Re: Goedel's undecidable G

In article <4335E52C.DB45F760@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
Jim Spriggs <jim.sprigs@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxx> wrote:

>Peter_Smith wrote:
>>
>> The Godel sentence is formed (in one version) by substituting into a
>> certain open wff U(x) the standard numeral for the Godel number of that
>> open wff.
>>
>> So even if we could fairly readily write down U(x) over a few dozen
>> pages, its Godel number at least on Godel's own scheme will be
>> horrendous (vastly more than the number of particles in the known
>> universe),
>
>Thanks. That was my worry, though I had not realized it was quite
>_that_ bad.
>
>> so writing down Godel sentence which embeds the standard
>> numeral SSS...S0 with that number of occurrences of the successor
>> function will be .... erm ...difficult!
>>
>> Which just dramatically makes the point that the size of "the" Godel
>> sentence here is evidently entirely dependent on the scheme of
>> Godel-coding that we use.

The good news is that John McCarthy gave a different (and more natural)
encoding in terms of "S-expressions" (with axioms analogous to those of
PA) that enables G to be written down in a page or 2.

--
---------------------------
| BBB b \ Barbara at LivingHistory stop co stop uk
| B B aa rrr b |
| BBB a a r bbb | Quidquid latine dictum sit,
| B B a a r b b | altum viditur.
| BBB aa a r bbb |
-----------------------------
.

Relevant Pages

  • Re: Goedels undecidable G
    ... > certain open wff Uthe standard numeral for the Godel number of that ... its Godel number at least on Godel's own scheme will be ... > so writing down Godel sentence which embeds the standard ...
    (sci.logic)
  • Re: Goedels undecidable G
    ... The Godel sentence is formed by substituting into a ... certain open wff Uthe standard numeral for the Godel number of that ... its Godel number at least on Godel's own scheme will be ... so writing down Godel sentence which embeds the standard ...
    (sci.logic)