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From: David C. Ullrich on 30 Jun 2010 06:48
On Tue, 29 Jun 2010 18:24:59 -0700 (PDT), Charlie-Boo
<shymathguy(a)gmail.com> wrote:

>On Jun 29, 5:25�pm, MoeBlee <jazzm...(a)hotmail.com> wrote:
>> On Jun 28, 7:04�pm, Charlie-Boo <shymath...(a)gmail.com> wrote:
>>
>>
>>
>>
>>
>> > On Jun 28, 12:44�pm, MoeBlee <jazzm...(a)hotmail.com> wrote:
>>
>> > > On Jun 26, 9:19�pm, Charlie-Boo <shymath...(a)gmail.com> wrote:
>>
>> > > > It would be cool if the following 3 things were equivalent:
>>
>> > > > 1. |- (allX)P(X)
>> > > > 2. (allX) |- P(X)
>> > > > 3. ~ |- (existsX)~P(X)
>>
>> > > I can help you here, if you're interested in understanding this.
>>
>> > > (1) is well formed.
>>
>> > > (2) is not well formed as you've given it. The reason is that you've
>> > > mixed meta-language and object language in an incorrect way.
>>
>> > Did you read the definition of the syntax and semantics in the
>> > previous post?
>>
>> Sorry, I made the mistake that your first post was intelligible
>> standalone.
>>
>> > "P(x)" is a wff that is said to be
>> > provable. �So it expresses the proposition that for all values of X,
>> > the wff P(X) is provable.
>>
>> Then your formulations as given make even LESS sense.
>
>What is wrong with the proposition that for all values of X the wff
>P(X) is provable?

Unless there's something you're not telling us about what sort
of "values" you're considering, the problem is it simply doesn't
make any sense. If X is an expression in the formal language
in question then P(X) is reasonable informal notation for the
result of a certain substitution. But if X is a "value" external
to the language then there's simply no such thing as P(X).

>As a 3rd problem, what does it prove to prove that these are not all
>equivalent?
>
>C-B
>
>> I'm out of time for you. I can't do what no one else in these threads
>> has ever done: get you to understand ANYTHING.
>>
>> MoeBlee- Hide quoted text -
>>
>> - Show quoted text -

From: William Hale on 3 Jul 2010 17:28
In article
<7651ddde-47b8-4c75-8c63-049624ea23f2(a)t10g2000yqg.googlegroups.com>,
Charlie-Boo <shymathguy(a)gmail.com> wrote:

> On Jul 3, 5:30�am, Frederick Williams <frederick.willia...(a)tesco.net>
> wrote:
> > Charlie-Boo wrote:
> >
> > > Well, let's see. �I call this system ABC because I represent wffs
> > > using letters where
> >
> > > A = |-
> > > B = ~
> > > C = (all X)
> >
> > > Notice that P is actually free. �The empty string [] represents P. �So
> > > we have e.g.
> >
> > > A = |-P
> > > B = ~P
> > > C = (allX)P(X)
> > > AA = |- |- P
> > > AB = |- ~P
> > > AC = |- (allX)P(X)
> > > BA = ~|-P
> > > BB = ~~P
> > > BC = ~(allX)P(X)
> > > CA = (aA)|-P(A)
> > > CB = (aA)~P(A)
> > > CC = (allX)(allY)P(X,Y)
> > > etc.
> >
> > Is this alphabet soup of interest to anyone other than you?
>
> Are you saying that you don't understand it? Do you know what I'm
> doing? I'm listing the first few wffs. Their representation is any
> string of alphabet {A,B,C} so it's real easy to list wffs. Then the
> idea is to see how each would be represented using the provability
> predicate, to compare the two approaches.
>
> Does that help?

1) Why is CA = (aA)|-P(A) rather than CA = (aX)|-P(X) or even (all
X)|-P(X)?

2) If the empty string [] represents P, can I have: A = |- P P?
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