Exam 10: Deduction and Induction: A Closer Look

For each set of values, determine the mean, median, and mode. -Seven people were interviewed about their incomes and they reported the following figures (in thousands): 25, 30, 35, 25, 45, 65, 25. Determine the mean, median, and mode for this set of values. otal: 250. Mean: 35.71. Median:30. Mode: 25

The following is a valid argument: Amy is good at math. All chemists are good at math. Therefore, Amy is a chemist.

More enthymemes. In each case, fill in the missing element (i.e., add a premise or conclusion) so as to turn the enthymeme into a valid deductive argument. -If it rains, then we will swim. If we swim, then we will need towels. So if it rains ...

On deductive arguments. -If an argument has premises that are certain to be true, then the argument must be valid.

Think with Socrates does not contain a section on enthymemes. However, the concept can be defined briefly. This exercise defines an enthymeme and gives students a chance to practice filling in holes in incomplete deductive arguments. An enthymeme is an argument that is missing one or more premises or a conclusion. Each of the following deductive arguments is missing either a premise or a conclusion. (Thus, each is an enthymeme.) Add a statement to each so as to turn the enthymeme into a valid argument. -If Archie thinks someone is a dingbat, then the person is a dingbat in Archie's eyes … So Meathead is a dingbat in Archie's eyes.

Assume each of the following is a deductive argument. In each case, is the argument valid or invalid? (V or I) -If there is a drought, the crop will be small. The crop will be small. So there will be a drought.

In an analogical argument, the more qualities the items compared have in common, the weaker the argument.

On deductive arguments. -If an argument has a conclusion that is certainly false, then the argument must be invalid.

The following is an invalid argument: Jim is at least sixty. Jan is at least as old as Jim. So Jan is at least sixty.

An empirical hypothesis is one that makes observational predictions.

Assume each of the following is a deductive argument. In each case, is the argument valid or invalid? (V or I) -Chris is shorter than Ed, and Ed is shorter than Pat. So Pat is taller than Chris.

An argument with a false conclusion cannot possibly be a sound deductive argument.

Is the argument deductive (D) or inductive (I)? -Professor Smith says there will be no depression. He is an expert on depressions and business cycle theory. Therefore, there will probably be no depression.

On critically evaluating inductive arguments. Read the following arguments and carry out the instructions below. -Arnold is fifty years old, one hundred pounds overweight, and eats a diet that includes lots of candy, ice cream, and cake. Helen, forty-six, is 108 pounds overweight, and eats a diet that includes lots of sweets. Arnold was just been diagnosed with clogged arteries. Therefore, Helen will probably get clogged arteries, too. a. List several irrelevant dissimilarities that would have no bearing on the argument. b. List several additional relevant similarities that would strengthen the argument. c. Change the conclusion so that the argument is weaker. d. Change the conclusion so that the argument is stronger. e. Add a premise that makes the argument stronger. f. Add a premise that makes the argument weaker.

Think with Socrates does not contain a section on enthymemes. However, the concept can be defined briefly. This exercise defines an enthymeme and gives students a chance to practice filling in holes in incomplete deductive arguments. An enthymeme is an argument that is missing one or more premises or a conclusion. Each of the following deductive arguments is missing either a premise or a conclusion. (Thus, each is an enthymeme.) Add a statement to each so as to turn the enthymeme into a valid argument. -If Sloopy hangs on, then the bad part of town will not be as bad as many people think. The bad part of town will not be as bad as many people think. Therefore, …

If an argument is cogent, then its conclusion is likely true.

In a generalization from a sample, the less random the sample, the stronger the argument.

One way to strengthen an analogical argument is to show further similarities between the things compared in the premises.

Hypothetical syllogism is a form of deductive reasoning.

On deductive arguments. -If an argument is sound, then it must have a true conclusion.