Re: Infinite dimensional oo-ML

On Jun 5, 8:32 am, zuhair <zaljo...@xxxxxxxxx> wrote:
On Jun 4, 5:35 pm, MoeBlee <jazzm...@xxxxxxxxxxx> wrote:





On Jun 4, 2:50 pm, zuhair <zaljo...@xxxxxxxxx> wrote:

On Jun 4, 4:34 pm, MoeBlee <jazzm...@xxxxxxxxxxx> wrote:

On Jun 4, 1:31 pm, zuhair <zaljo...@xxxxxxxxx> wrote:

I know what you mean exactly. I know what you are babling about
'metatheory' and the a like.

All what you said doesn't affect what I am saying.

Listening never was your strong suit.

MoeBlee

Same applies to you Moe.

Nope, not when it comes to set theory.

All what you wanted to say is that
in the metatheory of this theory
that defines the language of this theory
one should define when f equal g

WRONG. I never said or suggested anything like that. Like I said,
you're not listening.

and when Vf equal Vg.
That's understood.
one can say(in the metatheory) that the two finite sequences of
natural numbers f and g would be equal if and only if they have the
same number of entries
and the i-th entry in f equal the i-th
entry in g.

Yeah, and that was never in question with me. You're not listening.

And when f=g then Vg=Vf

Yeah, that's basic identity theory and was never in question with me.
You're not listening.

and when ~f=g then ~Vg=Vf
all this is pretty clear.

That is clear only if you stipulate it or trust that it will be taken
for granted in such contexts as defining a set of symbols. And as V is
a function that indexes symbols of your language, that V is 1-1 is not
something that you prove in the object theory but rather is something
that you either stipulate or leave as implicitly understood in your
meta-theory.

and it is actually trivial.
You made big thing out of such a trivial thing.

I made a post to remark on a way that you could make more precise your
definition. You didn't get what I meant (and still don't), thus an
exchange of several posts over what indeed is a simple matter.

actually it is forgranted.

You can see authors who take care to stipulate that the function is
1-1. It is either stipulated or taken to be understood by context.

I will only stipulate that when I am
dealing with a computer, not with human beings.

Suit yourself whether you stipulate it or not. But the point is that
it is not something that you'd prove in your theory. Rather it is part
of a definition that is stated in the meta-language and is either
stipulated in the meta-language or taken to be understood by context,
but not by proof in the object theory.

Actually one should not stipulate such an obvious
thing.

So you say. And you know virtually nothing about mathematical logic.
Certain authors who wish to be precise do indeed stipulate such
things.

one should stipulate things that are not obvious,
so suppose that I wanted the converse to be true, then since it was
not the expected thing then I should stipulate it.

You can say that it is obvious enough not to have to stipulate it. I
said from nearly the start of this exchange that in such contexts we
may take it for granted that V is 1-1. But you are incorrect that it
is even the kind of thing that you'd prove in the object theory.

In addition to all of that, this theory do
prove that if ~f=g then the objects Vf and Vg
are different.

The objects Vf and Vg are constants of the language of the theory.
You're really in a bad way if you think that it is in the theory
itself (without Godelization or something of that kind) that we find
out about the constants of its own language.

When I read that for every finite sequence of natural numbers f, we
have that Vf is a constant of the language of the theory, then I don't
expect to wait to find out what the theorems of the theory say about
whether there are denumerably many constants; I expect that the
definition of the langugae (which includes how many constants there
are) is given to me before I have to start reading proofs in the
theory. And that V is 1-1 may be stipulated or it may be regarded as
naturally supposed by context, but it is not the kind of information
that the theory itself will yield.

Why don't you get a damn textbook in mathematical logic to find out
about formal languages before you write back to me yet another of your
pigheaded, ignorant and insulting posts in which you unwittingly
reveal that you did NOT listen to what I said even as you think you're
proving that you did.

MoeBlee

Trust me Moe, you didn't understand what I was saying.
When I read your replies it is clear that you are not addressing what
I am saying. You greatly misunderstood me,Trust me. I always take your
replies seriousely, something that you don't do with mine.

What I wanted to say is that Regarding this particular case, I mean
regardins this particular theory, we don't need to stipulate what you
said, because it is clear from the context that we don't need to do
so, But obviouselly you didn't understand what I mean by the word
'contex', what I meant by context is two types: a pre type contex, and
a post type contex. A pre type context refers to the aim of the
wrighter when he right such symboles, it is generally understandable
that when one right such symboles like
Vf Vg etc... it is understandable that he intende if~g=f then ~Vf=Vg
and the opposite direction , and if he doesn't stipulate it then its
to be taken forgranted that he means so, So the pre.type contex is
understood BEFORE we start wrighting the axioms. Regarding this point
of view you appear to agree with me, and actually you said it from the
first post. But what you are not understanding is my concept of 'post.
type context', I meant that since this theory CAN prove that for every
f and g if ~f=g then ~Vg=Vf, then it would be understood that the
writer of the theory meant this to be beforhand(preaxiomaticaly, in
the metatheory).It is a kind of a backward orientation were the prior
is understood from the posterior, However you made the
misunderstanding of my argments, you thought I mean that the prior is
to be proved from the posterior, you thought that I am proving
something in the metatheory from the object theory, I didn't mean
that, what I meant is that since this theory CAN ( not ought to) prove
your statement then it would be very clear and obvious that I meant
this statement beforhand (preaxiomatically, or in the metatheory).

Anyhow.

Just look at various books on mathematical logic and you will see that
often authors make clear - one way or another - that, for example
(same holds for constants), each xi is a distinct variable. Such
authors do not just assume that that will be taken for granted but
rather indeed stipulate it explicitly, in one way or another. And
you're mixed up when you think that your theory itself determines such
things about the syntax of its own language.

MoeBlee

.

Relevant Pages

  • Re: Infinite dimensional oo-ML
    ... 'metatheory' and the a like. ... That is clear only if you stipulate it or trust that it will be taken ... a function that indexes symbols of your language, that V is 1-1 is not ... It is either stipulated or taken to be understood by context. ...
    (sci.math)
  • Re: Infinite dimensional oo-ML
    ... 'metatheory' and the a like. ... a function that indexes symbols of your language, that V is 1-1 is not ... It is either stipulated or taken to be understood by context. ... Certain authors who wish to be precise do indeed stipulate such ...
    (sci.math)
  • Re: Infinite dimensional oo-ML
    ... 'metatheory' and the a like. ... a function that indexes symbols of your language, that V is 1-1 is not ... It is either stipulated or taken to be understood by context. ... Certain authors who wish to be precise do indeed stipulate such ...
    (sci.math)
  • Re: Infinite dimensional oo-ML
    ... That is clear only if you stipulate it or trust that it will be taken ... a function that indexes symbols of your language, that V is 1-1 is not ... something that you prove in the object theory but rather is something ... It is either stipulated or taken to be understood by context. ...
    (sci.math)
  • Re: Infinite dimensional oo-ML
    ... That is clear only if you stipulate it or trust that it will be taken ... a function that indexes symbols of your language, that V is 1-1 is not ... something that you prove in the object theory but rather is something ... It is either stipulated or taken to be understood by context. ...
    (sci.math)
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