TFY Chapter 12

Summary

Deductive reasoning is the process of drawing conclusions from a set of facts. We learn deductive reasoning by studying formal logic. Deductive reasoning differs from inductive reasoning in that inductive reasoning draws an inference from a set of facts, while deductive reasoning evaluates the relationship of facts, called premises. An example of deductive reasoning goes as follows:

All dogs bark. – This is a description of a class, which is dog.
Lassie is a dog. – Lassie is a member of the class.
Lassie barks. – This is the inference made from the premises.

The first two sentences are premises. The third sentence is reasoning of the premises, called a conclusion. The form of the arguments and reasoning is called a syllogism. The first premise is the major premise, and the second is the minor premise. There must be rules for deductive reasoning to determine validity and soundness. The conclusion above is valid because Lassie is a member of a class that barks. However, in invalid conclusion can be reached if the following premises are followed:

All dogs bark.
Lassie barks.
Lassie is a dog.

It is not valid to conclude that Lassie is a dog. Lassie may be another animal that barks. Soundness is the result of premises being true and the conclusion being correct. The second syllogism is unsound because, while the facts are true, the conclusion is faulty. But, premises and conclusions are not always explicitly syllogisms. I bought a Toyota because I think Toyotas are good cars, so when I was shopping for a car, a syllogism went as follows:

All Hondas are good cars.
This car is a Honda.
This is a good car.

This deductive reasoning may be unconscious, but it may be the reason you buy the car. Many decisions are made this way.

Exercises

1. A premise is a reason given to support a conclusion.

True

2. Syllogisms are used in logic because logicians like to make their knowledge arcane, or hidden and secret.

Syllogisms are used in logic because logicians like to make their arguments clearly visible for study and review.

3. Logic is less concerned with truth than with whether one statement follows reasonably from another.

True

4. Reasoning only occurs in deduction – not in induction.

Reasoning occurs in deduction as well as in induction

5. A generalization reached through induction can be a premise used in a deductive syllogism.

True

6. “All homeowners are taxpayers. He is a property owner. Therefore, he is a taxpayer.” This is a valid argument.

True

7. “Bloodletting reduces fever. This patient has a fever. This patient needs bloodletting.” This syllogism shows valid reasoning although both premises may not be true.

True

8. “White-skinned people are superior to dark-skinned people. Therefore, it is manifest destiny of white-skinned people to rule dark-skinned people.” No country could ever accept such fallacious reasoning as this.

This fallacious reasoning, accepted in the past, has been rejected in the vast majority of nations, but may still exist.