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

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 membership 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.]


It clarifies the problem, for which I am still looking for a solution.

A and B have nothing in common in the scenario you potray. Only one is actually in the union. The other has nothing to do with it. If A is in the union, then B is no more pertinent than C, or X. Y. Z..
.

Relevant Pages

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