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Lecture 4

01:730:103 Lecture Notes - Lecture 4: Thanetian, Ds 5


Department
Philosophy
Course Code
01:730:103
Professor
professor Steve
Lecture
4

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Assignment 4:
Part 1:
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[44-1] Exercise designed to appreciate comparative merit of CP:
with the same argument below,
[44-1.1] do the 1st proof without using CP; &
[44-1.2] do the 2nd proof by using CP:
44-1.1:
C: M -> R
1: ~M V N
2: ~R -> ~N
3: M -> N 1 Impl
4: N -> R 2 Contra
5: M -> R 3,4 HS ... QED
44-1.2:
C: M -> R
1: ~M V N
2: ~R -> ~N
-->3: M AP
4: N 1,3 DS
5: R 2,4 MT
6: M->R 3-5 CP ... QED
----------------------------------------------------
[44-2] Exercise designed to employ CP as part of the whole proc ess:
with the same argument below,
[44-2.1] do the 1st proof by using CP with ~P as AP
[44-2.2] do the 2nd proof by using CP with R as AP; & then Contra
[44-2.1]
C: ~P -> ~R
1: R -> (L & S)
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2: (L V M) -> P
--> 3: ~P AP
| 4: ~(L V M) 2,3 MT
| 5: ~L & ~M 4 DeM
| 6: ~L 5 Simp
| 7: ~L V ~S 6 Add
| 8: ~(L & S) 7 DeM
| 9: ~R 1,8 MT
---------------------------------
10: ~P -> ~R 3-9 CP .... QED
[44-2.2]
C: ~P -> ~R
1: R -> (L & S)
2: (L V M) -> P
--> 3: R AP (to get P)
| 4: L & S 1,3 MP
| 5: L 4 Simp
| 6: L V M 5 Add
| 7: P 2,6 MP
--------------------------------
8: R -> P 3-7 CP
9: ~P -> ~R 8 Contra ... QED
--------------------------------------------------------
[44-3] Exercise designed to see CP as a self-contained module:
use CP to the get the 1st part of conjunction;
use the conditional as a premise to get the 2nd part; &
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