Re: Disjunction in propositional logic
From: William Elliot (marsh_at_privacy.net)
Date: 09/10/04
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Date: Thu, 9 Sep 2004 19:15:17 -0700
On Thu, 9 Sep 2004, Karl Weber wrote:
> Here is a basic question regarding propositional logic... take the
> proposition
> P = "Easter falls in March or Easter falls in April"
>
> which seems reasonably true to me. P is a disjunction of two simple
> propositions, A and B:
>
> A = "Easter falls in March"
> B = "Easter falls in April"
> P = A or B
>
> However, in propositional logic, every statement is either true or
> false. Obviously, it does not make sense to assign a truth value to A
> (or B for that matter), like "it is true that Easter falls in March",
> since this proposition is too 'general'. The best you can do is this:
> A = "In 2004, Easter falls in March"
> B = "In 2004, Easter falls in April"
>
> now, A and B can be assigned definitive truth values.
>
That is correct.
> From the above, I conclude that the original proposition P is not a
> valid proposition with respect to propositional logic. Am I missing
> something?
>
Yes, that "Easter falls in March" isn't an atomic statement,
it's a propositional function of one variable. Thus you say
M(t) when Easter in the year t falls in March
A(t) when Easter in the year t falls in April
for all years t, (M(t) or A(t)
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