Validity or Probability

Question 1

Test for Validity

Answer 1

Assuming that the premises are true, is it possible for the conclusion to be false? If it is then the arguement is invalid.

Question 2

Test for Probability

Answer 2

Assuming the premises are true, what degree of probability would they confer upon the conclusion?

Question 3

A valid argument must have a true conclusion

Answer 3

FALSE: A valid argument must have a true conclusion only if all of the premises are true. So it is possible for a valid argument to have a false conclusion as long as at least one premise is false.

Question 4

A sound argument must have a true conclusion.

Answer 4

TRUE: If an argument is sound, then it is valid and has all true premises.

Question 5

If a valid argument has a false conclusion, then at least one premise must be false.

Answer 5

TRUE: A valid argument cannot have all true premises and a false conclusion. So if a valid argument does have a false conclusion, it cannot have all true premises. Thus at least one premise must be false.

Question 6

If an invalid argument has all true premises, then the conclusion must be false

Answer 6

FALSE: It is possible for an invalid argument to have all true premises and a true conclusion.
P1: All dogs are mammals
P2: All terriers are mammal
C: All terriers are dogs.

Question 7

If an argument has all true premises and a true conclusion, then it is valid.

Answer 7

FALSE: It is possible for an argument to have all true premises and a true conclusion but still be invalid. See above (#4).

Question 8

If an argument has all true premises and a false conclusion, then it is invalid.

Answer 8

TRUE: A valid argument cannot possibly have all true premises and a false conclusion. So the argument is invalid.