Posted: January 26th, 2023

Analyze the following arguments in terms of validity and soundness

Instruction
Please analyze the following arguments in terms of validity and soundness. (a) No valid arguments are arguments with mood and figure OAO-3 since no sound arguments are valid (b) No valid arguments are arguments with mood and figure IOE-4 and some valid arguments are arguments with false premises and a true conclusion; so, we know that some arguments with mood and figure IOE-4 are arguments with false premises and a true conclusion 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. The hints are in the textbook and the course packet. 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. Both arguments (a) and (b) have O statements. Do not drop the word ‘not’. 5. When you discuss OAO-3, and IOE-4, 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 Salmon’s 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. 6. 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 detail—your reader should not have to infer anything. 7. 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. 8. You do not need to obvert, contrapose, or convert any statement. So, don’t do it.  9. Arguments are generally single-spaced and indented. Other than this, I don’t worry about whether you double-space or single-space material. Present arguments in this way: All cats are dogs No dogs are mice No mice are cats (I don’t worry about the line separating the premises from the conclusion. Do NOT present an argument in this way: all cats are dogs. No dogs are mice. No mice are cats
Argument (a)
All arguments with mood and figure OAO-3 are arguments with invalid arguments
No sound arguments are valid arguments
Therefore, all arguments with mood and figure OAO-3 are arguments with unsound arguments
The argument form of the standard logical form for this argument is as follows:
S = arguments with mood and figure OAO-3
P = invalid arguments
M = unsound arguments

Premise 1: All S are P
Premise 2: No P are M
Conclusion: All S are M

In this argument, the premises and conclusion seem to be logically valid and therefore the argument is valid. However, the premises themselves are not necessarily true. The statement “No valid arguments are arguments with mood and figure OAO-3” is a negative universal proposition, which is often considered to be problematic in syllogistic logic. In order to establish the truth of this statement, one would need to show that all arguments with mood and figure OAO-3 are invalid, which is not necessarily the case.

Argument (b)
No valid arguments are arguments with mood and figure IOE-4
Some valid arguments are arguments with false premises and a true conclusion
Therefore, some arguments with mood and figure IOE-4 are arguments with false premises and a true conclusion
The argument form of the standard logical form for this argument is as follows:
S = arguments with mood and figure IOE-4
P = valid arguments
M = false premises and a true conclusion

Premise 1: No S are P
Premise 2: Some P are M
Conclusion: Some S are M

In this argument, the conclusion does not logically follow from the premises. The first premise states that no arguments with mood and figure IOE-4 are valid, while the second premise states that some valid arguments have false premises and a true conclusion. These two premises are inconsistent with each other and therefore the argument is invalid.

In conclusion, argument (a) is valid while argument (b) is invalid. The validity of an argument depends on the logical relationship between the premises and the conclusion, and whether or not the conclusion logically follows from the premises.

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