> At 05:38 PM 04/11/96 MST, Jason McVean wrote:
[CLIP]
> >It should be written in a fully consistent language that is
> >derived in Appendix A from first principles in such a way that
> >the meaning of any bit of the book is unambiguous. Because of
> >this, it is really tedious to read. Note that the book doesn't
> >contain information on whether cubism is better than realism.
> >Can such a language exist? I don't know. But I'm also not sure
> >that the lack of such a language prevents us from communicating
> >things such as "the helium atom is more massive than the
> >hydrogen atom" and an endless collection of similar statements
> >unambiguously. In the end, that's what I'm getting at.
>
> So you agree that even if the language this book is written in
> can't exist, and ipso facto the book can't possibly exists, we
> can still communicate true statements? I agree.
Or perhaps the language is not derivable from first principles, but still
is a language?
I'm going to recall some theory of languages from the viewpoint of CIS.
These numbers are arbitrary conventions, and I'm going to be liberal with
the descriptions. Don't worry about meaning; that's too slippery for *this*.
"Recursively ___" is one way to formalize "derived from first
principles".
Type 3: "Context-free translation, finite-time".
Type 2: "Recognizable in finite time, symbols may have different
translations depending on context."
Type 1: "Recursively recognizable, but not necessarily finite time."
Type 0: "Recursively enumerable; definitely not finite time."
None of the above.
Note that Type 0 is NOT recursively recognizable, and "none of the above"
is not even recursively enumerable.
Needless to say, computer languages have undesirable compilation
properties at Type 1 and lower.
[CLIP]
> >If I work from that definition then the AT must be true since it
> >is composed only of true statements. So the contention must be
> >either that such a conjunction is not possible, or that there are
> >no true statements. I don't think many here would concede the
> >latter. So is the sticking point the former?
>
> The sticking point might be that there are no absolutely true
> statements (except maybe within formal systems like math) or that
> the conjunction is impossible because there are an infinite number
> of true statements.
The second caveat is IFFY. I could abusively interpret it to say that basic
arithmetic rules cannot be stated, because they could be broken down
into an infinite conjunction of statements.
One of the common techniques for making progress in math is to create
notation that allows discussion of infinitely many rules/objects in a
finite space.
[CLIP]
//////////////////////////////////////////////////////////////////////////
/ Towards the conversion of data into information....
/
/ Kenneth Boyd
//////////////////////////////////////////////////////////////////////////