Assignment
Writing Assignment #5
Please put the following argument in standard logical form:
If an argument has a true conclusion and at least one false premise, then it has
mutually consistent premises. An argument has at least one false premise only if
it is sound. If an argument is sound or it has a tautology as a conclusion, then it
has a true conclusion. If an argument has a true conclusion, then it has at least
one false premise. An argument has a contradiction as a premise if it either has
mutually consistent premises or it is valid. If an argument has a contradiction as a
premise, then it has a tautology as a conclusion. Therefore, an argument has a
true conclusion if and only if it has a contradiction as a premise.
Prove this argument is valid by means of a derivation. Is the argument sound? Please
explain why each premise is true or false, and whether the conclusion is true or false. Use
examples where relevant.
Further Instructions:
1. You want to rewrite this argument in standard logical form. This means that you will provide a
dictionary and symbolize the argument. To keep down the number of letters, use ~. If you use ‘V’
for ‘an argument is valid’, use ‘~V’ for ‘an argument is invalid’. You will need seven statement
letters. Reread 2.14 from the textbook (2.12 in the old version).
2. Your argument and dictionary must appear in the main text. After all, it’s what you’re discussing.
Don’t hide it. Your argument, dictionary, and symbolization should appear on page 1 of the paper.
3. To prove this argument is valid by a derivation, you need to make a provisional assumption. Your
derivation may appear in an appendix. However, if so, it should be the only thing there.
4. To determine whether the premises are true or false, rely on your dictionary. You will have to plug
in values and determine what each statement actually says. If you have ‘V only if S’ where ‘V’
stands for ‘an argument is valid’ and ‘S’ stands for ‘an argument is a categorical syllogism’, then
you want to treat this statement as ‘VS’. This says that if an argument is valid, then it is a
syllogism. To prove this is false, you need a valid argument that is not a syllogism.
5. It is easier to explain why ‘if , then ’ statements are true or false than ‘only if’ or ‘y, if x’
statements. A good way to make a mistake is to focus on ‘only if’, since ‘only if’ does not mean
that there is just one way for something to occur. This is why you should rewrite each premise as
an ‘If , then ’ statement. You are less likely to make mistakes.
6. When you discuss the truth or falsity of each premise, spend a paragraph on each premise. That
way you are less likely to skimp on your discussion. You need to rely on definitions as you do!
7. Look over the conceptual material in chapter 3 again for guidance on this assignment.
8. There may be more than one way to complete this derivation. As long as you get one of the
correct ways, that is acceptable.
9. Please note that this calls for a derivation. Do not make a truth table! If you do, then you will end
up with a truth table that has 128 lines. I am fairly certain that you do not want to make that truth
table, and I am very certain that I do not want to grade it. (In contrast, the derivation can be done
in less than 20 lines. That is much easier for all of us.)
Instructions
Writing Assignment #5 Outline
1. Introduction
a. Present the argument
b. Present your dictionary
c. Present the argument in standard logical form
2. Validity
a. Prove the argument is valid by means of a derivation. This may appear in an appendix at
the end of the paper. But mention that you have proven that the argument is valid, and
describe the proof strategy that you used to do it to show you understand the rules.
3. Soundness
a. Explain why each statement is true or false
b. Explain why the first premise is true or false
c. Explain why the second premise is true or false
d. Explain why the third premise is true or false
e. Explain why the fourth premise is true or false
f. Explain why the fifth premise is true or false
g. Explain why the sixth premise is true or false
h. Explain why the conclusion premise is true or false
4. Conclusion
a. Is the argument sound? Why or why not?
