Logical syllogisms
Contrast the notions of truth and validity in terms of the following two syllogisms:
(a) Some sound arguments are not valid since all arguments with mood and figure EIO-4 are sound.
(b) Some arguments with true premises and a true conclusion are arguments with mood and figure IOO-3 and some arguments with mood and figure IOO-3 are not sound so we know that some arguments with true premises and a true conclusion are not sound.
Put both arguments in standard logical form and provide the mood and figure for each syllogism. You do not have to explain how you put either argument in standard logical formjust do it. (While the first syllogism mentions EIO-4 and the second syllogism mentions IOO-3, neither syllogism has these forms. They have different forms.) Determine the validity or invalidity of each syllogism by using both a Venn diagram and Salmons rules (you must use all three of Salmons rules.) Explain why each statement (the two premises and conclusion) in each argument is true or false. Is either argument sound? When you discuss why the premises and conclusion are true for each syllogism, you only need to use one technique to prove that EIO-4 and IOO-3 are valid or invalid.
Additional Instructions
1. You must put each argument in standard logical form as categorical syllogisms. This means that you must use the variables S,P, and M. The S,P, and M must appear in the appropriate locations in the argument. You must also provide either either a dictionary or an instance along with the form. Your reader needs to know what S, P, and M stand for. And you need this when you explain why each statement is true or false.
2. The terms for S,P and M may be fairly long. You will be using terms such as arguments with mood and figure EIO-4. This is longer than cats and dogs.
3. The first argument is an enthymeme. You are not given all three statements. You will need to infer the missing statement. Use the hints. Remember, in this class, you should infer the missing statement so that you end up with a valid form. The second argument is not an enthymeme and it is invalid.
4. When you discuss EIO-4 and IOO-3, you are required to give the forms (at least once.) I want to see that you can provide the form when given a mood and figure. If I do not see the form, I will mark down. Generally, we cannot reconstruct a form from Salmons rules (the same set can apply to more than one form.) Do not present these forms before you discuss why certain premises are true or false. If you discuss these forms before you present either arguments (a) or (b) in standard logical form, then it shows that you do not know how to analyze arguments. You are muddling your discussion.
5. When you discuss why each premise and each conclusion for each argument is true or false, give a paragraph for each statement. This way, you are less likely to skimp on the discussion. Do not discuss premise 2 before premise 1 and do not discuss both premises and the conclusion in one big paragraph. Discuss the material in detailyour reader should not have to infer anything.
6. Give examples when relevant. We are training you to give examples. The examples are the proof or evidence that often justifies your explanation. Your examples should be categorical syllogisms.
7. You do not need to obvert, contrapose, or convert any statement.
8. Arguments are generally single-spaced and indented. Other than this, I dont worry about whether you double-space or single-space material. Do not present an argument in this way: all cats are dogs. No dogs are mice. Thus, no mice are cats.
Present arguments in this way:
All cats are dogs
No dogs are mice
No mice are cats
(I dont worry about the line separating the premises from the conclusion.
9. Good writing counts. Your paper should be clear and well-organized.
