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

Mitch wrote:
On Jul 17, 2:36 pm, John Jones <jonescard...@xxxxxxx> wrote:
Mitch wrote:

Or are you saying inclusive-or is composed of 'and' and 'or' somehow?
That -is- the case, if you consider 'or' to be exclusive or. I showed
you how to do that above. Did those examples make sense? Did you think
those defintions are wrong or misguided or lead to erroneous
deductions or do not capture the meaning of what people really think?

I think what we need now is a definition, if the one I have is wrong. There must be some reason why one of two items must be included in a definition of an object when only the other item is present in its construction.


But isn't there no such thing as a 'union' 'with' other sets?

The grammar here confuses me. You -can- union two (or more) sets. If
you want to say 'Take the union of A with B' for 'A union B', I
wouldn't turn my nose up at that.


I have
beentold that there is no bringing together of A and B in any form
whatever.

What does 'bring together' mean? Saying there is 'no bringing
together' in that way sounds wrong.

'Bringing together' could mean union, as it does when you say "You -can- union two (or more) sets". So there IS some common regard (bringing together) at work. But then contrarily, a union is announced AFTER we have made the necessary initial consideration of two sets.

So I am now wondering which comes first, the union? or some other bringing together?

But please note - I am loathe to use the images that set theorists normally use for bringing items together, because employing brackets have no obvious purpose except as a sort of pleasant, visual, picture-book convenience eg {1,5,8,}. 'Bringing together' appears confusing only because the thing it points to - the brackets and other visual devices, are themselves confusing.


When you say 'I have been told', that leads me to believe that your
experience with logic is very much second hand. Not that that's a
problem, it just makes the expectation that you'd be open to more
explanation. As it stand though, you sound like you're trying to
support someone else's argument without knowing what they meant or
what the original meant.


Further, If x is in A then we are not forced to look for
something x is not in.

That might be the case but it is so lacking in context to have much
importance. It depends so much on the other things that you might be
talking about.

But if-

"If x is in A then we are not forced to look for something x is not in"

-is lacking in context, then so is

"If x is in A then we are not forced to look for B"


I mean that in the equation a + 3=b, we need not consider c. C doesn't
exist - all we have is the app;ication in front of us.

Hm...OK. right, we don't need to consider c in this case. It is surely
not relevant in that equation. It might be relevant.

I wouldn't want to say, however, that a is 'relevant' in a+3=b. What would not being relevant look like?

But so far it is
not. If one talks about A union B and x is in A, then yes, it is
irrelevant whether x is in B in order to determine if x is in A union
B.


So... I would like to know why B is included in the picture AuB. The ONLY reason is that B was included before we made the definition of a union. Yes?


There's no mathematical justification for bringing in
terms (like B, C, D, ) which don't contribute to the mathematical
picture or proposal of x in A, or AuB.
You're introducing way too many external random irrelevancies, hidden
made-up motivations.
I don't want to introduce any random elements. B is a random element in
AuB where x is in A.

I'm not sure axactly what you mean by random (it happens to be a
technical term too), but you seem to be using it like I might use
'irrrelevant'. And with that reading, I could sort of see some glimmer
of meaning in your statement.

I was using it in the way I thought you were using it eg. irrelevant.

If x is in A then why can't we say Au not-A? Because like AuB, it's
informationless. All we need say is x is in A. AuB is extraneous.

But now you're going off on a tangent where you don't seem to be
holding on to what you've already said (pardon the mixed metaphor). So
let's put together what you've just said. You've just said in effect:
1- consider A union B where x is in A
2- if x is in A then why can't we say A union not-A
3- A union not-A is like A union B, they're both informationless
4- all we need say is x is in A
5- A union B is extraneous

1 is fine.
2 is weird: what does it mean to 'say' something?

I wasn't being literal. We can say something follows from something else-
So Aunot-A follows from AuB.

Are you propsing
it's truth (but that would be a syntax error, you can't say whether a
set is true. You -can- say whether a set has a particular element
though.
3- what does informationless mean? Sure, given only sentence 1,
there's not much more to say that you don't already know (that A union
B includes x, that A unioin not-A is the universe)

The two latter cases you mention: A union B includes x, that A union not-A is the universe, are the same because of the identity of indiscernibles.

4- 'need'? nobody -needs- to say anything.

But then I am told that B must be presented when it does not contribute to AuB.

We don't need to formulate AuB. We need not go to the trouble of writing AuB. AuB is informationless. It is informationless because it tells us no more than what we already know - that x is in A.


maybe ou mean that all we
really know is that x is in A. By the givens (sentence 1), that is
surely the case, but sorta 'so what?'

I agree. X is in A. Well, it may not have been, but it is. I suppose we could know how to find x if we had to look for it - it's in A.

And if only mere looking finds it, then the information is utterly useless. eg. I am going to have a shower, but a car peeps its horn outside.

5- A union B might be extraneous if you don't need it for your
application, again 'so what?' that is not a general objection to being
able to use A union B, or A intersect B, or A\B (set difference), or
whatever.

Please use AuB, but I need to know the starting conditions that allow us to speak of both A and B.


No, have another look: to find x in A "OR" B, where OR is excliusive,
then A, and B, must be a composite and not contained or grouped
together.

I think you mean to say A -union- B. But now, what does it mean for
you when you say -composite-? To me I can't make any interpretation of
'composite', contained' or 'grouped' to make sense.

To find x in A or B, where or is exclusive, I must be able to distinguish A from B. I cannot do this if A and B are in the same bag, or bracketed together, according to set theory visual aids. In order to find x in A or B, A and B must be distinguishable.

I think you might
be falling back on your physical bag metaphor, which will fail you at
some point. Use the property metaphor (which frankly is not really a
metaphor). Surely two different properties can be contained or grouped
together?

If I use the property metaphor then A and B have the property of being bracketed together, and not being bracketed together in AuB. An infinite regress looms. For at some point A and B themselves are bracketed.
.

Relevant Pages

  • Re: My talk about Godel to the post-grads.
    ... you want to say 'Take the union of A with B' for 'A union B', ... I would like to know why B is included in the picture AuB. ... holding on to what you've already said (pardon the mixed metaphor). ... 3- A union not-A is like A union B, they're both informationless ...
    (sci.logic)
  • Re: My talk about Godel to the post-grads.
    ... people use 'A union B' in mathematics. ... bag and put everything that is in B into the same bag. ... container to show that we can have AuB in its particular, ...
    (sci.logic)
  • Re: My talk about Godel to the post-grads.
    ... To address your objection that "it makes no distinction between them." ... union B, A union C, A union D, A union E, etc? ... B is a random element in AuB where x is in A. ...
    (sci.logic)
  • Re: analysis with uniformly continuous..
    ... f is uniformly continuous on AUB. ... Although delta can be found that is independent ... 'A union B', ... to the closure of 'A union B'. ...
    (sci.math)
  • Re: How to create a union table
    ... will not allow any other brackets ... this will cause this "SQL construction" to fail. ... if saving the union query is not possible, ... "Gary Walter" wrote: ...
    (microsoft.public.access.queries)
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