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

Chris Menzel wrote:
On Wed, 09 Jul 2008 22:04:12 +0100, John Jones <jonescardiff@xxxxxxx>
said:
David C. Ullrich wrote:

B doesn't come into it any more than C.
B is irrelevant to a statement about A and B? Huh.
Yes, it is irrelevant. Either A or B is irrelevant in the formation of
a union in which only either A or B has elements in common with x.

C is a {banana,orange}. DO YOU SEE WHAT I AM GETTING AAAT??? Sorry
to shout, but do you see what I am getting at?
No, and neither will anyone else - your comment about C has no
relevance whatever.
Okay, you don't see what I am getting at. Try this:
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?

Goodness, you really are having trouble with the very simplest of
standard definitions. You do seem *sincerely* confused, at least, so
let me have a go. Consider the following sets:

A = {1,2,3}
B = {2,3,4}

The set theoretic union of these sets (forget please for the moment
about all the other vaguely related but distinct ordinary language
homophones) is the set containing all of their members together, namely:

C = A union B = {1,2,3,4}

Now, how can we describe C with complete logical clarity? Like this:
it's the set that contains an object x just in case either (i) x is in A
*or* (ii) x is in B. That description "x is in A or x is in B" is
exactly the property common to all and only the members of A and B,

No it isn't. x is common to only one of them, A or B. The term that is left is not relevant, as it turns out, and so should not be in this scenario.

On the other hand, if the x's refer to any of the elements in either A or B, then you can make a case for saying "x is in A or x is in B" and make a union of A and B. I think you call it an intersection. But there's a problem with an intersection too:

The problem is that in order to assert that "x is in A or x is in B" I must already have assumed a union, prior to claiming that there is one.

and
hence it is what we use to pick them all out and gather them into a
single set. ("gather" is of course a metaphor here.) Note that, if
instead you asked for the set that contains an object x just in case x
is in A *and* x is in B, you would get a very different set, namely,
the *intersection* of A with B:

D = A intersect B = {2,3}.

Does that help?

[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.]

Honestly, it isn't. Check *any* text on set theory. Now, who is more
likely to be confused here? Every author of every text on set theory
ever written, including Georg Cantor? Or you, the earnest Cardiff Uni
philosophy grad student who has never studied a lick mathematical logic?

Nietszsche will come and burn down your huts.

.

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