DeductionInductionFallacies

The basic aim of deductive reasoning is to start with some assumption or premise and extract from it a conclusion—a logical consequence—that is concealed but implicit in it.

Thus: 1a. Nuclear power poses more risks of harm to the

environment than fossil fuels. 1b. Fossil fuels pose fewer risks of harm to the

environment than nuclear power. We may infer 1b from 1a. The premise, 1a, implies the conclusion, 1b.

However, the inference does not depend upon the truth of the premise.

Another example: 2a. President Truman was underrated by his critics. 2b. His critics underrated President Truman.

Both propositions are equivalent, because the rules of English grammar permit us to shift the subject/predicate phrases without changing the conditions that make the proposition true.

Remember: Even if a proposition follows from another

proposition, they need not be true.

If we propose that: 3a. The Gettysburg Address is longer than the

Declaration of Independence. We know that 3a is false, but we may validly

deduce that: 3b. The Declaration of Independence is

shorter than the Gettysburg Address. However, the inference is valid, because

conclusion follows logically (viz., deductively) from 3a.

Rule: Valid conclusions are not necessarily true.

Texas is larger than California. (1st Premise)

California is larger than Arizona. (2nd Premise)

Texas is larger than Arizona. (Conclusion)

Rule: The conclusion is derivable from the two premises. If the two premises are true, then the conclusion must be true.

The concept of being larger than has a quality called transivity.

For example: If A > B If B > C Then A > C

Therefore, it follows from the premises that: If Texas is larger than California. If California is larger than Arizona. Then Texas is larger than Arizona.

The validity of deductive inference is a formal property of argument.

This syllogism is valid: African American slaves were treated worse

than white indentured servants. Indentured white servants were treated worse

than free white labor. Therefore, African American slaves were

treated worse than free white labor.

If A, then B. A Then, B. So, based upon the previous syllogism:

If a youth is an African American slave, he is probably treated worse than a youth in indentured service.

This youth is an African American slave. Therefore, he is probably treated worse than if

he had been an indentured servant.

Valid deductive arguments that can only be true if they have meaning.

The form of this syllogism is valid, but the syllogism is not true, because it has no meaning. If the slithy toves, then the gyres gimble. The slithy toves. Therefore, the gyres gimble.

False or meaningless conclusions can be drawn from false or meaningless assumptions. The Met has the finest collection of abstract

impressionist paintings in the world. The finest collection of abstract impressionist

paintings includes dozens of canvasses by Winslow Homer.

Therefore, the Met has dozens of paintings by Winslow Homer.

The conclusion follows, but all of the propositions may be false.

If President Truman knew the Japanese were about to surrender, then is was immoral for him to order that the atom bombs be dropped on Hiroshima and Nagasaki.

Truman knew the Japanese were about to surrender.

Therefore, it was immoral of him to order dropping those bombs.

The second premise (Truman knew) may be true on moral grounds, not historical grounds.

The first premise (If Truman knew, then he was immoral to drop the bombs), implies a principle of moral responsibility. The truth of the conclusion, therefore, relies on

our acceptance of a general rule of moral responsibility.

To the extent we accept the premises as true, then we decide if the premises prove the conclusion.

Either censorship of television shows is overdue, or our society is indifferent to the education of its youth.

Our society is not indifferent to the education of its youth.

Therefore, censorship of television is overdue. Assert a disjunction with two or more disjuncts

in the major premise; then deny all but one in the minor premise; and infer the validity of the remaining disjunct as the conclusion.

Dilemmas occur when a forced choice between two or more equally unattractive alternatives. If the U.S. bombs targets in Libya, innocent people

will be killed, and the Arab world will be angered. If the U.S. doesn’t bomb Libyan targets, then

terrorists won’t be punished, and the U.S. will lose respect among other governments.

Either the U.S. bombs Libyan targets or it doesn’t. Therefore, unattractive consequences will follow: the terrorists will be killed, or terrorists will go unpunished.

If the President bombs terror sites in an African country, she will prevent a horrible genocide.

If the President bombs the terror sites, African terrorists (who have a top-secret air-traffic control device) will down all American planes in flight—thereby killing thousands of Americans.

Either the President will bomb the terror sites or not. Unattractive consequences will follow: genocide will be prevented or Americans will die.

If Sophie chooses one of her children to die in the gas chambers of Auschwitz, she and the other child will live.

She will suffer, no matter whom she chooses.

She will either choose her son or daughter. She will suffer. One of them will die in a gas chamber.

Were there any ways out of the dilemma?