Re: Disjunction in propositional logic

From: converter (mrclaws_at_gmail.com)
Date: 09/11/04 

Date: 11 Sep 2004 11:16:29 -0700

Karl Weber <dudendude@hotmail.com> wrote in message news:<41423d65_1@news.arcor-ip.de>...
> Converter wrote:
>
> > Both A and B are valid elementary propositions and the statement P is
> > a valid disjunctive proposition, A is valid because it asserts that
> > Easter will fall in March and B is valid because it asserts that
> > Easter will fall in April.
>
> Hmmm... isn't it a problem that A/B do not in any way specify _which_ Easter
> will fall in March/April? Of course it should be ok if it is taken to mean
> "This year, Easter ..."

That doesn't mean the propositions aren't valid in propositional
logic. That is one of problems with propositional logic, it doesn't
deal with the content of the propositions, it deals with the structure
of the reasoning.

>
> > I think where the confusion comes in is that you have already come to
> > the conclusion that easter will always fall within these two months
> > and you haven't added it into your logic (your statement about not
> > making sense wasn't symbolized within the propositional logic). So,
> > the statement will always be true according to you.
>
> I think, my problem was that the original P could be interpreted in two
> different ways:

Yes, but that doesn't imply that the proposition isn't valid in
propositional logic, that's one of the deficiencies of propositional
logic.

The reasoning can go even farther, as in defining what a year is and
what march is and what easter is, predicate logic, with it's ability
to deal with the content of the proposition makes that much clearer,
propositional logic doesn't have that capability.

>
> P1 = "Every year, Easter will fall in March or in April"
> P2 = "This year, Easter falls in March or in April"
>
> As I see it, P1 would be a statement of predicate logic, while P2 is a
> statement of propositional logic... ?

Both P1 and P2 are valid disjunctive propositions in propositional
logic, propositional logic doesn't work with the content of the
propositions. Predicate logic can be used to refine the logic of the
content of the proposition, traditional propositional logic doesn't do
that.

Here is an example of two valid elementary propositions and a valid
implication:

A - Paris is the capital of France.
B - The number 2 is even.

A and B are valid elementary propositions under propositiona logic.

Here is the implication:
A->B

(read, if A then B)

Since Paris is the capital of France and the number 2 is even, this
implication is true, but the content doesn't seem to have anything to
do with each other. That again, is the major deficiency with
propositional logic.

Relevant Pages

  • Re: Disjunction in propositional logic
    ... > Both A and B are valid elementary propositions and the statement P is ... A is valid because it asserts that ... > Easter will fall in April. ...
    (sci.logic)
  • Re: Disjunction in propositional logic
    ... >> Both A and B are valid elementary propositions and the statement P is ... A is valid because it asserts that ... >> Easter will fall in April. ... Well, sort of. ...
    (sci.logic)