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From: Ben Bacarisse <ben.usenet@bsb.me.uk>
Newsgroups: comp.theory
Subject: Re: Simply defining =?iso-8859-1?Q?G=F6del?= Incompleteness and Tarski Undefinability away V33 (Mendelson Satisfiability)
Date: Tue, 28 Jul 2020 03:11:15 +0100
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olcott <NoOne@NoWhere.com> writes:

> On 7/27/2020 5:41 PM, Ben Bacarisse wrote:
>> olcott <NoOne@NoWhere.com> writes:
>>
>>> On 7/27/2020 8:12 AM, Ben Bacarisse wrote:
>>>> olcott <NoOne@NoWhere.com> writes:
>> <cut>
>>>>> Thus Father_of(a26, a87) would be Boolean where a26, a87 are in the
>>>>> Domain of Humans.
>>>>
>>>> I'm going to stop commenting on this sort of issue.  You won't say what
>>>> Father_of is and you won't even say what language you are using.
>>>> Mendelson uses 'a' with a subscript for constants in a formal language,
>>>> but you talk of a26 and a87 as being "in the domain" (with a capital
>>>> letter for some reason).  I just don't have time to try to unravel what
>>>> you mean.  It's possible that even you don't know if Father_of is a
>>>> predicate or a function symbol in the formal language, or a
>>>> corresponding relation or function in some interpretation of it.
>>>
>>> You can' possibly imagine that I a referring to the exactly same
>>> context as Mendelson unless I always copy his whole page 57 ?
>>
>> (a) I don't sit here with Mendelson open at page 57 (it's 58 in my very
>> old edition).
>>
>> (b) You changed the name so if I /was/ looking at Mendelson I would
>> assume you were referring to something different.
>>
>> (c) You write a26 and a87 which Mendelson uses for constants in a
>> language and therefore make no sense in the context to his 'father of'
>> relation.
>>
>> So get off your high-horse and make yourself understood.  I won't keep
>> trying to work out what you mean.  You tell me what you mean.  By all
>> means use the same terms, syntax and wording as Mendelson, but you will
>> need to know how to use them correctly.
>>
>> I still have no idea what you mean by "Father_of(a26, a87) would be
>> Boolean".  If you mean what Mendelson talks about as 'father of' it is a
>> set of pairs.  A subset of DxD.  Boolean (whatever you mean by that in
>> this context) does not come into it.
>>
> For a particular ordered pair of individual humans the first
> individual human either is the father_of the second one or not.
>
> I don't see why this is so difficult for you.

It is not.  That is why I advise you to use words.

-- 
Ben.