Chapter 1 Supplement: (Be sure to read Chapter 1 before reading this supplement.)
 

In addition to helping you see logic as a practical tool, one of the most important goals of this chapter is to begin the process of having you understand what logic is and what it is not. Many students will probably enter this class believing that being logical means being always right and successful. Similarly, they will want to think of valid and invalid arguments in black and white terms. That validity is always associated with truth and invalidity is always associated with falsehood. It is difficult, but very important, to see that the practical value of logic is less immediate and more abstract. In this regard, every effort should be made to see that valid arguments do not guarantee truth unless you start with it in the premises, and that valid arguments may have false conclusions but that this implies a test of the premises.

Related to this understanding is the transformation that should be made in many students from what I call categorical thinking to hypothetical thinking. Most students, and probably most people for that matter, react very holistically to a controversy, argument, discussion, or claim. One of the reasons students have trouble with the notion of validity is that the examples in Chapter 1 require that they not react to an argument as a whole, but separate the reasoning from the content. They must judge the premises hypothetically, pretending momentarily that they are true rather than deciding immediately and conclusively whether they believe they are true. They must understand that once the implications of the premises are understood and the argument is judged to be valid or invalid, then they can shift mental gears so to speak and judge the content. Because of their categorical judgmental tendencies, students react immediately to the premises. Again and again it must be stressed that judging the reasoning does not mean judging the truth of the premises. Students must be reminded that the focus is always the same. If these premises are true, what follows? What are the premises saying and what are they not saying? And does the conclusion square with what the premises are saying.

The blind man example is a warm-up exercise for the more technical presentation of validity that follows. You can understand that because he is blind, z does not know for sure if his premises are all true. Some students, however, will need some help understanding all the reasoning steps. Every student will get the first step: The only way x could be deductively sure what color hat he has on would be if he saw two red hats. Since he said that he could not tell what color hat he had on, we know that he did not see two red hats. However, some students will fail to "hold on" to this thought while contemplating y's situation and response. What must be stressed at this point is that once x says "no," everyone knows that x saw at least one white hat. If both can't be red on y and z, then one has to be white. The one-eyed man (y) knows that x did not see a red hat on his (y's) head and simultaneously a red hat on the blind man (z). So, he is hoping to see a red hat on the blind man, which would guarantee that he (y) had on a white hat. Because y was not able to deductively conclude the color of his hat, we know that he did not see a red hat on z.

Here are some goals that we should have accomplished in Chapter 1.

Goals:

  1. Connect turning on one's logical ability with using a tool to defend oneself against marketing and political manipulation. Connect logic, empowerment, and self-interest. 

    2. The test items on the first page and the example of buying a car help in this regard. Being logical is like being picky. We don't need to be picky all the time, but when something like buying a car and a lot of money are at stake, it is important to turn on one's picky (critical) ability.

    One should also be very picky when deciding to go to war or not.

    Here is example related to the "up to" trick in advertising.  In the fall of 2002 President Bush was busy making his case to the American people about the necessity of a war with Iraq.  Other than the possession of weapons of mass destruction by Saddam Hussein the claim was made again and again that Al Qaeda and bin Laden were working with Saddam to hurt Americans, even though most intelligence and cultural experts claimed that they were enemies, that Saddam had persecuted Shiite Muslims for many decades (bin Laden is Shiite) and that Saddam was not likely to give any biological, chemical, and/or nuclear weapons, if he had any, to someone like bin Laden who might use them against him.

    So, in a speech on October 7, 2002 Bush stated that as for the Saddam-Osama link there were "high-level contacts that go back a decade."  In the context of Bush's speech the insertion of this phrase made it seem that there was a dangerous ongoing relationship.  But similar to the "up to" phrase, this phrase is vague and to be minimally true all one had to establish was that a decade ago there were some contacts.  In fact, all that any intelligence agency could establish was that there were contacts between Saddam and a just developing Al Qaeda organization in the early 1990s.  There was no evidence that Saddam was involved in 9/11 or that there was any current contact with bin Laden's organization.  Eventually Bush was forced to admit publicly that there was no evidence that Iraq was involved in 9/11.
     

  2. Understand what deductive validity is and what it is not. 

    3. We will be using the concept of validity repeatedly throughout the semester and it will haunt you again and again in terms of understanding other concepts and, of course, performance on future tests if you don't make an effort to thoroughly understand it now.  

  3. Understand that the use of valid reasoning forces us to test our beliefs. Connect the technical points of valid and invalid arguments with a philosophical commitment to the value of critical thinking, testing beliefs, and individual growth and self-actualization.


Although this model is somewhat oversimplified, from one point of view our actions are like conclusions from a web of beliefs. If we reason validly, but don't like the way our conclusions turn out, then we have tested our beliefs -- we know that there is a problem with at least one of them. On the other hand, if we don't reason validly, then we will know nothing about our beliefs when the conclusions don't turn out the way we predicted.

There is a value judgment involved in the worth of being logical -- one that can be traced back to the culture of the ancient Greeks. We are assuming, as did the ancient Greeks, that it is good to test our beliefs. Not every culture has agreed with this judgment and it could be wrong. However, I don't believe it is and the book assumes the stance that in the long run we grow as individuals by testing our beliefs, even though the process is not always pleasant.

Below are some more examples of valid and invalid arguments.  To judge if each is valid or invalid, ask the question, "If the premises are true, would we be locked in to accepting the conclusion?"  If the answer is "yes," then the argument is valid.  If the answer is "no," then the argument is invalid.  Remember that both examples on page 20 are valid, even though it is not true that Sandy Beach is south of Kona, etc.  What matters is that "if" the premises in both arguments were true, we would be locked in to accepting the conclusion as true.  Also, both examples on page 21 are valid, even though the people who are likely to make either of these arguments (Pro-choice vs. Pro-life) do not agree on the conclusions.  The arguments are still valid.  However, if they disagree on the conclusion, they must disagree with at least one of the premises.

More Valid and Invalid Examples:

#1

Anyone who lives in the city Honolulu, HI also lives on the island of Oahu.

Kanoe lives on the island of Oahu.

Therefore, Kanoe lives in the city Honolulu, HI.
 

#2

Anyone who lives in the city Honolulu, HI also lives on the island of Oahu.

Kanoe does not live on the island of Oahu.

Therefore, Kanoe does not live in the city Honolulu, HI.
 

#3

Anyone who lives in the city Honolulu, HI also lives on the island of Oahu.

Kanoe does not live in the city Honolulu, HI.

Therefore, Kanoe does not live on the island of Oahu.
 

#4

Anyone who lives in the city Honolulu, HI also lives on the island of Oahu.

Kanoe lives in the city of Honolulu, HI.

Therefore, Kanoe lives on the island of Oahu.

#5                                                                                #6

All crows are black.                                          Only crows are black.

John is black.                                                    John is black.

Therefore, John is a crow.                                Therefore, John is a crow.
 

Remember the key to judging deductive arguments to be valid or invalid is not whether the premises are true or false. Rather, the question is what are the premises saying and what are they not saying, and whether if they were true would the conclusion be true. If the answer is yes, then the argument is valid. If the answer is no, then the argument is invalid.

Answers:

#1 Invalid

#2 Valid

#3 Invalid

#4 Valid

#5 Invalid

#6 Valid
 

After you do at least some of the problems in Exercise III, take the practice quiz.  Please note the details of a complete answer.  My answers to #s 1 and 5 to Exercise III (pp. 36-37) follow the following format:

Valid or Invalid?  Give the definition (p. 18 or 22).  Explain how the definition fits by explaining what the premises are saying, if valid, or what the premises are not saying, if invalid.  Finally, answer the follow-up question or questions.  (The follow-up question is right after the question, "valid or invalid?")

Hint -- Why Logicians Don't Think

Finally, although it is not necessary at this stage, as a preparation for our coverage of symbolic logic, you should know how professional logicians would figure out if these arguments are valid or invalid.  They would not be thinking.  They especially would not be thinking hard as you will be.  Mostly what any logician would be doing is staring at the underlying PATTERN that exists for any argument.  By simply recognizing the pattern, a logician would know instantly if the argument is valid or invalid.

For instance, for #1 above that pattern is:

For any x, if x is an A, then x is a B.
x is a B.
So, x is an A.

Or simplified:

If A, then B.
B
So, A

These patterns are ALWAYS invalid, so any argument that fits one of these patterns is always invalid.

For #2, the pattern is:

For any x, if x is an A, then x is a B.
x is not a B.
So, x is not an A.

Or simplified:

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

These patterns are ALWAYS valid.

For #3, the pattern is:

For any x, if x is an A, then x is a B.
x is not an A.
So, x is not a B.

Or simplified:

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

These patterns are ALWAYS invalid.  For a local joke that illustrates this invalid argument, click here.

For #4, the pattern is:

For any x, if x is an A, then x is a B.
x is an A.
So, x is a B.

Or simplified:

If A, then B.
A
So, B.

These patterns are ALWAYS valid.

Can you see how #5 has the same pattern as #1?  Invalid.

As for #6, it is really the pattern of #4 in disguise.  Here is the trick to all "Only" statements.  To say that "Only C's are B's" is the same as saying "All B's are C's."  So #6 has the pattern:

For any x, if x is a B, then x is a C.
x is a B.
So, x is a C.

Or simplified:

If B, then C.
B.
So, C.

The initial judgment of valid or invalid for Ex. III and the practice quiz will be much easier if you know how to look for patterns.