Exam 10: Deduction and Induction: A Closer Look

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 the British march to Lexington and attempt to arrest Sam Adams, then there will be an armed conflict ... There will be an armed conflict.

Assume each of the following is a deductive argument. In each case, is the argument valid or invalid? (V or I) -Jones is over eighty years old. Smith is not as old as Jones. So Smith must be less than eighty years old.

Strong or Weak? -Almost every time that Pete has gone to Gorditos restaurant, he has ordered a large taco. He has eaten there many times. He just left for Gorditos. He will probably order a large taco.

Is the argument deductive (D) or inductive (I)? -My doctor says this drug is safe. She is an expert in this area. So the drug is likely safe.

Deductive arguments have an air of certainty, whereas inductive arguments do not.

If an argument is weak, then its conclusion cannot be true.

The following is a strong argument: It has been snowing for three days straight. Thus, tomorrow it will probably snow.

The following is a strong argument: Joe hasn't eaten lunch at the taco stand for sixty days straight. Thus, tomorrow he will probably not eat there again.

Assume each of the following is a deductive argument. In each case, is the argument valid or invalid? (V or I) -If the Chicago Bulls win, then Ed will collect ten bucks. The Chicago Bulls will win. So Ed will collect ten bucks.

If an argument is weak, then it must have at least one false premise.

Is the argument deductive (D) or inductive (I)? -If Orangie, the cat, is hungry, he will meow and let you know it. He is not meowing. Therefore, Orangie is surely not hungry.

In the case of an inductive argument:

The following is a valid argument: Jim is at least sixty. Jan is older than Jim. So Jan is older than sixty.

On deductive arguments. -All deductively sound arguments are also deductively valid.

Some inductive arguments claim that the conclusion must be true.

Is the argument deductive (D) or inductive (I)? -If we move to Colorado, then we will ski often. If we ski often, then we will become better skiers. So if we move to Colorado, then we will surely become better skiers.

The following is a valid argument: All splogs are crogs. No crogs are blonks. So no splogs are blonks.

On deductive arguments. -Some invalid arguments have true premises and a true conclusion.

Inductive arguments aim to show not that the conclusion must be true but rather that it is likely true.

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