Groups | Search | Server Info | Login | Register

Groups > comp.theory > #21873

Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V32 (Analytical knowledge)

Cross-posted to 4 groups.

Show all headers | View raw

On 2020-07-23 16:08, Keith Thompson wrote:
> olcott <NoOne@NoWhere.com> writes:
> [...]
>> The semantic meaning of the conceptual class of natural numbers is
>> defined as an ordered set of names that are associated with an ordered
>> set of finite strings of numeric digits. Functions and predicates have
>> also been stipulated to define semantic meaning this conceptual class.
> [...]
> 
> Why would you define the natural numbers that way?  Sequences of
> digits (I'm guessing you meant decimal, but you didn't say)
> are just a convenient way of representing them -- and it doesn't
> make sense until you've defined or derived a lot more knowledge.
> You need addition and multiplication before you can even say what
> "123" means, or demonstrate that 9+1=10.

I'm not sure 9+1=10 would be part of Olcott's language. Recall that the 
definition of of his 'language' included things like this:

ASCII_DIGITS "+" ASCII_DIGITS "=" ASCII_DIGITS

Note these aren't just ANY digits. They are ASCII_DIGITS. Interestingly, 
though, we don't use ASCII_PLUS or ASCII_EQUALS. There we just use plain 
ordinary + and =.

So presumably your 9+1=10 should really be 39+31=3130.

Unless of course he intends ASCII_DIGITS to be represented in binary 
rather than hex. And then there is the question of whether these should 
be 7 bits long each in accordance with the ASCII standard, or whether a 
looser, 8-bit interpretation should be used.

So many burning questions...

André

-- 
To email remove 'invalid' & replace 'gm' with well known Google mail 
service.

Back to comp.theory | Previous | Next — Previous in thread | Find similar

Thread

Simply defining Gödel Incompleteness and Tarski Undefinability away V32 (Analytical knowledge) olcott <NoOne@NoWhere.com> - 2020-07-23 15:01 -0500
  Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V32 (Analytical knowledge) André G. Isaak <agisaak@gm.invalid> - 2020-07-23 14:49 -0600
  Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V32 (Analytical knowledge) Keith Thompson <Keith.S.Thompson+u@gmail.com> - 2020-07-23 15:08 -0700
    Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V32 (Analytical knowledge) André G. Isaak <agisaak@gm.invalid> - 2020-07-23 16:51 -0600

csiph-web