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Re: On recursion and infinite recursion (reprise)

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From: polco...@gmail.com (olcott)
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Subject: Re: On recursion and infinite recursion (reprise)
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Date: Tue, 3 May 2022 13:06:24 -0500
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by: olcott - Tue, 3 May 2022 18:06 UTC

On 5/3/2022 12:17 PM, Mikko wrote:
> On 2022-05-03 14:38:57 +0000, olcott said:
>
>> On 5/3/2022 4:36 AM, Mikko wrote:
>>> On 2022-05-02 16:18:36 +0000, olcott said:
>>>
>>>> It seems to me that all infinitely recursive definitions are invalid
>>>> and I am having an excellent dialogue with some Prolog folks about
>>>> this in comp.lang.prolog.
>>>
>>> One of the rules that define Prolog language is
>>>
>>> arguments ::= argument | argument "," arguments
>>>
>>> which is infinitely recursive. Is it invalid? Is Prolog invalid because
>>> of this and other infinitely recursive rules?
>>>
>>> Mikko
>>>
>>
>> If would have to be invalid because it can never be resolved.
>
> What would be invalid? Prolog? Definition of Prolog?
> Why "would be" and not "is"?
>
> Mikko
>

Expressions that cannot be resolved in Prolog that fail the
unify_with_occurs_check test proves that these expressions are
semantically incorrect.

It is generally the case that every expression of any natural of formal
language that cannot be derived by applying truth preserving operations
(such as Prolog rules) to expressions known to be true (such as Prolog
facts) cannot possibly be correctly construed as true.

Dogs are animals (purely analytic)
There is a small dog in my living room right now (Empirical).

This is true for the entire body of analytic knowledge which only
excludes expressions of language that rely on sense data from the sense
organs to verify truth.

The proof that this is correct is that no counter-examples exist.
When G is considered true and unprovable there is some way the "true" is
derived, it is not merely a wild guess.

Just like Prolog databases True is limited to a specific formal system,
one formal system is the entire body of analytic knowledge: EBAK. This
is an entirely different formal system than PA.

unprovable in PA and true in EBAC is not the same thing as true and
unprovable. unprovable in PA means not true in PA, and true in EBAC
means provable in EBAC.

--
Copyright 2022 Pete Olcott "Talent hits a target no one else can hit;
Genius hits a target no one else can see." Arthur Schopenhauer

Subject	Author
Re: On recursion and infinite recursion (reprise)	olcott