A logic question

TheMadFool August 01, 2017 at 09:01 2325 views 3 comments

@Srap Tasmaner @andrewk @Nagase or anyone else

1. All living things suffer
2. No living thing wants to suffer
3. No living thing that doesn't want to suffer wants to live
Therefore,
4. No living thing wants to live

Lx = x is a living thing, Sx = x has to suffer, Wx = x wants to live

Translating premises and conclusion in sequence:

1. (x)(Lx > Sx)
2. (x)(Lx > ~Wx)
3. (x)(~Wx > ~Lx)................/~(Ex)(Lx)
4. (Ex)(Lx).............................assume for reductio
5. Ly > ~Wy...........................2 UI
6. ~Wy > ~Ly.........................3 UI
7. Ly > ~Ly.............................5, 6 HS
8. La.......................................4 EG
9. (x)(Lx > ~Lx).....................7 UG
10. La > ~La..........................9 UI
11. ~La..................................8, 10 MP
12. La & ~La..........................8, 11 Conj
13. ~(Ex)(Lx).........................4 to 12 reductio

Is my proof good?

Why is premise 1 redundant? It seems necessary in the English language argument?

Comments (3)

Meta August 01, 2017 at 11:25 #92181 0 likes

The proof is correct. Your premises however are not equivalent with the English axioms because you need one more predicate to express "x wants to suffer".

noAxioms August 01, 2017 at 11:55 #92183 0 likes

Sort of its own disproof then. The logic is sound, and the conclusion obviously contradicts reality, thus at least one of the premises must be wrong. I happen to take issue with all three of them.

TheMadFool August 01, 2017 at 13:20 #92190 0 likes

Reply to Meta(Y) Thanks

Reply to noAxioms Purely a logic exercise. Nothing more. :)