The Little Blue Reasoning Book - Brandon Royal [39]
The following appeared as part of a campaign to sell advertising to local businesses through various Internet service providers.
“The Yuppie Café began advertising on the Internet this year and was delighted to see its business increase by 15% over last year’s total. Their success shows that you too can use the Internet to make your business more profitable.”
Analyze the above argument according to classic argument structure, identifying the conclusion, evidence, and at least three assumptions. How persuasive do you find this argument? What would make this argument more persuasive?
Chapter 5
Mastering Logic
When you have eliminated the impossible,
whatever remains, however improbable,
must be the truth.
— Sherlock Holmes
OVERVIEW
This chapters focuses on four interrelated topics:
1. “If … then” statements
2. “No-some-most-all” statements
3. Mutual inclusivity and exclusivity
4. Logical equivalency statements
To introduce formal logic, consider the following statements:
Original: If you work hard, you’ll be successful.
Now ponder these related statements.
Statement 1: If you’re successful, then you’ve worked hard.
Statement 2: If you don’t work hard, you won’t be successful.
Statement 3: If you’re not successful, then you didn’t work hard.
The question becomes: Which of the above statements are logical deductions based on the original statement above?
Upon closer examination, statement 1 isn’t necessarily correct. The fact that you’re successful (whatever this means!) doesn’t mean that you have necessarily worked hard. There could be several other ways to become successful. For example, perhaps you’re skillful, intelligent, or downright lucky.
Likewise, statement 2 is not necessarily correct. Just because you don’t work hard doesn’t mean that you won’t be successful. As already mentioned, you might be skillful, intelligent, or lucky as opposed to hardworking. However, statement 3 is a perfectly logical deduction based on the original. If you’re not successful, then you must not have worked hard. This doesn’t mean, however, that there are not other explanations for why you might not have been successful. For example, perhaps you were neither intelligent in your approach nor skillful or lucky in your application.
“IF … THEN” STATEMENTS
“If … then” statements are another way to represent causal relationships. Take the following generic statement: “If A, then B.” This is sometimes written in a more formulaic manner: i.e., “If A → B.” Consider the statement “If it is U.S. money (dollar bills), then it is green (colored).” This can also be written: If $US → Green. Another way to illustrate an “if … then” relationship is to draw circles. The “If” item always represents the innermost circle while the “then” item always represents the outermost circle. See Exhibit 5.1.
Exhibit 5.1 – Diagramming “If … then” Statements
If it is U.S. money, then it is green (if US$, then Green)
The above diagram illustrates in picture form the relationship between U.S. money and all green things. We can read from the inside circle to the outside circle, but we cannot read from the outside circle to the inside circle. “If U.S. money then green” does not equal “If green then U.S. money.”
What can we logically infer from this type of statement? Exhibit 5.2 contains four statements that may seem to the casual observer all to be inferable. However, only the fourth version is correctly inferable. In “if … then” statements, it is important that you read in one direction only, as the reverse is not necessarily true. Based on the original statement “If it is U.S. money, then it is green,” the only thing we can infer logically from this statement is that it is true that “If it is not green, then it is not U.S. money.”
Exhibit 5.2 – American Money
To master “if … then” statements it is essential to memorize the information contained in Exhibit 5.3. According to formal logic, the contrapositive is always correct. That