Analysis - Inductive and Deductive Arguments

Analysis: Deductive & Inductive Arguments

DEDUCTION & INDUCTION

Deductive Argument

DEDUCTIVE ARGUMENTS DEDUCTIVE ARGUMENTS try to PROVE their

conclusions with rigorous, inescapable logic.

Example 1:

All humans are mortal Socrates is human Therefore, Socrates is mortal

Example 2: If the Queen lives in Buckingham Palace, then

she lives in London. The Queen does live in Buckingham Palace So, the Queen lives in London.

DEDUCTIVE ARGUMENTS Notice how the conclusions of these arguments flow

from the premises with a kind of inescapable logic.

Each conclusion follows necessarily from the premises; this means that, given the premises, the conclusion could not possibly be false.

Arguments are deductive when their premises are intended to provide this kind of rigorous, airtight logical support for the conclusions.

EXERCISE Instruction: Solve the following mini-mysteries on your

own, using your own native reasoning abilities. Then discuss your solutions your classmate sitting next to you.

Either Alain was the murderer, or Stephen was the murderer.

If Stephen was the murderer, then traces of cyanide should have been found on the body.

No traces of cyanide were found on the body.

Who is the murderer??

EXERCISE

The following logic problems are slightly more difficult than the ones in the previous exercise. See if you can solve the problems on your own, then discuss solutions with a partner.

EXERCISE At a picnic, Mike went for soft drink for Amy, Brian, Lisa, and Bill, as

well as himself. He brought back iced tea, grape juice, Diet Coke, Pepsi, and 7-up.

Mike doesn't like carbonated drinks.

Amy would drink either 7-up or Pepsi.

Brian likes only sodas.

Lisa prefers the drink she would put lemon and sugar into.

Bill likes only clear drinks.

What drinks did Mike bring for each person?

EXERCISE Mr. Green, Mr. Red, and Mr. Blue were at the

Cafeteria eating lunch. One of the men was wearing a red suit; one man was wearing a green suit; and the other was wearing a blue suit. "Have you noticed," said the man wearing the blue suit, "that although our suits have colors corresponding to our names, not one of us is wearing a suit that matches our own names?" Mr. Red looked at the other two and said, "You’re absolutely correct." What color suit is each man wearing?

Inductive Argument

INDUCTIVE ARGUMENTS Inductive arguments simply claim that their

conclusions are likely or probable given the premises offered.

Example 1:

Polls show that 75% of Republicans favor a school prayer amendment.

Joe is a Republican.

Therefore, Joe probably favors a school

INDUCTIVE ARGUMENTS Example 2:

The bank safe was robbed last night.

Whoever robbed the safe knew the safe’s combination.

Only two people know the safe’s combination: Lefty and Bugsy.

Bugsy needed money to pay his gambling debts.

Bugsy was seen sneaking around outside the bank last night.

It is reasonable to conclude, therefore, that Bugsy robbed the safe.

KEY DIFFERENCES BETWEEN DEDUCTIVE AND INDUCTIVE ARGUMENTS

Deductive arguments claim that…

If the premises are true, then the conclusion must be true.

The conclusion follows necessarily from the premises.

The premises provide conclusive evidence for the truth of the conclusion.

It is impossible for the premises to be true and the conclusion false.

It is logically inconsistent to assert the premises and deny the conclusion, meaning that if you accept the premises, you must accept the conclusion.

KEY DIFFERENCES BETWEEN DEDUCTIVE AND INDUCTIVE ARGUMENTS Inductive arguments claim that…

If the premises are true, then the conclusion is probably true.

The conclusion follows probably from the premises.

The premises provide good (but not conclusive) evidence for the truth of the conclusion.

It is unlikely for the premises to be true and the conclusion false.

Although it is logically consistent to assert the premises and deny the conclusion, the conclusion is probably true if the premises are true.

The Indicator Word Test

THE INDICATOR WORD TEST DEDUCTION INDICATOR WORDS:

Certainly Definitely Absolutely Conclusively It logically follows that It is logical to conclude that This logically implies that This entails that

THE INDICATOR WORD TEST

INDUCTION INDICATOR WORDS:

Probably Likely It is plausible to suppose that It is reasonable to assume that One would expect that It is a good bet that Chances are that Odds are that

The Strict Necessity Test

THE STRICT NECESSITY TEST The strict necessity test can be stated as follows:

An argument’s conclusion either follows with strict logical necessity from its premises or it does not.

If the argument’s conclusion does follow with strict logical necessity from its premises, the argument should always be treated as deductive.

If the argument’s conclusion does not follow with strict logical necessity from its premises, the argument should normally be treated as inductive.

THE STRICT NECESSITY TEST

Now let’s apply this test to a couple of examples. Consider the following arguments:

Alan is a father. Therefore, Alan is a male. Jill is a six year old girl. Therefore, Jill cannot

run a mile on one minute flat.

So, which argument is deductive and which is inductive?

Common Patterns inDeductive & Inductive Arguments

COMMON PATTERNS OF DEDUCTIVE REASONING

There are FIVE COMMON PATTERNS of deductive reasoning:

Hypothetical syllogism Categorical syllogism Argument by elimination Argument based on mathematics Argument from definition

COMMON PATTERNS OF DEDUCTIVE REASONING HYPOTHETICAL SYLLOGISM

A syllogism is simply a three-line argument, an argument that consists of exactly two premises and one conclusion.

Example: (Modus Ponens)

If A, then B. A. Therefore, B.


Other common varieties of hypothetical syllogism include the following:

Chain argument Modus tollens (denying the

consequence) Denying the antecedent Affirming the consequent

COMMON PATTERNS OF DEDUCTIVE REASONING Chain Arguments:

If A, then B. If B, then C. Therefore, if A, then C.

Example: If Raikonen don’t stop for fuel soon, then he will run out of fuel. If he run out of fuel, then he will lose the race. Therefore, if he don’t stop for fuel soon, he will lose the race.


Modus tollens: (denying consequent)

If A, then B. Not B. Therefore, not A.

Example: If we are in Dundee, then we are in Scotland. We are not in Scotland. Therefore, we are not in Dundee.

COMMON PATTERNS OF DEDUCTIVE REASONING Denying the antecedent:

If A, then B. Not A. Therefore, not B.

Example: If Patricia Cornwell wrote DaVinci Code, then she is a great writer. Patricia Cornwell did not write DaVinci Code. Therefore, Patricia Cornwell is not a great writer.

COMMON PATTERNS OF DEDUCTIVE REASONING Affirming the consequent:

If A, then B. B. Therefore, A.

Example: If we are on Neptune, then we are in the solar system. We are in the solar system. Therefore, we are on Neptune.

COMMON PATTERNS OF DEDUCTIVE REASONING CATEGORICAL SYLLOGISM

This is another patter of deductive reasoning. A categorical syllogism may be defined as a three-line argument and each statement begins with the word all, some or no.

Examples 1: All oaks are trees. All trees are plants. So, all oaks are plants.


CATEGORICAL SYLLOGISM

Examples 2: Some Democrats are elected officials. All elected officials are politicians. Therefore, some Democrats are politicians.


ARGUMENT BY ELIMINATION

This reasoning seeks to logically rule out various possibilities until only a SINGLE possibility remains OR such arguments is to logically exclude every possible outcome except ONE, such arguments are always deductive.

COMMON PATTERNS OF DEDUCTIVE REASONING ARGUMENT BY ELIMINATION

Example 1: Either Micah walked to the college or he drove. But Micah did not drive to the college. Therefore, Micah walked to the college.

Example 2: Either Adrian committed the murder, or Johnson committed

the murder, or Catherine committed the murder. If Adrian or Johnson committed the murder, then the weapon

was a rope. The weapon was not a rope. So, neither Adrian nor Johnson committed the murder. Therefore, Catherine committed the murder.

COMMON PATTERNS OF DEDUCTIVE REASONING ARGUMENT BASED ON MATHEMATICS

Mathematics is a model of logical, step-by-step reasoning. The arguments prove that the conclusion is on the basis of precise mathematical concepts or reasoning.

Example 1: Eight is greater than four. Four is greater than two. Therefore, eight is greater than two.

Example 2: Light travels at a rate of 186,000 miles per second. The sun is more than 93 million miles distant from the

earth. Therefore, it takes more than eight minutes for the sun’s

light to reach the earth.

COMMON PATTERNS OF DEDUCTIVE REASONING BUT!!!!! CAN ARGUMENT BASED

ON MATHEMATICS BE INDUCTIVE ARGUMENT???? YES!!!

EXAMPLE: My blind uncle told me that there

were 8 men, 6 women and 12 kids at the party.

By simple addition, therefore, it follows that there were 26 people at the party.


ARGUMENT FROM DEFINITION

In this argument, the conclusion is presented as being “true by definition”, from some key word or phrase used in the argument.

Example 1: Alex is a cardiologist. Therefore, Alex is a

doctor.

Example 2: Jane is an aunt. It follows that she is a woman.

END. COMMON PATTERNS OF DEDUCTIVE REASONING. NEXT, COMMON PATTERNS OF INDUCTIVE REASONING!

COMMON PATTERNS OF INDUCTIVE REASONING

There are SIX (6) common patterns of inductive reasoning.

INDUCTIVE GENERALIZATION

PREDICTIVE ARGUMENT

ARGUMENT FROM AUTHORITY

CAUSAL ARGUMENT

STATISTICAL ARGUMENT

ARGUMENT FROM ANALOGY


INDUCTIVE GENERALIZATION

An inductive generalization is an argument in which generalization is claimed to be probably true based of information about some members of a particular class.

COMMON PATTERNS OF INDUCTIVE REASONING INDUCTIVE GENERALIZATION

Example 1: All dinosaur bones so far

discovered have been more than 65 million years old.

Therefore, probably all dinosaur bones are more than 65 million years old.

COMMON PATTERNS OF INDUCTIVE REASONING INDUCTIVE GENERALIZATION

Example 2: Eight months ago I met a doctor from

Perth, and he was friendly. Five months ago I met a car mechanic

from Perth, and he was friendly. Three months ago I met a waitress from

Perth, and she was friendly. I guess most people from Perth are

friendly.


PREDICTIVE ARGUMENT

A prediction is a statement about what may or will happen in the future. A prediction is defended with reasons. This is among the most common patterns of inductive reasoning.


PREDICTIVE ARGUMENT

Example 1: It has rained in Toronto every February

since weather records have been kept. Therefore, it will probably rain in Toronto

next February.


PREDICTIVE ARGUMENT

Example 2: Most U.S. presidents have been tall. Therefore, probably the next U.S.

president will be tall.

COMMON PATTERNS OF INDUCTIVE REASONING ARGUMENT FROM AUTHORITY

An argument from authority asserts a claim and then supports that claim by citing some presumed authority or witness who has said that the claim is true.

Because we can never absolutely certain that a presumed authority or witness is accurate or reliable, arguments from authority should normally be treated as inductive.

COMMON PATTERNS OF INDUCTIVE REASONING Examples:

More Americans die of skin cancer each year than die in car accidents. How do I know? My doctor told me.

Malaysia is a safe place for everyone, according to a statement from a minister.


CAUSAL ARGUMENT

A causal argument asserts or denies that something is the cause of something else.

Example 1: I cannot receive my emails. The

network must be down.

COMMON PATTERNS OF INDUCTIVE REASONING Example 2:

Medical care is the number one cause of sudden rapid aging among middle-aged people. Ask yourself how many times you have heard somebody tell you a story like this: “Ralph was feeling fine, no problems at all, and then he went in for a routine physical checkup, and the next thing we heard he was in critical condition with the majority of his internal organs sitting in a freezer in an entirely different building.”

COMMON PATTERNS OF INDUCTIVE REASONING STATISTICAL ARGUMENT

A statistical argument rests on statistical evidence, that is, evidence that some group has some particular characteristic.

Because statistical evidence is generally used to support claims that are presented as probable rather than certain, statistical arguments are usually inductive.


85% students of the high school are color blind.

Alan is one of the student there.

So, Alan is probably color blind.

COMMON PATTERNS OF INDUCTIVE REASONING ARGUMENT FROM ANALOGY

An analogy is a comparison of two or more things that are claimed to be alike in some relevant respect.

In an argument from analogy, the conclusion is claimed to depend on an analogy (i.e., a comparison or similarity) between two or more things.


Alvin is a graduate of Hawaii Pacific University, and he is bright, energetic, and dependable.

Aaron is a graduate of Hawaii Pacific University, and he is bright, energetic, and dependable.

Evangeline is a graduate of Hawaii Pacific University.

Therefore, most likely, Evangeline is bright, energetic, and dependable too.

Education

Analysis - Inductive and Deductive Arguments