Review of Conditional Syllogism; Hypothetical Syllogism
Let's review what we have discussed thus far in chapter four. We have been discussing compound claims, that is, claims that consist of one or more claims, but which must be viewed as one claim to assess their truth. We have discussed two types of compound claims, "either-or" claims, those that are expressed "Either A or B," and conditionals, those expressed as If A, then B. With both types of compound claims, we discussed the contradictory of a claim.
Remember that the contradictory of a claim has the opposite truth value of the original claim: when the original claim is true, then the contradictory must be false; and, when the original claim is false, the contradictory must be true.
Test your memory: (don't' look at your notes or book) Which of the following is the contradictory of Either A or B? (Click on the O beside the correct answer.)
Neither A nor B O
Not A nor Not B O
Not A and Not B. O
Not A but B O
A, but not B. O
To discuss an example of the contradictory of an "either - or" claim, click here.
Test your memory again: (don't look at your notes or book) Which of the following is the contradictory for If A, then B?
If not A, then not B. O
If A, then not B. O
If not B, then not A. O
A, but not B O
Neither A nor B. O
For a discussion of a specific example of the contradictory of a conditional, click here.
We have also said that from an "either-or" claim we can develop an argument form or pattern that will always be valid. That form is: Either A or B, Not A, Therefore B. We call this argument pattern disjunctive syllogism or excluding alternatives. We must beware, as we also pointed out, of the use of the disjunctive syllogism to create a false dilemma. An individual is guilty of creating a false dilemma if he or she tries to make you choose between only two alternatives, when there are other possible alternatives.
We have spent a considerable amount of time talking about four argument forms or patterns that can be derived from a conditional claim. Two of these forms are valid and two are invalid. Test yourself: Without looking at your notes or book, write the four patterns. You should know them by now. Click here to get a quick reminder.
If A, then B.
If B, then C.
Therefore if A, then C.
If we know, for example, that if Victor comes to the dance, then Tasha will be there. And if we know that if Tasha comes to the dance, then Angela will be there too. Then we know that if Victor comes, then Angela will be there too.
Consider the following argument to see if you can identify the chain argument pattern:
If more students enroll at FSU, then the University will have more funds. The University has already said that if it receives increased funding, then it will spend those additional funds on increasing the number of computers laboratories. Therefore, if more students enroll at FSU, the University will increase the number of computer laboratories.
Identify the A, B, and C and then identify the pattern. Write it out in your notes and then click here to check your answer.
Consider the following example. See if you can find the A, B, and C and the pattern.
If Dana is sick, then Demetrius will not be in class today. I say this because if Demetrius is sick, then he will not be in class today and if Dana is sick, then Demetrius is sick also.
After you have tried to complete this on your own, click here to see the answer. (Don't look at the answer before you try it on your own!)
Please note that the argument forms we have discussed can be combined. Consider the following example.
If 90% of Professor X's students fail his courses, then either he is a bad teacher or 90% of the students are bad students. But since, it is impossible that 90% of the students are bad, he must be a bad teacher. And if Professor X is a bad teacher, then he should not be promoted.
See if you can find the patterns (there are more than one) in this argument. Note: The conclusion is not stated. After you have tried the problem, click here to see the answer. (Don't sneak a peak before you've tried on your own!)
We saw earlier that the disjunctive syllogism can be used to create a bad argument that we called a false dilemma. Similarly, the form of the chain argument can be used to create a bad argument which we call "slippery slope." A slippery slope argument is a chain argument with one or more conditionals that are either false or dubious.
Consider the following example:
If we legalize abortion, then it won't be long before doctors will think it's okay to commit euthansia. And if doctors are free to commit euthansia, then elderly people, chronically sick people, mentally retarded people will not be safe. So, if we permit abortion, then before you know it we will be another Nazi Germany.
Consider another example:
If you start watching soap operas, then you will become addicted to them. If you become addicted to them, then you will allow your other work to go unattended. And, if you do that, you will have to drop out of school, and if you drop out of school, then your life will be ruined. So, if you start watching soap operas, then your life will be be ruined.
How should respond to this argument? Write an answer, and then click here to see an example of a response.