Re: Please critique my set theoretic approach to a classic syllogistic fallacy

On Sep 30, 5:03 pm, G. Frege <nomail@invalid> wrote:
On Sun, 30 Sep 2007 08:26:06 -0700, Dan Christensen <d...@xxxxxxxxxxx>
wrote:



But maybe "c=" for a subset

Right. At ASCII level. But this might be converted to

c
=

in the main window of your system/application, no?

This would be a pain to key in. I like to keep all symbols on the same
line of text.

Sure. Actually, I meant a single symbol here (but you see, I can't
reproduce it in an ASCII environment). :-)



I'm sure it would mean an improvement of [to?] your system.

Yes.

In the mean time, you can reuse the <= and < relations for subset and
proper subset respectively with the following initial premises:

ALL(a):ALL(b):[Set(a) & Set(b) => [a<=b <=> ALL(c):[c e a => c e b]]]

ALL(a):ALL(b):[Set(a) & Set(b) => [a<b <=> ALL(c):[c e a => c e b] &
EXIST(c):[c e a & ~c e b]]]

Right. This makes sense - seems to be a reasonable (ad hoc)
workaround:



This shouldn't cause a conflict with the <= and < relations for
natural numbers because they not defined to be sets in my system (see
Numbers menu).

I see.

F.
--

E-mail: info<at>simple-line<dot>de

Did study the proof a bit
think there are to many equivalences in (<==>)
while I guess they should be implications (==>)

For readability use much more parentheses

what do you mean by ~a =x ?
~(a=x) or (~a =x)



I am missing an existential elimination to undue the E-spec of line 5.
(or are you thinking it isn't necesary?)

Hope this helps am not a pro in set theory.

.

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