Philosophy Forums


Need help prroof with no premise
P or ~P

PrintPrint


Need help prroof with no premise
rickydream
Initiate

Usergroup: Members
Joined: Oct 01, 2009

Total Topics: 1
Total Posts: 1
Posted 10/01/09 - 10:13 PM:
Subject: Need help prroof with no premise
quote post
#1
need to prove P or ~P is logically true by formal proof with no premise.
Please help
Jean Francoise
Protege of Being
Avatar

Usergroup: Members
Joined: Feb 04, 2009

Total Topics: 3
Total Posts: 63
Posted 10/02/09 - 01:37 AM:
quote post
#2
rickydream wrote:
need to prove P or ~P is logically true by formal proof with no premise.
Please help


What axiomatic system, and language are you working in? Without this the best suggestion I can give you is:

Proof by contradiction

1. ~(Pv~P) Hypothesis

2. ~P&~~P De Morgan Law

3. ~P&P Double Negation, RAA (Reductio ad absurdum)

Since the hypothesis leads to a contradiction the original formula Pv~P is true QED.

Emptiness whispers in riddles.
ClaudeHooper
Student

Usergroup: Members
Joined: Aug 10, 2009

Total Topics: 2
Total Posts: 53
Posted 10/02/09 - 05:49 AM:
quote post
#3
>> C1. (P or (not P))
by intro C1
|
+- >> C2. P
| >> C3. (not P)
| by intro C3
| |
| +- H1. P
| | >> C2. P
| | by hyp H1, C2
Timothy
Undead Mariachi
Avatar

Usergroup: Members
Joined: Dec 18, 2004
Location: 04°34'N 74°00'W

Total Topics: 83
Total Posts: 2078
Posted 10/02/09 - 10:20 AM:
quote post
#4
Claude, were you trying to prove P v ~P by introducing v? I don't get the schema you presented.

But if you start by assuming P, as I think you did, then at most you will end up with

p -> (P v ~P)

which is not the same as proving P v ~P

"Neither Aristotelian nor Russellian rules give the exact logic of any expression of ordinary language; for ordinary language has no exact logic." P.F. Strawson
ClaudeHooper
Student

Usergroup: Members
Joined: Aug 10, 2009

Total Topics: 2
Total Posts: 53
Posted 10/02/09 - 07:05 PM:
quote post
#5
Here is my same proof in a more traditional sequent presentation:

Start off with a hypothesis sequent:

P |- P

Perform not-introduction on the hypothesis:

|- P, (not P)

Perform or-introduction on the two conclusions:

|- P or (not P)
Banno
Old goat
Avatar

Usergroup: Sponsors
Joined: Aug 15, 2004
Location: Oz

Total Topics: 111
Total Posts: 6301
Posted 10/02/09 - 07:18 PM:
quote post
#6
rickydream wrote:
need to prove P or ~P is logically true by formal proof with no premise.
Please help

To P or not to P, that is the question.


Davidson: We make maximum sense of the words and thoughts of others when we interpret in a way that optimizes agreement.
Russel Morris: There's a meaning there, but the meaning there doesn't really mean a thing...
Ned: Such is life
frank2010
Aspirant
Avatar

Usergroup: Members
Joined: Oct 11, 2009

Total Topics: 2
Total Posts: 33
Posted 10/13/09 - 11:48 AM:
quote post
#7
Here's the one I prefer:

(1) l ~(p v ~p) H for introduction of ~
(2) ll p H for introduction of ~
(3) ll p v ~p 2, introduction of v
(4) ll (p v ~p) & ~(p v ~p) 1, 3 introduction of &
(5) l ~p 2-4, introduction of ~
(6) l p v ~p 5, introduction of v
(7) l (p v ~p) & ~(p v ~p) 1, 6 introduction of &
(8) ~~(p v ~p) 1-7, introduction of ~
(9) p v ~p 8 double negation

That's how you can prove the theorem (that is, that is the way you can prove the relevant wff without non-hypothetical assumptions)
See you
Download thread as


Sorry, you don't have permission to post. Log in, or register if you haven't yet.