Deductive & Inductive (Validity/Strength)

Circle A has exactly twice the diameter of circle B. From this we may conclude that circle A has exactly twice the area of circle B.

Deductive Invalid

nce John loves Nancy and Nancy loves Peter, it follows necessarily that John loves Peter.

Deductive Invalid *The word "necessarily" suggests that this argument should be interpreted as deductive. But the word "loves" is not a transitive relation. The fact that A loves B, and B loves C, does not imply that A loves C.

Since Phyllis is the cousin of Denise, and Denise is the cousin of Harriet, it follows necessarily that Harriet is the cousin of Phyllis.

Deductive Invalid *The word "necessarily" suggests that this argument is deductive. However, if the premises are assumed true it does not follow necessarily that the conclusion is true.

Since Michael is a Pisces, it necessarily follows that he was born in March.

Deductive Invalid *This is an argument from definition; hence deductive. All of the astrological signs cover a part of two months. Thus, if the premise is assumed true, it is not necessarily the case that the conclusion is true. Hence, the argument is invalid.

Since x + y = 10, and x = 7, it follows that y = 4.

Deductive Invalid *This is an argument from mathematics; hence, deductive. The correct value for y is 3, not 4; thus, the argument is invalid.

Suppose figure A is a triangle having two equal angles. It follows that figure A has two equal sides.

Deductive Valid

Determine whether the following argument is deductive or inductive. If an argument is inductive, determine whether it is strong or weak. If it is deductive, determine whether it is valid or invalid. Since Tom is the brother of Agatha, and Agatha is the mother of Raquel, it follows that Tom is the uncle of Raquel.

Deductive Valid *If you assume the premises are true, then the conclusion follows necessarily. So the argument is both deductive and valid for the same reason.

The Japanese attack on Pearl Harbor happened in either 1941 or 1951. But it didn't happen in 1941. Therefore, it happened in 1951.

Deductive Valid *This argument is a disjunctive syllogism; hence it is deductive. If the premises are assumed true, the conclusion is necessarily true, so the argument is valid. But note that the second premise is false, so the argument is unsound.

If inflation heats up, then interest rates will rise. If interest rates rise, then bond prices will decline. Therefore, if inflation heats up, then bond prices will decline.

Deductive Valid *This argument is a hypothetical syllogism; hence deductive. If the premises are assumed true, the conclusion is necessarily true; thus, the argument is valid. Note that the premises and conclusion link together like a chain.

If acupuncture is hocus pocus, then acupuncture cannot relieve chronic pain. But acupuncture can relieve chronic pain. Therefore, acupuncture is not hocus pocus.

Deductive Valid *This argument is a hypothetical syllogism; hence, deductive.

Since Christmas is always on a Thursday, it follows that the day after Christmas is always a Friday.

Deductive Valid *This is an argument from definition. By definition, Friday is the day after Thursday, so the argument is valid. However, the premise is false, so the argument is unsound.

A cogent argument may have a probably false conclusion.

False

A sound argument may be invalid.

False

A sound argument may have a false conclusion.

False

A statement may legitimately be spoken of as ''valid'' or ''invalid.''

False

A strong argument may have true premises and a probably false conclusion.

False

An argument may legitimately be spoken of as ''true'' or ''false.''

False

If an argument has true premises and a true conclusion, we know that it is a perfectly good argument.

False

Invalid deductive arguments are basically the same as inductive arguments.

False

Select True or False. Some arguments, while not completely valid, are almost valid.

False

Statistics reveal that 86 percent of those who receive flu shots do not get the flu. Jack received a flu shot one month ago. Therefore, he should be immune, even though the flu is going around now.

Inductive Strong *This argument is a causal inference, from cause to effect. Thus, it is inductive. The likelihood that Jack is immune is 86%. Anything more than 50% is strong.

Harry will never be able to solve that difficult problem in advanced calculus in the limited time allowed. He has never studied anything beyond algebra, and in that he earned only a C-.

Inductive Strong *This argument is a prediction; thus, it is inductive. If the premises are assumed true, the conclusion is probably true, so the argument is strong.

By accident Karen baked her brownies two hours longer than she should have. Therefore, they have probably been ruined.

Inductive Strong *This is a causal inference, from cause to effect. Brownies are normally cooked for around 20 minutes. Cooking them for two hours and twenty minutes would be seven times as long as they should be cooked. They have certainly been ruined.

The Broadway Theater marquee says that The Phantom of the Opera is playing nightly. Therefore, it must be that case that Phantom is playing there tonight.

Inductive Strong *This is an argument from signs. You can usually trust what a theater marquee says about what is playing there.

After taking LSD, Alice said she saw a flying saucer land in the shopping center parking lot. Since Alice has a reputation for always telling the truth, we must conclude that a flying saucer really did land there.

Inductive Weak

Robert has lost consistently at blackjack every day for the past several days. Therefore, it is very likely that he will win today.

Inductive Weak *Robert is probably a rotten player who will continue to lose as long as he plays this game. In any event, there is very little reason to think that he will win today.

This cash register drawer contains over 100 coins. Three coins selected at random were found to have dates earlier than 1960. Therefore, probably all of the coins in the drawer have dates earlier than 1960.

Inductive Weak *This argument is a generalization, hence it is inductive. But the sample is too small to support the conclusion.

When a cook cannot recall the ingredients in a recipe, it is appropriate that she refresh her memory by consulting the recipe book. Similarly, when a student cannot recall the answers during a final exam, it is appropriate that she refresh her memory by consulting the textbook.

Inductive Weak *This is an argument from analogy, which makes it inductive. However, if you assume the premise is true, it is not probable that the conclusion is true.

The picnic scheduled in the park for tomorrow will most likely be cancelled. It's been snowing for six days straight.

Inductive Strong

A cogent argument must be inductively strong.

True

A strong argument may have false premises and a probably false conclusion.

True

A valid argument may have a false premise and a false conclusion.

True

A valid argument may have a false premise and a true conclusion.

True

If a deductive argument has true premises and a false conclusion, it is necessarily invalid.

True

Inductive arguments allow for varying degrees of strength and weakness.

True