Philosophy Homework Worksheet Page 2
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10. No unsound arguments have a false conclusion.
• Argument (A
) above is a counterexample to this claim.
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11. If the conclusion of a valid argument is false, then at least one of its premises is false.
• By definition, if a valid argument has all true premises, then its conclusion must also be true.
Therefore, if the conclusion of a valid argument is false, then it can’t be the case that all of its
premises are true. So, if the conclusion of a valid argument is false, then some (i.e., at least one)
of its premises must also be false.
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12. Some invalid arguments have a false premise.
• We have seen (in our big table from lecture #3) an example of this. Here it is:
All wines are whiskeys.
Chardonnay is a whiskey.
(A
)
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∴ Chardonnay is a wine.
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13. No sound arguments have a false conclusion.
• Let X = the sound arguments, Y = the valid arguments with (all) true premises, and Z = the
arguments with true conclusions. The following is a (predicate-logically) valid form:
1. All Xs are Y s.
2. All Y s are Zs.
(A
)
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∴ 3. All Xs are Zs.
Premise (1) is true by the definition of soundness. Premise (2) is true by the definition of
validity. The conclusion (3) follows, since (A
) is valid. Therefore, all sound arguments are
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arguments with true conclusions. In other words, no sound arguments are arguments with
false conclusions. QED.
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14. Some invalid arguments have a true conclusion.
• Argument (A
) above is an example of this.
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15. Every invalid argument has a true conclusion.
• Argument (A
) above is a counterexample to this claim.
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16. A valid argument with twenty true premises and one false premise is more sound than an argu-
ment with three true premises and one false one.
• Soundness (and validity) are absolute (i.e., “black-and-white”) — they do not come in “degrees”.
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17. Some unsound arguments have a false conclusion.
• Argument (A
) above is an example of this.
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18. Some valid arguments are unsound.
• Any valid argument with some false premises will do, e.g., argument (A
) above.
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