Re: Godel proved maths inconsistent not incompleteness theorem

On Wed, 12 Mar 2008 19:55:01 -0700 (PDT), Charlie-Boo
<shymathguy@xxxxxxxxx> said:
...
Wffs refer to relations (sets.) Can they refer to non-sets there?
Wffs contain operations on relations. Can those operations be done on
nonrelations?

The problem was they figured every wff defined a set based on the wff
being true when a value is substituted for a free variable. Then they
thought of {x|~(x e x)} and there was a wff that was not a set. So
they said, ok, a wff is not always a set.

My god. What must it be like to be so profoundly muddle-headed? I
really do feel badly for you.

But there are only aleph-1 wffs

Goodness me. (aleph_1 is uncountable. You probably mean aleph_0.)

and aleph-2 sets of numbers alone,

You probably mean aleph_1 -- though, so understood, your claim assumes
the continuum hypothesis. You might find it helpful to try to
understand why. Good luck!

so there are plent more sets than wffs and we can say that there is in
fact a set for every wff. It is counter-intuitive to say sets do not
include what all wffs define.

In any case, they set out to define what any set can define, when the
real problem was they needed to be exact about terms such as wff.

If you first decide if a wff can make a reference to something that is
not a set, then if yes, then naturally these wffs are not sets, and if
no, then the {x|~(x e x)} example is NOT a set and we still have each
wff defining a set. So we don't really need to worry about what's in
a set as we do in ZF. We just need to be careful about the formal
system - what is the real syntax of a wff? Can it contain references
to nonsets?

The depth of your confusion is truly great. In this light your profound
ignorance of the history and content of set theory is more
understandable. I will read your posts with more compassion in the
future.

.

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