Philosophy Homework Worksheet

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Philosophy 1115 (Logic) Homework Assignment #1 Solutions
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1. If an argument has a false conclusion it is invalid.
• We have seen (in our big table from lecture #3) a counterexample to this claim. Here’s another:
All wines are whiskeys.
Chardonnay is a wine.
(A
)
1
∴ Chardonnay is a whiskey.
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2. The moon is made of green cheese.
• I threw this in to make sure you’re awake. This is not a logical falsehood, but it’s a falsehood.
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3. No unsound arguments have a true conclusion.
• We have seen (in our big table from lecture #3) two counterexamples to this claim. Here’s one:
All wines are beverages.
(A
)
Chardonnay is a beverage.
3
∴ Chardonnay is a wine.
(A
) is invalid, hence it is unsound (it happens to also have true premises and a true conclusion).
3
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4. If it is not possible for the conclusion of an argument to be false, then the argument is valid.
• This is one of the two “odd cases” of validity I discussed in lecture. If it is impossible for the
conclusion to be false (period), then it is also impossible for the conclusion to be false while
the premises are true. So, by the definition of validity, all such arguments are valid.
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5. Every invalid argument has a false conclusion.
• Argument (A
) above is a counterexample to this claim.
3
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6. Some invalid arguments have a false conclusion.
• We have seen (in our big table from lecture #3) two examples of this. Here’s one of them:
All wines are beverages.
Ginger ale is a beverage.
(A
)
6
∴ Ginger ale is a wine.
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F
7. All sound arguments are valid.
• This is just part of the definition of soundness.
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8. If two arguments have identical logical form, then either they are both valid or they are both
invalid.
• If two arguments have identical logical form (in a general sense), then they instantiate all the
same logical forms (of all kinds). Since an argument is valid iff it instantiates some valid form
(of some kind), this claim is (generally) true.
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9. If an argument has true premises and a true conclusion, then it is sound.
• Argument (A
) above is a counterexample to this claim.
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