On Apr 14, 4:51 am, Rudy Canoza wrote:
Goo - ****wit David Harrison, THE GOOBER, a colossally stupid ****wit
and a stupid credulous Southern Baptist shitworm - lied and presented no
challenge:
On Thu, 10 Apr 2008, Rudy Canoza humiliated Goo****wit *again*:
Goo - ****wit David Harrison, THE GOOBER, a colossally stupid ****wit and a stupid credulous Southern Baptist shitworm - lied and presented no challenge:
On Thu, 10 Apr 2008, Rudy Canoza humiliated Goo****wit *again*:
Goo - ****wit David Harrison, THE GOOBER, a colossally stupid ****wit and a stupid credulous Southern Baptist shitworm - lied and presented no challenge:
On Thu, 10 Apr 2008, Rudy Canoza humiliated Goo****wit *again*:
On Tue, 8 Apr 2008 00:51:51 -0700 (PDT), Rupert wrote:
In Moshé Machover's "Set Theory, Logic and their Limitations" there is
a section titled "Axiomatizability" in which a detailed and precise
definition of "axiomatizable" is given. The word appears in the
statement of a theorem in that section. It also appears in the
statement of an important theorem in Stephen Simpson's highly
acclaimed "Subsystems of Second Order Arithmetic".
I typed "Shorter Oxford English Dictionary axiomatizable" into Google
and clicked "I'm feeling lucky". I got a logic paper published by
Oxford University Press. Unfortunately the Shorter Oxford English
Dictionary is not available on-line for free.
The number of hits for "axiomatizable" on Google is astronomical. This
article might be of some interest:
http://en.wikipedia.org/wiki/Elementary_class
We also have this:
http://encyclopedia.thefreedictionar...atizable+class
When we type "axiomatizable dictionary" into Google, the first hit we
get are the entries for "axiomatize" and "axiomatization" in Merriam-
Webster, which was Ball's original source. Similarly, Merriam-Webster
contains "plagiarize" but not "plagiarizable", although the latter
word gets a large number of hits on Google.
So maybe according to Ball's philosophy, "axiomatize" is a real word
but "axiomatizable" is not, "plagiarize" is a real word but
"plagiarizable" is not. I don't know. Would that I could fathom Ball's
subtle mind.
So anyway, apparently when I used "axiomatizable" in my paper I was
engaging in "inappropriate use of specialized jargon". (Ball, please
note: this is satire, I am not conceding your point of view here.
Sorry, people, Ball needs to have points like that explained to him).
Presumably Stephen Simpson was also doing so in his highly-acclaimed
"Subsystems of Second Order Arithmetic". And so Ball was entitled to
call me a "pompous fat ****". And I'm continuing to debate Ball on the
matter out of a masochistic compulsion rather than a desire for comic
material. And the fact that he "mockingly and derisively snips my
posts" means that he is winning.
And so the fun goes on.
Too funny, rupie - just too ****ing funny!
It's funny that you think so Goo, no doubt about it.
No
Now that
you've had some time to settle down from the horrible confusion
the information overload caused to your tiny crumb of brain, why
not try to address some of the facts that were presented to you,
Goo?
rupie's oh-so-earnest effort, and need to show how smart he
is, are what's funny.
LOL! Your cowardly reaction to them is funny Goober, but
there's nothing funny about the information he provided. It's
funny that you can't comprehend it and are afraid to comment
on it...your confusion is hilarious Goo. If you ever think you
have some clue about any of it, it would no doubt be great
fun to see you try to comment, especially if you can get back
to the reason he introduced you to the term to begin with. Since
you've already made a complete fool of yourself by crying about
the fact that he presented you with information, you don't really
have much to lose by trying to understand it Goo.
He provided no "information", Goo, just as you do not "point out"
or "explain". You bullshit, Goo - that's all.
Try to at least comprehend that
He provided no "information", Goo. You do not "point out" or "explain.
You bullshit.
In this post
http://groups.google.com/group/alt.s...5?dmode=source
I wrote:
`I have a nice book by Moshé Machover called "Set Theory, Logic, and
their Limitations". You might enjoy it; it's at an introductory level.
Let me quote.
"Section 8. Axiomatizability
Recall (Def. 2.7) that a set of postulates (a.k.a. extralogical
axioms) for a theory Sigma is a set of sentences Gamma such that Sigma
equals the deductive closure of Gamma. Having a set of postulates is
no big deal: every thery Sigma has one, because (by Def. 2.5) Sigma
equals the deductive closure of Sigma. In order to qualify as an
axiomatic theory, Sigma must be presented by means of a postulate set
Gamma specified by a finite recipe. This does not mean that Gamma
itself must be finite. (Of course, if Gamma is finite then so much the
better, for then its sentences can be specified directly by means of a
finite laundry list.) Rather, it means that we are provided with an
algorithm - a finite set of instructions - whereby the sentences of
Gamma can be generated mechanically, one after the other. By Church's
Thesis, this is equivalent to saying that T_Gamma must be given as a
recursively enumerable property.
8.1. Conventions
(i) When we say that a set Gamma of sentences if recursive (or
recursively enumerable), we mean that T_Gamma is a recursive (or
recursively enumerable) property.
(ii) When we say that Gamma is given as a recursive (or recursively
enumerable) set, we mean that it is given in such a way as to enable
us to program a computer to operate as a dedice-T_Gamma (or enumerate-
T_Gamma) machine. Similarly, when we say that we can find a recursive
(or recursively enumerable) set of sentences Gamma, we mean that we
can describe Gamma in such a way as to indicate how a computer can be
programmed to operate as a decide-T_Gamma (or enumerate-T_Gamma)
machine.
8.2. Definition
(i) A theory Sigma is axiomatic if it is presented by means of a set
of postulates Gamma, which is given as a recursively enumerable set.
(ii) A theory Sigma is axiomatizable if there exists a recursively
enumerable set Gamma of posulates for Sigma.
8.3. Remark
Note that being axiomatic is an intensional attribute; it is not a
proerty of a theory as such, in a Platonic sense, but describes the
way in which a theory is presented. On the other hand,
axiomatizability is an extensional attribute of a theory as such,
irrespective of how it is presented.
[...]
Theorem 8.12. The set of true sentences in the first-order language of
arithmetic is not axiomatizable."
That last theorem is a version of Gödel's theorem, proved in 1931, the
most famous theorem in mathematical logic of all time and widely
regarded as the most important contribution to logic since Aristotle.'
This provides some information.
In the first post in this thread, I wrote:
`In Moshé Machover's "Set Theory, Logic and their Limitations" there
is
a section titled "Axiomatizability" in which a detailed and precise
definition of "axiomatizable" is given. The word appears in the
statement of a theorem in that section. It also appears in the
statement of an important theorem in Stephen Simpson's highly
acclaimed "Subsystems of Second Order Arithmetic".
I typed "Shorter Oxford English Dictionary axiomatizable" into Google
and clicked "I'm feeling lucky". I got a logic paper published by
Oxford University Press. Unfortunately the Shorter Oxford English
Dictionary is not available on-line for free.
The number of hits for "axiomatizable" on Google is astronomical. This
article might be of some interest:
http://en.wikipedia.org/wiki/Elementary_class
We also have this:
http://encyclopedia.thefreedictionar...atizable+class
When we type "axiomatizable dictionary" into Google, the first hit we
get are the entries for "axiomatize" and "axiomatization" in Merriam-
Webster, which was Ball's original source. Similarly, Merriam-Webster
contains "plagiarize" but not "plagiarizable", although the latter
word gets a large number of hits on Google.
So maybe according to Ball's philosophy, "axiomatize" is a real word
but "axiomatizable" is not, "plagiarize" is a real word but
"plagiarizable" is not. I don't know. Would that I could fathom Ball's
subtle mind.'
That provides some information.
There is no reason why you should try to understand all this
information if you don't want to. I proved beyond the slightest
rational doubt that "axiomatizable" is a real word a long time ago.
That is the main point. Any sensible person can confirm that it is a
real word by typing it into Google. Your continued denials that it is
a real word are what has everyone rolling in the floor. Say it one
more time for us, Ball. Go on
