Re: kung fu mereotopology

On Dec 23, 11:32 pm, lwal...@xxxxxxxxx wrote:

MoeBlee seems to imply that because the word "SET theory"
is used, tommy1729's proposed theory must a priori prove
certain properties, and he uses those assumed properties
in his proposed proof that TST is inconsistent.

No I don't "seem" to imply that AT ALL. I make no such implication
about "a priori" or even that a set theory must prove certain
properties. Rather, I said that when tommy1729 presents "the axiom of
the empty set" and "the empty set exists" then, unless he specifies
some other sense, I take him to mean the ordinary empty set axiom -
that there is a set that has no members - and I mentioned that he
calls his theory a 'set theory' in contrast as additional context that
IS present as opposed to 'mereology' which was NOT mentioned by him.

For example, MoeBlee assumed that because tommy1729 used
the word "SET theory" and stated that it has an Empty Set
Axiom, said axiom must be of the form:

Ex (Ay (y not-in x)).

(1) I don't claim that one can't have a variant of the empty set
axiom. But he didn't specify any variance. (2) And I mentioned that he
was in the context of set theory in response to the claim that he was
in the context of mereology. (And I did not even claim that there is
NECESSARILY not a theory that combines set theory and mereology, but
only that tommy1729 gave the names of ordinary set theoretic axioms in
context of his self-described set theory.)

And thus Tonio implied that galathaea, in her defense of
tommy1729, must have redefined "SET theory" (or maybe
"Empty Set Axiom") to avoid MoeBlee's inconsistency proof,
in the same way that one must redefine 1 to get "1+1 = 3."

I'm not sure whether galathaea's definition, or MoeBlee's
implied definition, of "SET theory" is the correct one.

I didn't even imply a definition of 'set theory'.

But
I disagree that a theory that is reasonably sound, such as
the theory of flattened mereology, can become inconsistent
just because one attached the name "SET theory" to it.

Oh, come on! Now you are waxing VERY silly. tommmy1729 didn't specify
a "flattened mereology". And I didn't try to make a "flattened
mereology" inconsistent just because it is named a 'set theory'.
Rather, he specified that there is a set that has no members and that
x in [x] while [x] has x as its only member, which is inconsistent.

MoeBlee



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Relevant Pages

  • Re: the return of the master : tommy1729
    ... MoeBlee's translation from tommy1729's axiom from ... English ("axiom of the empty set") to object language ... a _mereology_ theory that such an object exists. ...
    (sci.math)
  • Re: the return of the master : tommy1729
    ... | 1) axiom of extensionality ... Apart from the case of an empty set containing an empty set. ... There's no provision for this mentioned by tommy. ... In mereology this is: Given two sets, there is a set whose members are exactly the two given sets. ...
    (sci.math)
  • Re: the return of the master : tommy1729
    ... | 1) axiom of extensionality ... as the mereology page at Stanford. ... this definition of empty set: ... If you want some kind of Union to exist, ...
    (sci.math)
  • Re: the return of the master : tommy1729
    ... | 1) axiom of extensionality ... Apart from the case of an empty set containing an empty set. ... Basically if the axiom is for a flat mereology or related it is considered as the " existence " of the empty set axiom. ... | game theory can be restated in this set theory. ...
    (sci.math)
  • Re: Axiom of Pairing, Scheme of Replacement from others
    ... separation follows from the axiom of replacement together with the axiom ... Your hypothesis has uniqueness but not existence. ... Proof of separation from replacement: ... empty set is required. ...
    (sci.math)