Philosophy Homework Worksheet (Page 3 of 4) in pdf

19. No invalid arguments have a false conclusion.

• Argument (A

) above is a counterexample to this claim.

20. If the conclusion of a valid argument is false, then all of its premises are false as well.

• Argument (A

) above is a counterexample to this claim (since its second premise is true).

21. If the conclusion of a valid argument is true, the premises must be true as well.

• We have seen (in our big table from lecture #3) a counterexample to this claim. Here it is:

All wines are soft drinks.

Ginger ale is a wine.

)

∴ Ginger ale is a soft drink.

22. If an argument is sound, then its conclusion follows from its premises.

• By deﬁnition, all sound arguments are valid. And, “A is valid” is synonymous with “A’s con-

clusion follows from A’s premises”.

23. All unsound arguments are invalid.

• We have seen (in our big table from lecture #3) two counterexamples to this claim. Here’s one:

All wines are whiskeys.

Ginger ale is a wine.

)

∴ Ginger ale is a whiskey.

24. Some valid arguments have a true conclusion.

• Argument (A

) above is an example of this.

25. Every sound argument has a true conclusion.

• We already proved this in our answer to #13 above.

26. If an argument is valid absolutely, then it is also sententially valid.

• Any predicate-logically valid argument (which is not also sententially valid) will be a counterex-

ample to this claim. For instance, argument (A

) above. Argument (A

) is predicate-logically

valid (hence, “absolutely” valid, to use Forbes’s term — which just means that it instantiates

some valid form of some kind). But, it is not sententially valid.

If P then Q

27. The following is a valid sentential form:

∴ P

• This is aﬃrming the consequent, which is not a sententially valid form (which just means that

it has some invalid instances).

Either P or Q

28. The following is an invalid sentential form:

∴ P

Philosophy Homework Worksheet Page 3