Re: Formal systems that cannot possibly be incomplete except for unknowns and unknowable

On 5/5/25 10:46 AM, Mr Flibble wrote:

On Mon, 05 May 2025 07:04:15 -0400, Richard Damon wrote:
 

On 5/4/25 10:23 PM, olcott wrote:

When we define formal systems as a finite list of basic facts and allow
semantic logical entailment as the only rule of inference we have
systems that can express any truth that can be expressed in language.
>
Also with such systems Undecidability is impossible. The only
incompleteness are things that are unknown or unknowable.

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Can such a system include the mathematics of the natural numbers?
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If so, your claim is false, as that is enough to create that
undeciability.
>
>

The language of such a formal system is an extended form of the
Montague Grammar of natural language semantics. I came up with this
mostly in the last two years. I have been working on it for 22 years.
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The Montague Grammar Rudolf Carnap Meaning postulates are organized in
a knowledge ontology inheritance hierarchy.
https://en.wikipedia.org/wiki/
Ontology_(information_science)

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And the problem is that either your claim is wrong, or your logic system
is just shown to be too small to be useful for many of the things we
want to be able to do because it can't support the mathematics of
Natural Numbers.
>
You don't seem to understand that all the properties you don't like
about Logic Systems are all conditioned on the ability for the system to
have a certain level of power in their ability to do logic. "Tpy"
systems that have been limited below that level will not experiance the
problems, but also are too weak to do the problems we typically want to
do with logic.
>
This ultimate shows your fundamental misunderstanding of what you are
talking about, especially your inability to handle abstractions, and
things that can create "infinities".

 You are fucking clueless about mathematics it seems: it is not possible to
create infinites using the mathematics of natural numbers (clue: division
by zero is undefined and infinity is not a number).
 /Flibble

Then what is the size of the set of Natural Numbers?
what is the sum of all the Natural Numbers?
The properties of the Natural Numbers deal with the infinite.