Re: My talk about Godel to the post-grads.

David C. Ullrich wrote:
On Mon, 14 Jul 2008 21:44:00 +0100, John Jones <jonescardiff@xxxxxxx>
wrote:

David C. Ullrich wrote:
On Sun, 13 Jul 2008 19:49:50 +0100, John Jones <jonescardiff@xxxxxxx>
wrote:

David C. Ullrich wrote:
On Sun, 13 Jul 2008 13:45:58 +0100, John Jones <jonescardiff@xxxxxxx>
wrote:

David C. Ullrich wrote:
On Fri, 11 Jul 2008 19:59:24 +0100, John Jones <jonescardiff@xxxxxxx>
wrote:

David C. Ullrich wrote:
On Thu, 10 Jul 2008 13:04:50 +0100, John Jones <jonescardiff@xxxxxxx>
wrote:

MoeBlee wrote:
On Jul 9, 2:04 pm, John Jones <jonescard...@xxxxxxx> wrote:

IF a union of A and B is described only in terms of either A or B, then
how can a union be a union of A AND B?
ie. how can you have a union of EITHER A OR B?
Here's the definition:

AuB = U{A B}

and that is equivalent to

AuB = y <-> As(sey <-> (seA v seB))

and that is equivalent to

AuB = {s | seA v seB}

So let's focus on that equation:

AuB = {s | seA v seB}

I.e., the union of A with B is the set whose members are all and only
those s that are either in A or in B. (Where 'or' is the inclusive
sense of 'or', i.e., "either in A or in B or in both A and B").

The definition mentions BOTH A and B (in both the definiens and
definendum), but the CONDITION for membrship in the UNION is simply
that of being in either A or in B (or in both).

Does that clear it up for you?

MoeBlee


[C comes into it because if the union is only of either A or B, then C
can be associated with either term. Honestly, your definition must be
wrongly transcribed.]
And/then was not stated earlier. The problem is still with us though, as the either/or case still applies.

The problem is that A and B are announced as a union when, in fact, it may be that only EITHER A or B that is a union.

What is important is that if only A has elements of s, B doesn't come into it at all, any more than C,D,E,etc.
My gosh you're dense. People take great pains to explain the
simplest points in detail and you continue babbling nonsense.
You are banging your rattle. Address the objection.
There's nothing to address - the supposed objection simply
makesa no sense. Really - when you say things like
"The problem is that A and B are announced as a union when, in fact, it may be that only EITHER A or B that is a union" you're just making no sense at all - we're talking about
the definition of "the union of A and B" - saying that the
problem is that "A and B are announced as a union" is
not the sort of "objection" that _can_ be "addressed".

When you say things that simply make no sense at all,
indicating that you literally have no idea what you're
talking about, one might try to explain. At least three
people _have_ explained, at some length, quite clearly.
Your comments simply ignore the explanations - you're
not in a position to complain about people not
addressing objections.

What's funny about _this_ subthead is that you've
descended from saying silly things about Godel's
theorem to saying incoherent things about an
utterly elementary concept, the union of two sets.

No, the fact that something is routinely understood
by children does not prove that there are no possible
philosophical issues reagarding that something - it
could well be that there are valid or at least reasonable objections to our supposed understanding
of said elementary concept. But _that_ fact does not
imply that anything you've said makes any sense.

It's like the topic was whether the Earth goes around
the Sun or vice versa. People assert that the Earth
goes around the Sun, not the other way around.
Someone might point out that taking the Sun
to go around the Earth is in fact equally valid,
it's just a choice of coordinates that makes the
math more complicated. But you're not raising
anything remotely like that sort of objection -
the things you're saying make as much sense
as if you'd said "the problem is that the Sun
is a rutabaga". Hmm, actually your objections
here make less sense than that - let's say
instead your objection is "the problem is
that Sun Earth", taking "Sun" to be a verb.

When you say "the problem is that Sun Earth"
in that context it would be very charitable for
people to try to explain to you that you're
simply making no sense, and why. When,
after they explain that "Sun" is a noun and
not a verb, you simply repeat that the problem is that Sun Earth, and complain the people are not addressing the objection, you look very stupid.

Honest. You're free to take that as an ad hominem
attack and declare that you win. If you're interested
in sounding less stupid in the future instead you'll
try to understand _why_ all the things you've said
about this are utterly stupid (if you're interested
iu that reread a few posts).

The 'union' is not a mathematical device but a statement of contingency, and contingencies aren't logical or mathematical. Explanation: Not knowing whether it is A or B that has s, when only one of them is actually the case cannot be posed as a mathematical function. It isn't really a case of either/or A and B, but simply a case of not knowing which.
David C. Ullrich

"Understanding Godel isn't about following his formal proof. That would make a mockery of everything Godel was up to."
(John Jones, "My talk about Godel to the post-grads."
in sci.logic.)
David C. Ullrich

"Understanding Godel isn't about following his formal proof. That would make a mockery of everything Godel was up to."
(John Jones, "My talk about Godel to the post-grads."
in sci.logic.)
I've checked the problem with my friend.
The problem is that you have not properly transcribed your account of what is a union. You failed to state the starting conditions, the form in which A and B are brought together. Only then does what you have written make sense. Without saying what these starting conditions are, then it makes no sense to say that A and B are a union when x is either in A or B. That's just nonsense as it is.
What the heck are you talking about?

The only possible "starting condition" you could be referring
to is that A and B are sets. If your complaint is that I didn't
say A and B are sets then (i) that's silly, because it's clear
from the context - when we talk about "unions" we're talking
about sets (ii) silly or not, I _was_ explicit about that at
the start of all this, (iii) curiously the current "only problem"
seems to have nothing to do with the supposed objections
that you've been complaining we haven't been addressing.

If on the other hand your friend is talking about some
other "starting condition" then your friend is simply wrong.

Why don't you tell us what "starting condition" you're talking about?

And by the way, I never said "A and B are a union when x is either in A or B." _That_ statement _is_ nonsense. The definition is:
"The union of A and B is the set of x such that x is an element
of A or x is an element of B". Getting from there to
"A and B are a union" is just one more instance of the fact
that you seem unable to get anything straight.

David C. Ullrich

"Understanding Godel isn't about following his formal proof. That would make a mockery of everything Godel was up to."
(John Jones, "My talk about Godel to the post-grads."
in sci.logic.)
The starting conditions are that A and B are brought together in some way, prior to any consideration of a union.

If I bring together a set of oranges and bananas (A), and a set of oranges (B), then I can say that
"the union of A and B is the set of x such that x is an element of A or x is an element of B",
where x is a banana.
Ignoring for a second the fact that this idea that A and B must
be "brought together", that final "where x is a banana" is imply
wrong. The union of A and B is the set of x such that x is an
element of A or x is an element of B, period. In the example
you give the union will contain bananas and also oranges.

But the point is, in order for this union to be valid, I MUST have already brought the two sets together, prior to their being considered for a union. Without this prior 'bringing together' it makes no sense to say that a set of an element that belongs to A but not to B is a 'union'.
This is simply nonsense.
It's no point you saying that because what you think of as nonsense I can deliver as plain sense, and vice versa.

Find a book on set theory that agrees
that before we can form the union of A and B we must "bring
them together in some way".
"Bring them together" is qualified by "in some way". It is up to you to stipulate how that should be done, such that your definition of a union makes sense.

I am content with the fact that your definition does not make sense, unless you can present a relationship between A and B. You might want to use diagrams, but using symbols to argue your case won't do.

Better yet, give a precise mathematical definition of what it
_means_ to "bring together" two sets.
As I say, the onus is on you to provide a definition of this, because such a definition allows your claim to make sense.

You're really not getting tired of making an idiot of yourself
in public about incredibly elementary concepts, eh? Good
for you.
Oh. That's it. I expected more.
You're bollocksed on this aren't you Ulrich. You haven't given a cogent description for this definition. And that's it, really.

You're aware of course that you're saying that you're right and
every mathematician on the planet is wrong.

Well, all the mathematicians can't be right. That would be too much of a coincidence. But collaboration might make it seem otherwise, for agreement is stronger than truth, and made stronger by secrecy. Who can discern the clandestine agreements forged in our institutions midst the whispers that echo down their corridors and inner vestibules.

It's not up to _me_ to provide a definition of "bring together
in some way" when you introduced that term out of the blue.

It's not a term. It's a pointer that may help you to provide some way of stating the relationship between A and B such that A and B can be said to have a union.

The definition _is_ that the union of A and B is the set of
x such that x is an element of A or x is an element of B.

Yes, and that won't do. For it to make sense you must have already established some sort of relatinship between A and B in order to announce a union. I am inviting you to state what that relationship, or bringing together in some way, is.

So far you've made a lot of stupid objections to this definition, and you've said some truly amazing things,
for example saying that it's the same as "the set of x
such that x is an element of A or the set of x such
that x is an element of B". You haven't explained
_why_ the actual definition requires that A and B
"be brought together in some way", you've simply
asserted this.

I have explained why.
- The definition - that the union of A and B is the set of x such that x is an element of A or x is an element of B - requires A and B to be in prior relationship. For as it stands, their relationship is announced by the fact there is a union. But there can't be such a relationship if x is not an element of either A or B.

There. I've stated it.
.

Relevant Pages

  • Re: My talk about Godel to the post-grads.
    ... how can a union be a union of A AND B? ... Address the objection. ... goes around the Sun, ... "Understanding Godel isn't about following his formal proof. ...
    (sci.logic)
  • Re: My talk about Godel to the post-grads.
    ... how can a union be a union of A AND B? ... There's nothing to address - the supposed objection simply ... goes around the Sun, ... "Understanding Godel isn't about following his formal proof. ...
    (sci.logic)
  • Re: My talk about Godel to the post-grads.
    ... how can a union be a union of A AND B? ... Address the objection. ... goes around the Sun, ... "Understanding Godel isn't about following his formal proof. ...
    (sci.logic)
  • Re: My talk about Godel to the post-grads.
    ... how can a union be a union of A AND B? ... There's nothing to address - the supposed objection simply ... goes around the Sun, ... "Understanding Godel isn't about following his formal proof. ...
    (sci.logic)
  • Re: My talk about Godel to the post-grads.
    ... how can a union be a union of A AND B? ... Address the objection. ... goes around the Sun, ... "Understanding Godel isn't about following his formal proof. ...
    (sci.logic)