Logic For Dummies, 2nd Edition

Chapter 15

Expressing Quantity with Quality: Quantification Logic

IN THIS CHAPTER

Getting an overview of quantification logic (QL)

Going beyond SL with the universal and existential quantifiers

Distinguishing statements from statement forms

In Chapter 3, I show you that logic is all about deciding whether an argument is valid or invalid. So, if you’ve read Chapter 3 and I ask you to take a look at the following argument, you can probably tell me that it’s a perfectly valid argument.

Premises:

• All of my children are honest.
• At least one of my children is a lawyer.

Conclusion:

At least one honest lawyer exists.

This argument is indeed valid. However, the problem arises when you try to use sentential logic (SL) to show that it’s valid. None of these three statements contains familiar words such as and, or, if, or not, so you can’t use the five SL operators to express them.

The best you can do is express the statements as SL constants. For example:

• Let C = All of my children are honest.
• Let L = At least one of my children is a lawyer.
• Let H = At least one honest lawyer exists.

After you express the statements as constants, you can put together the following argument:

C,