ /
           9

5. Use the Modern Square of Opposition to decide if the following arguments are valid or invalid. (This problem is intended partly to test your knowledge of the Modern Square of Opposition, so points may be deducted if you don't use it here. Explain your work.)

(a) It is not true that all sane people are people who can do logic. Therefore, it is not true that some sane people are people who can do logic.

Suppose that the premise is true. Then the A-statement all sane people are people who can do logic is false. The conclusion involves the corresponding I-statement some sane people are people who can do logic. Since I is not diagonally across from A on the Modern Square of Opposition, then it follows that we can not say with certainty if the conclusion is true or false. Therefore the argument is invalid.

(b) It is false that some women are police officers. Therefore no women are police officers.

Suppose the premise is true. Then the I-statement some women are police officers is false. Consequently, the corresponding E-statement no women are police officers is true, because E is daigonally across from I on the Modern Square of Opposition. Therefore, if the premise is true, then the conlusion must be true as well, so the argument is valid.

(c) It is false that all weddings are light-hearted celebrations. Therefore some weddings are not light-hearted celebrations.

Suppose the premise is true. Therefore the A-statement all weddings are light-hearted celebrations is false. Then the corresponding O-statement some weddings are not light-hearted celebrations is true, since O is diagonal to A on the Moderen Square of Opposition. This means that if we assume the premise to be true, then the conclusion must be true as well. Therefore the argument is valid.