EXERCISES: METHODOLOGY #2

Please, type your answers and bring them to class in duplicate. No late unexcused answers will be accepted.

PART I Here are some schemata representing valid arguments

(1)
1. If P, then Q.
2. P.
_______
3. Q.

(2)
1. All As are Bs.
2. x is an A.
_________
3. x is a B.

(3)
1. If P, then Q.
2. ~Q.
_________
3. Hence, ~P.

(4)
1. All As are Bs.
2. x is not a B.
_________
3. x is not an A.

(5)
1. P or Q.
2. ~P.
__________
3. Hence, Q.

(6)
1) x is an A or a B
2) x is not an A
___________
3) x is a B

(7) 
1) If P, then Q
2) If Q, then R.
________
3) Therefore, if P then R

8)
1) All As are Bs
2) All Bs are Cs.
_____
3) Hence, all As are Cs

(9) 
1) a is an F
2) a=b
____________
3 )Thus, b is an F

(10)
1) P or Q
2) If P, then R
3) If Q, then R.
______

4) R

For each pattern, identify its name (i.e. is it Modus Tolens, Modus Ponens, etc). Then, illustrate each pattern by an original example. Altogether, you'll have 10 examples. The premises of your arguments must be grammatically well-formed statements. Use the handout "Philosophical Methods" as a model and guide.
Notice that in every case in which your argument has all true premises, it also has a true conclusion. Such an argument is sound. Sound arguments prove their conclusions.

PART II

SOME PATTERNS OF INVALID ARGUMENTS

 (11)
1. If P, then Q.
2. ~P.
_______
3. ~Q.

(12).
1) All As are Bs.
2) x is not an A.
_______
3. x is not a B.

 (12)
1. If P, then Q.
2. Q.
_______
3. P.

(13).
1) All As are Bs.
2) x is a B.
_______
3. x is an A

A) Illustrate each pattern by an original examples. The premises of your arguments must be grammatically well-formed statements. The arguments in your examples must clearly have all true premises but a false conclusion.
B) Briefly explain how/why, in your examples, the conclusions are false although the premises are true. (Alternatively, use examples where the premises are obviously true yet the conclusion is obviously false.)

PART III: Can there be a valid argument that has all true premises but a false conclusion? If yes, give an example; if no, why not? Give a brief explanation of your answer.