Re: Why Tarski is wrong --- Montague, Davidson and Knowledge Ontology providing situational context.

On 3/22/25 11:00 AM, olcott wrote:

On 3/22/2025 7:05 AM, Mikko wrote:

On 2025-03-21 22:47:04 +0000, olcott said:
>

On 3/21/2025 3:10 PM, Richard Heathfield wrote:

On 21/03/2025 11:48, Richard Damon wrote:

On 3/21/25 5:33 AM, Richard Heathfield wrote:

>
<snip>
>

>
But what if they were /both/ right? It was an obvious worry, and so arose the great question: is mathematics consistent?
>
And Gödel proved not only that it isn't, but that it can't be.
>
Fortunately, to date inconsistency has tended to surface only in corner cases like the Halting Problem, but Gödel's Hobgoblin hovers over mathematics to this day.
>

>
Godel didn't prove that Mathematics wasn't consistent. He proved that it couldn't be proved to BE consistant within itself.

>
Yes, I rather overstated the case. Sorry about that.

>
Or we could simply define the rules for constructing a
formal system such that inconsistency cannot exist.

>
That is possible. An example is Horn clauses, which is the theory behind
Prolog. If the logic has no negation operator there is no posiibility to
express an inconsistency. But even then the question whether there is an
unprovable sentence is problematic.
>

 The body of human general knowledge that can be expressed
in language cannot possibly have any unprovable expressions
when truth preserving operations are the only category of
inference steps allowed.

So, your logic doesn't allow us to express the Goldbach conjecture in it?
We can't express the logic of Turing Machines?
It seems you are removing large swaths of "Human Knowledge" from your system.

 This system is somewhat similar to the restrictions that
ZFC set theory places on the creation of sets.
 

Nope. You might think so, but only because you don't understand what you are saying.
The only way to prevent the formation of unprovable expressions is to make your system too weak to be able to create the basic properties of the Natural Number system.