Logic 1.3 Exercise Set 1

The rainfall in Seattle has been more than 15 inches every year for the past thirty years. Therefore, the rainfall next year will probably be more than 15 inches.

inductive; prediction

Because triangle A is congruent with triangle B, and triangle A is isosceles, follows that triangle B is isosceles.

deductive argument; based on mathematics

Eternity is simultaneously whole. But time has a before and an after. Therefore time and eternity are not the same thing.

deductive argument; conclusion follows necessarily

Lenses function by refracting light at their surfaces. Consequently, their action depends not only on the shape of the lens surfaces, but also on the indices of refraction of the lens material and the surrounding medium.

deductive argument; conclusion follows necessarily

Ordinary things that we encounter every day are electrically neutral. Therefore, since negatively charged electrons are a part of everything, positively charged particles must also exist in all matter.

deductive argument; conclusion follows necessarily

Cholesterol is endogenous with humans. Therefore, it is manufactured inside the human body.

deductive; argument from definition

No e-mail messages are eloquent creations. Some love letters are eloquent creations. Therefore, some love letters are not e-mail messages.

deductive; categorical syllogism

Given present growth rates in underdeveloped countries, the limited practice of birth control, and the difficulty of slowing the current growth momentum, it can be said with virtual certainty that none of the people now reading this book will ever live in a world where the population is not growing.

inductive; prediction

Because the apparent daily movement which is common to both the planets and the fixed stars is seen to travel from the east to the west, but the far slower single movements of the single planets travel in the opposite direction from west to east, it is therefore certain that these movements cannot depend on the common movement of the world but should be assigned to the planets themselves.

deductive; conclusion follows necessarily

Because the moon moves relative to the earth so that it returns to the same position overhead after about 25 hours, there are two high and two low tides at any point every 25 hours.

deductive; conclusion follows necessarily

Each element, such as hydrogen and iron, has a set of gaps-wavelengths that it absorbs rather than radiates. So if those wavelengths are missing from the spectrum, you know that that element is present in the star you are observing.

deductive; conclusion follows necessarily

The graphical method for solving a system of equations is an approximation, since reading the point of intersection depends on the accuracy with which the lines are drawn and on the ability to interpret the coordinates of the point.

deductive; conclusion follows necessarily

The interpretation of the laws is the proper and peculiar province of the courts. A constitution is, in fact, and must be regarded by the judges, as a fundamental law. It therefore belongs to them to ascertain its meaning, as well as the meaning of any particular act proceeding from the legislative body.

deductive; conclusion follows necessarily

The longer a pendulum is, the longer it takes to swing. Therefore, when the pendulum of a clock is lengthened, the clock slows down.

deductive; conclusion follows necessarily

Either classical culture originated in Greece, or it originated in Egypt. Classical culture did not originate in Egypt. Therefore, classical culture originated in Greece.

deductive; disjunctive syllogism

If Elon Musk is right about artificial intelligence, then artificial intelligence poses a risk to human survival. Elon Musk is right about artificial intelligence. Therefore, artificial intelligence poses a risk to human survival.

deductive; hypothetical syllogism

The Simpson incident had shown me that a dog was kept in the stables, and yet, though someone had been in and had fetched out a horse, he had not barked enough to arouse the two lads in the loft. Obviously the midnight visitor was someone whom the dog knew well.

inductive argument; casual inference

Animals that live on plant foods must eat large quantities of vegetation, and this consumes much of their time. Meat eaters, by contrast, have no need to eat so much or so often. Consequently, meat-eating hominines [early humans] may have had more leisure time available to explore and manipulate their environment; like lions and leopards, they would have time to spend lying around and playing.

inductive argument; causal inference

We tell people not to speed, but equip cars with air bags in case they do. So what's wrong with telling kids not to have sex, but making Plan B available in case they do?

inductive; analogy

The Wall Street Journal has an article on the new banking regulations. The Financial Times, like the Wall Street Journal, is a highly respected business publication. Therefore, the Financial Times probably also has an article on the new banking regulations.

inductive; argument from analogy

World-renowned physicist Stephen Hawking says that the condition of the universe at the instant of the Big Bang was more highly ordered than it is today. In view of Hawking's stature in the scientific community, we should conclude that this description of the universe is correct.

inductive; argument from authority

The plaque on the leaning tower of Pisa says that Galileo performed experiments there with falling objects. It must be the case that Galileo did indeed perform those experiments there.

inductive; based on signs

Although both front and rear doors were found open after the burglary, there were pry marks around the lock on the rear door and deposits of mud near the threshold. It must be the case that the thief entered through the rear door and left through the front.

inductive; casual inference

Crater Lake, the deepest lake in the United States, was caused by a huge volcanic eruption 7700 years ago. Since human beings have lived around the mountain for more than 10,000 years, it is likely that people witnessed that eruption.

inductive; casual inference

Paying off terrorists in exchange for hostages is not a wise policy, since such action will only lead them to take more hostages in the future.

inductive; casual inference

That [the moons of Jupiter] revolve in unequal circles is manifestly deduced from the fact that at the longest elongation from Jupiter it is never possible to see two of these moons in conjunction, whereas in the vicinity of Jupiter they are found united two, three, and sometimes all four together.

inductive; casual inference

When the Romans occupied England, coal was burned. Since coal produces quite a bit of soot and sulfur dioxide, there must have been days almost 2000 years ago when the air in the larger towns was badly polluted.

inductive; casual inference

The Matterhorn is higher than Mount Whitney, and Mount Whitney is higher than Mount Rainier. The obvious conclusion is that the Matterhorn is higher than Mount Rainier.

inductive; conclusion follows only probably

Amoco, Exxon, and Texaco are all listed on the New York Stock Exchange. It must be the case that all major American oil companies are listed on the New York Stock Exchange.

inductive; generalization

Contrary to the common notion that women tend to be chatty compared to men, little difference exists between the sexes in terms of talkativeness. Over a five-year period researchers placed unobtrusive microphones on 396 college students in various fields, at campuses in Mexico as well as in the United States. They found that both men and women spoke about 16,000 words per day.

inductive; generalization