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Chapter FiveThe Logic Machine: Deductive and Inductive Reasoning

Second Thoughts, 4th. ed.Wanda TeaysMcGraw-Hill Higher Ed.

© 2010. Wanda Teays. All rights reserved.

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Inductive ArgumentsIn an inductive argument the evidence alone is

not enough for the conclusion to be certain, even if the premises are true.

The evidence offers only partial support for the conclusion and, consequently, you cannot be certain that the conclusion is true.

EXAMPLE:63% of people in the GRNGO poll preferred tamales to hot

dogs. Therefore, Max will probably like a tamale when he’s at the Dodger game this weekend.

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Deductive ArgumentsIn a deductive argument the premises are claimed

to be sufficient for the conclusion, that no further evidence is needed in order to draw the conclusion.

When it is asserted or implied that this set of premises sufficiently supports the conclusion, we’ve got a deductive argument.

EXAMPLE:No one who eats eggs for breakfast will want quiche

for lunch. All weight lifters like eggs for breakfast. Therefore, no weight lifter will want quiche for lunch.

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Key Terms in Arguments

An argumentisa group of propositions, some of which (called the premises) act as supporting evidence for another proposition (called the conclusion or thesis).

An inference is a conclusion drawn (hopefully!) on the basis of evidence, though not necessarily supported by that evidence.

Note that the words “inference” and “conclusion” are interchangeable, as are the assertions “I infer” and “I conclude.”

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PropositionsA proposition is an assertion that is either true or

false. A proposition can be expressed in the following form:

Standard Form of a Proposition

SUBJECTis/arePREDICATE

Skunks [subject] are nocturnal animals [predicate].

EXAMPLES:Tigers are ferocious beasts.Today is Wednesday.Mombasa is in Kenya.Dim sum is fun to share.Bruce has nightmares about bats.

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Categorical PropositionsCategorical propositions are in one of the following forms:

All A is B. UNIVERSAL PROPOSITIONSNo A is B.Some A is B. PARTICULAR PROPOSITIONSSome A is not B.72% of golfers are men.

EXAMPLES:No raccoon are creatures that can run fast.All raccoons are animals fond of cat food.Some raccoons are pets.Some raccoons are not well-trained animals.

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Generalizations A generalization is an inference from a smaller group (or one individual) to a larger group. When we generalize we are asserting what is true or false of one or more members of a group to some or all of the group. People often state generalizations as a result of what they see, hear, or learn. For instance, we may see some ducks eating snails and infer that “All ducks eat snails” or “Most ducks eat snails.”

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Value claimsA value-claim is a prescriptive

statement of values—moral, aesthetic, or personal taste.

Value claims cannot be treated like empirical claims that are either true or false, but they can function in arguments.

They are not statements that can be assigned a truth-value (i.e., determined to be either true or false), which is the case with propositions.

Non-PropositionsYikes!”“Where’s my Tweetie costume?”“Congratulations!”

Non-propositions cannot be assigned a truth-value and cannot be assumed to be either true or false for purposes of testing validity

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Key Deductive Arguments

Categorical SyllogismsThese are three-line arguments, consistingof two premises and a conclusion, with all the propositions in the form of categorical propositions.

EXAMPLE:All wrestlers are big, burly men.Some big, burly men are chefs.Therefore, some wrestlers are chefs.

Modus Ponens These are arguments of the form: “If A then B. A is the case. Therefore, B is true also.”

EXAMPLE:If Eric gets a part in Terminator 5, he’ll have to shave his head.Eric got the part! Therefore, he’ll have to shave his head

Modus TollensThese are arguments of the form: “If A then B. B is not the case. Therefore, A is not true either.”

EXAMPLE: If Maria eats another bag of popcorn, she may not feel well. Maria felt fine.Therefore, she did not eat another bag of popcorn.

Disjunctive SyllogismThese are arguments of the form: “Either A or B. Not A. Therefore, B.”

EXAMPLE:Either there’s a skunk in the garage or someone is playing tricks on me.No one is playing tricks on me. Therefore, there is a skunk in the garage.

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More Deductive Arguments

Hypothetical SyllogismThese are arguments of the form: If A then B. If B then C. Therefore, if A then C. 

Constructive Dilemma. These are of the form: If A then B, and if C then D. Either A or C. Therefore, either B or D.

In other words, there’s a choice between two options—if you pick one or the other option, then either of the two effects will happen.

EXAMPLE of Hypothetical Syllogism: If Louie goes to the concert, he’ll miss the ball game.If Louie misses the ball game, he won’t get a chili dog. Therefore, if Louie goes to the concert, he won’t get a chili dog.

EXAMPLE of Constructive Dilemma:

If I go to Miami, I can get some vacation, but if I stay home I can visit with relatives. Either I’ll go to Miami or I’ll stay home. Therefore, either I’ll get some vacation or I’ll visit with relatives.

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Valid vs. Invalid ArgumentsA valid argument is an argument in which the

premises provide sufficient support for the drawing of the conclusion. That is, if we assume the premises were true, the conclusion must also be true.

Validity is not about whether any statements are actually true or not. Validity is about how the argument all fits together.

This is a structural issue, not an issue about what’s true or false. Our goal is to see what happens if we assume the premises to be true. An invalidargument is an argument in which the premises fail to adequately support the conclusion.

We can tell an argument is invalid when the premises could be true and the conclusion false.

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Sound vs. Unsound Arguments

CRITERIA FOR A SOUND ARGUMENT

The argument is valid The premises are actually true.

To check soundness: First check for validity. If the premises were true, is the conclusion forced to be true (it couldn't be false)? If so, the argument is valid. Next check for the truth of the premises. If the premises really were true, the argument is sound.

However, if either condition is not met, then the argument is unsound.

An argument can be unsound if it is valid but doesn’t have true premises. It can be unsound if it has true premises, but is invalid. Or both. If either or both conditions are not met, the argument is unsound.

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Key Inductive Arguments

1 Predictions: In predictions, an argument is made about the future based on past or present evidence.

2 Arguments about the past based on present evidence (also known as retrodiction):In these arguments, an inference is drawn about what happened at some earlier point in time based on current evidence.

3 Cause and effect reasoning:Here it is claimed that an event (effect) is based on one or more causal factors. Given the existence, then, of the causal factor, the effect should follow.

4 Arguments based on analogy: This argument rests on a comparison, from which it is claimed that a characteristic true of the one term in the equation will also be true of the other. In law this usually involves the application of a precedent or legal principle.

5 Statistical reasoning:These arguments draw from sample studies or statistical reasoning, from which an inference is drawn about the targeted population.

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The Wedge of DoubtIn an inductive argument the premises could be

true, but the conclusion will never follow with certainty.

Remember, there is always some wedge of doubt between the premises and the conclusion.

Because of this, inductive arguments are neither valid nor invalid—those terms ONLY apply to deductive arguments.

That then means inductive arguments cannot be sound or unsound either.

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Strength vs. ValidityInductive arguments cannot be assessed for

validity. We can assign them a relative strength—but

they do not fall in the “all-or-nothing” category found with deductive reasoning.

Validity/invalidity, and soundness/unsoundness only apply to deductive arguments.

Inductive reasoning is assessed differently; with induction we are looking for the relative strength of the argument.