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Author: lwalke3lwalke3
Date: Jan 5, 2008 22:49
On Dec 10 2007, 5:01 pm, Zaljo...@ gmail.com wrote: > TT is the set of all sentences entailed ( from first order logic with
> identity and the primitive binary relation e and the primitive
> constants V and k, and the primitive one place function symbole F and
> the primitive binary relation symbole < ) by the following non
> logical axioms:
Back in some of Zuhair's more recent threads, we were discussing a
proof of MoeBlee's, which proved some of Zuhair's theories
inconsistent.
It appears that TT is untouched by MoeBlee's proof -- we have _not_
proved TT to be inconsistent yet. To see why, let us consider what
exactly is going on in TT.
As I stated earlier, Zuhair based his TT on Quine's NF. Now I must
admit that I'm not as familiar with NF as I am with ZF. But before
MoeBlee (or anyone else for that matter) simply suggests that I read a
book on the subject, let me state that I already have. For you see,
there's an online book about NF (Holmes, 1995?):
http://math.boisestate.edu/~holmes/holmes/head.pdf
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4 Comments |
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Author: M_SHIRAISHIM_SHIRAISHI
Date: Jan 5, 2008 15:26
M_SHIRAISHI wrote:
> ＞飛行機を使われなかったことは確かだ
>
> Ooro（往路）wa tasuka-ni（確かに）airplane wo Stsukawa-na-katta,
> Sukasu（しかし）, Sukasu, sono mata Sukasu, Fukuro（復路）wa
> airplane wo tsukawa-zaru wo enakatta.
>
> Nannto, nannto, nanto...
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4 Comments |
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Author: lwalke3lwalke3
Date: Jan 5, 2008 15:02
> I already saw that all my theories has been inconsistent as lawl
> proved!
Actually, there's one theory I forgot to check -- Type Theory. And
it appears that TT is not destroyed by the Lesniewski Paradox,
because the formula MoeBlee uses to define r:
"Let Ay(yer <-> (~y=r & Ez(Ax(xey <-> (~x=y & x=z)) & ~yez)))."
is not stratified! For let us consider the types of the variables:
since
xey appears, x has a lower type than y. Since ~yez appears, y has
a lower type than z. So x has a lower type than z
-- but then we
have x=z, so it's not stratified!
I'll post more in the TT thread, as well as comment on V theory, as
well as the refutation of my claim that DST is inconsistent in due
time.
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no comments
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Author: olingaaolingaa
Date: Jan 5, 2008 09:46
I once read an article describing a fallacy committed by declaring
everyone who does not agree with a certain point-of-view is mentally
defective, unenlightened, or spiritually unreceptive. Typically this
fallacy is committed by extreme ideologues, cults, etc. to avoid
rational analysis of their views. I vaguely recall the term "closed
system" being applied. What is the name of this logical fallacy? Any
links to articles about it would be great!
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6 Comments |
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Author: ZaljoharZaljohar
Date: Jan 5, 2008 08:38
Hi all,
In the Wikipedia: Ackermann's set theory we read the following:
3) Reflection axiom schema: Let F(y,z1,...,zn) be any formula which
does not contain the constant symbol V or the variable x free. If
z1,...,zn e V then
Ay (F(y,z1,...,zn) -> yeV) -> Ex( xeV & Ay (yex<->F(y,z1,...,zn))).
are axioms.
what does z1,...,zn actually mean? is it a string of all free
variables in F ? or it is a string of all constants and free variables
in F?
It is clear that it should be mean the later, i.e it is a string of
all free variables and constants in F, otherwise if it meant the
former, then the theory will be inconsistent!
My question is: is there a name given to the z(s) in z1,...,zn, like
for example :the arguments of F or something like that, that can
reflect the use of this string to denote both constants and variables
in F.
Zuhair
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8 Comments |
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Author: ZaljoharZaljohar
Date: Jan 5, 2008 08:22
So this would be simply the corrected version of my last theory V.
V = Ackermann + self inclusion + universal comprehension schema.
self inclusion ( irregularity ): Ex xex
Universal comprehension schema: If P is a formula in which x is not
free, then all closures of
~Ay (P <-> (P & ~yey)) -> ExAy (yex<->P)
are axioms.
/Theory definition finished.
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1 Comment |
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Author: ZaljoharZaljohar
Date: Jan 5, 2008 08:17
> Hi all,
>
> I already saw that all my theories has been inconsistent as lawl
> proved!
>
> This is my last theory.
>
> V is the set of all sentences entailed (from FOL with identity and the
> primitives e and V) by the following non logical axioms.
>
> 1) Extensionality: as in Z
> 2) Class comprehension: if Q is a formula in which x is not free, then
> all closures of
> ExAy ( yex<-> (yeV & Q) )
> are axioms.
>
> The theorem E!xAy(yex<->(yeV & Q)) is not difficult to prove.
>
> Define: x={y|Q} <-> Ay(yex<->(yeV & Q)). ...
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Author: ZaljoharZaljohar
Date: Jan 5, 2008 04:16
> On Jan 4, 4:41 pm, Zaljo...@ gmail.com wrote:
>
>
>
>
> >> Hi all,
>
>> I already saw that all my theories has been inconsistent as lawl
>> proved!
>
>> This is my last theory.
>
>> V is the set of all sentences entailed (from FOL with identity and the
>> primitives e and V) by the following non logical axioms.
>
>> 1) Extensionality: as in Z
>> 2) Class comprehension: if Q is a formula in which x is not free, then
>> all closures of ...
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