Follow up to your answer from a few days ago

SoccerBoss
Category:
Philosophy
Price: $5 USD

Question description

The double-negation in 3 is inspired!  Just curious -- was there a reason behind your decision to start with this, rather than just enter as the assumption the C you ultimately get in the next line?  



Here is what I asked:

Part 1:
Select an argument from below to solve and discuss. 

1.   If either the sea turtle population continues to decrease or rescue efforts are commenced to save the sea turtle from extinction, then nesting sanctuaries will be created and the indiscriminate slaughter of these animals will be halted. If either nesting sanctuaries are created or poachers are arrested, then if the indiscriminate slaughter of these animals is halted, then the sea turtle population will not continue to decrease. Therefore, the sea turtle population will not continue to decrease. (C, R, N, I, P)

Here is your answer:

Part 1:

  The argument selected for this assignment is the first one regarding the sea turtles.  The first premise is a conditional statement stating that nesting sanctuaries will be created for sea turtles and the slaughter of sea turtles will be halted if the sea turtle population continues to decrease or if rescue efforts are started to save sea turtles form extinction.  The second premise is another conditional statement saying that if nesting sanctuaries are created or poachers are arrested, then if the slaughter of sea turtles is halted, then the sea turtle population will not continue to decrease.  The conclusion of the argument is that the sea turtle population will not continue to decrease if these two premises are met.

Part 2:

Premise 1: (C v R) à (N •I)

Premise 2: (N v P) à (I à ~ C)

Indirect Proof:

1.  (C v R) à (N •I)  (Premise 1)

2.  (N v P) à (I à ~ C) (Premise 2)

3.  ~~C (Assumption for indirect proof)

4.  C  (Derived from 3, double negation)

5.  C v R (from 4, Addition)

6.  N • I (from 1,5 Modus Ponens)

7.  N (from 6, Simplification)

8.  N v P (from 7, Addition)

9.  I à ~C (from 2,8, Modus Ponens)

10.  ~I (from 3,9 Modus Tollens)

11.  I • N (from 6, Commutativity)

12.  I (from 11, Simplification)

13. ~I and I (from 10,12, Conjunction)

14.  ~C (from 3-13, Indirect Proof)

Part 3:

Translation:

C = sea turtle population continues to decrease

R = rescue efforts are commenced to save the sea turtle from extinction

N = nesting sanctuaries will be created

I = indiscriminate slaughter of the sea turtles will be halted

P = poachers are arrested

Conclusion: ~C: sea turtle population will not continue to decrease



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