Need help prroof with no premise: Philosophy Forums

Need help prroof with no premise

rickydream
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Posted 10/01/09 - 10:13 PM: Subject: Need help prroof with no premise	#1
need to prove P or ~P is logically true by formal proof with no premise. Please help

Jean Francoise
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Posted 10/02/09 - 01:37 AM:	#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
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Posted 10/02/09 - 05:49 AM:	#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
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Posted 10/02/09 - 10:20 AM:	#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
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Posted 10/02/09 - 07:05 PM:	#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
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Posted 10/02/09 - 07:18 PM:	#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
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Posted 10/13/09 - 11:48 AM:	#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

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