Re: Logic question
- From: "Dan Christensen" <dchris@xxxxxxxxxxxxx>
- Date: Wed, 21 Dec 2005 15:40:02 -0500
"Peter Fairbrother" <zenadsl6186@xxxxxxxxx> wrote in message
news:BFCABB6C.BB844%zenadsl6186@xxxxxxxxxxxx
> The statement "if A then B" is considered true when A is impossible. Is
> this
> just a convenient definition?
>
This seems to come up a lot here (and sci.logic).
"If A then B" can defined as "~[A & ~ B]."
If ~A then it is easy to show that ~[A & ~B] is true:
1. Suppose ~A
2. Suppose to the contrary that [A & ~B].
3. Splitting 2, we have A.
4. We obtain the contradiction A & ~A. Therefore ~[A & ~B].
> I can think of cases where it can be proved that B would not be true were
> A
> to be true,
This is ruled out by the above definition; i.e., we cannot have A & ~B:
> but A is never true so ..
False. From the above defintion, if A is true, B is must also be true:
1. Suppose ~[A & ~B].
2. Suppose A.
3. Suppose ~B.
4. Joining 2 and 3, we have A & ~B
5. We obtain the contradiction [A & ~B] & ~[A & ~B]. Therefore B is true.
Confusion often arises between implications and causality. "If it is
raining, then it is cloudy" is not the same as "raining causes cloudiness."
I hope this helps.
Dan
Download my DC Proof software at http://www.dcproof.com
.
- References:
- Logic question
- From: Peter Fairbrother
- Logic question
- Prev by Date: Re: proof that inverse of continuous function is also continuous?
- Next by Date: Re: old number puzzle
- Previous by thread: Re: Logic question
- Next by thread: Re: Logic question
- Index(es):
Relevant Pages
|
