Re: Aristotles logic decidable?
From: Owen (oorionus_at_yahoo.com)
Date: 02/27/05
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Date: Sun, 27 Feb 2005 12:33:11 -0500
"David Costa" <hawaii1976lvr@hotmail.com> wrote in message
news:cvsoq4$2dc$1@reader08.wxs.nl...
>A question on Aristotles' logic:
>
> Does there exist an algoritm to decide in finite time whether a given
> categorial argument is valid?
Yes. Categorical argument forms are decidable. Incuding Aristotle's
Syllogistic.
I can produce the truth tables if you want to see.
Indeed, there are Wittgenstein'ian truth values (T, F).
> In other words: is the logic of Aristotles decidable?
Yes.
>
> To prevent miscommunications I provide below the definitions I'm using:
>
> 1. A categorial argument is a sequence of the form "p_1, ... , p_n |--
c" in
> which p_1 , ... , p_n are categorial premisses and c is a categorial
> conclusion.
>
> 2. A categorial argument is valid if the conclusion c holds in each
world
> for which the premisses p_1 , ... , p_n hold.
>
> 3. A categorial premisse or conclusion is of one of the following 4
forms:
>
> All A are S
> Some A are S
> Some A are not S
> No A is S
>
> Thanks!
> Costa
>
>
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