Groups | Search | Server Info | Login | Register

Groups > comp.theory > #21455

Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V21

Cross-posted to 4 groups.

Show all headers | View raw

On 2020-07-05 12:56, olcott wrote:
> On 7/5/2020 1:44 PM, André G. Isaak wrote:
>> On 2020-07-05 12:38, olcott wrote:
>>> On 7/5/2020 11:53 AM, André G. Isaak wrote:
>>>> On 2020-07-05 10:42, olcott wrote:
>>>>> On 7/5/2020 11:28 AM, André G. Isaak wrote:
>>>>>> On 2020-07-05 09:31, olcott wrote:
>>>>>>> On 7/5/2020 8:17 AM, André G. Isaak wrote:
>>>>>>>> On 2020-07-04 15:28, olcott wrote:
>>>>>>>>> On 7/4/2020 1:21 PM, André G. Isaak wrote:
>>>>>>>>>> On 2020-07-04 10:36, olcott wrote:
>>>>>>>>>>> OVERVIEW:
>>>
>>>>> Since I view all of these things from the formalist approach of 
>>>>> operations on finite strings I assume that every variable refers to a
>>>>> random finite strings unless somehow specified otherwise.
>>>>
>>>> The formalist approach doesn't involve 'random strings'. The 
>>>> formalist approach approach refers to a specific way of interpreting 
>>>> formal systems. Formal systems do not consist of 'random strings'.
>>>
>>> Formal systems can be construed as applying to random finite strings 
>>> through a two stage vetting process:
>>> (1) The finite string is a WFF
>>> (2) The finite is derived from a possibly empty set of premises.
>>>
>>>     A language L on Σ is said to be recursive if there exists a
>>>     Turing machine M that accepts L and halts on every w in Σ+.
>>>     In other words, a language is recursive if and only if there
>>>     exists a membership algorithm for it. (Linz 1990:288).
>>>
>>> If we focus on the most essential aspect of formal systems that is 
>>> common across all formal systems:
>>>
>>> formal systems are comprised of a membership algorithm that decides 
>>> whether or not finite string w of alphabet Σ is a theorem of formal 
>>> system F.
>>>
>>>
>>> On 7/2/2020 9:22 PM, David Kleinecke wrote:
>>>  >    There is a finite set called Alphabet
>>>  >    Strings is the set of all finite successions
>>>  >      of members of Alphabet
>>>  >
>>>  >    A FormalSystem is a function on Strings to Boolean.
>>>  >
>>>
>>>> I don't see any step at all. I see a link to a google search page. 
>>>> What is the supposed step involved here?
>>>>
>>>> André
>>>
>>> Do you understand and agree with the simplified essence of the most 
>>> generic basis of the notion of a formal system as specified in 
>>> computer science by me and specified in math by David?
>>
>>
>> No. I do not agree with it at all.
>>
>> André
> 
> So there are formal systems that don't have anything like the notion of 
> a theorem?

No. I am saying that isn't the definition of 'formal system'.

André

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

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

Thread

Simply defining Gödel Incompleteness and Tarski Undefinability away V21 olcott <NoOne@NoWhere.com> - 2020-07-04 11:36 -0500
  Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V21 André G. Isaak <agisaak@gm.invalid> - 2020-07-04 12:21 -0600
    Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V21 olcott <NoOne@NoWhere.com> - 2020-07-04 16:28 -0500
      Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V21 André G. Isaak <agisaak@gm.invalid> - 2020-07-05 07:17 -0600
        Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V21 olcott <NoOne@NoWhere.com> - 2020-07-05 10:31 -0500
          Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V21 André G. Isaak <agisaak@gm.invalid> - 2020-07-05 10:28 -0600
            Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V21 olcott <NoOne@NoWhere.com> - 2020-07-05 11:42 -0500
              Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V21 André G. Isaak <agisaak@gm.invalid> - 2020-07-05 10:53 -0600
                Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V21 olcott <NoOne@NoWhere.com> - 2020-07-05 13:38 -0500
                Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V21 André G. Isaak <agisaak@gm.invalid> - 2020-07-05 12:44 -0600
                Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V21 olcott <NoOne@NoWhere.com> - 2020-07-05 13:56 -0500
                Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V21 André G. Isaak <agisaak@gm.invalid> - 2020-07-05 13:16 -0600
                Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V21 olcott <NoOne@NoWhere.com> - 2020-07-05 15:25 -0500
                Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V21 André G. Isaak <agisaak@gm.invalid> - 2020-07-05 14:46 -0600
                Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V21 olcott <NoOne@NoWhere.com> - 2020-07-05 16:08 -0500
                Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V21 David Kleinecke <dkleinecke@gmail.com> - 2020-07-05 15:28 -0700
                Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V21 (axiomatic basis of truth) olcott <NoOne@NoWhere.com> - 2020-07-05 17:50 -0500
                Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V21 (axiomatic basis of truth) Keith Thompson <Keith.S.Thompson+u@gmail.com> - 2020-07-05 17:13 -0700
                Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V21 (axiomatic basis of truth) olcott <NoOne@NoWhere.com> - 2020-07-05 20:37 -0500
                Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V21 (axiomatic basis of truth) André G. Isaak <agisaak@gm.invalid> - 2020-07-05 20:46 -0600
    Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V21 olcott <NoOne@NoWhere.com> - 2020-07-04 17:39 -0500
    Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V21 olcott <NoOne@NoWhere.com> - 2020-07-05 13:15 -0500

csiph-web