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

David C. Ullrich wrote:
On Sun, 06 Jul 2008 19:39:41 +0100, John Jones <jonescardiff@xxxxxxx>
wrote:

David C. Ullrich wrote:
On Sat, 05 Jul 2008 20:04:48 +0100, John Jones <jonescardiff@xxxxxxx>
wrote:

David C. Ullrich wrote:

You _really_ don't know what the union of two sets is?
A 'union of sets' isn't anything. You can take that as a fact - in all possible contexts. What's the union of a set of cutlery and a bouquet?
It's irrelevant, since neither is a set in the current sense.

Your contempt for plain thinking is leading you to accept logical platitudes as fact.
Fascinating.

I'll give you a hint: If A and B are sets then the union of A and
B is the set of all x such that x is an element of A or x is an
element of B.
[Lets ignore the fact that a "set of all ...." is simply "all".]

Erm, that's not a fact. The set of all real numbers is one thing;
all real numbers _are_ many things.

(Ignoring the fact that a proposition of the sort 'a set of x' is not a set)

'All' (total) and 'set of all' are synonymous, by your lights.

Your definition is either wrongly transcribed or just wrong. It should read: If A and B are sets then the union of A and all other sets, and the union of B and all other sets is the set of all x such that x is an element of A or x is an element of B.

My gosh, you honestly don't know what the union of two sets is.

Perhaps you did not notice something quite strange about your definition, which needed tidying up or accounting for:

Consider the outcome that x is an element of A, and not B. This means that x is an element of A and not any other set.

In other words, you distinguished both A and B as a condition of a union, but only A or B actually figures as a condition of a union.
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