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

On 3/23/25 4:37 PM, olcott wrote:

On 3/22/2025 9:53 PM, Richard Damon wrote:

On 3/22/25 4:33 PM, olcott wrote:

On 3/22/2025 12:34 PM, Richard Damon wrote:

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:
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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:

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<snip>
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But what if they were /both/ right? It was an obvious worry, and so arose the great question: is mathematics consistent?
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And Gödel proved not only that it isn't, but that it can't be.
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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.
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Godel didn't prove that Mathematics wasn't consistent. He proved that it couldn't be proved to BE consistant within itself.

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

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

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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.
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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.

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So, your logic doesn't allow us to express the Goldbach conjecture in it?
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We can't express the logic of Turing Machines?
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The body of general knowledge that can be expressed in
language (is the actual body of general knowledge that
can be expressed in language) thus includes every tiny
detail about the Goldbach conjecture.

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Right, but knowing all the details doesn't get us the answer, we KNOW all the details that define the problem, we just can't test every number to see if it holds.
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 Part of the set of all general knowledge that can be
expressed using language is all of the details of
unsolved problems. It will know that no one knows
whether the Goldbach conjecture is true.

But it isn't being asked if anyone KNOWS the answer, it is being asked if the conjecture is TRUE or FALSE.
As has been pointed out, you are confusing TRUE(x) with KNOWN(x)
And this just shows you don't understand what you are talking about.

 

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I never defined "general" knowledge thus your critique
is apt. I had to make the set of basic facts finite
that is why I limited them to general knowledge.
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And either those define the basis of the Natural Numbers, at which point the various theorem will hold, or you don't at which point your
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 How do you say:
"I was going to go to the store to buy some vanilla
ice cream but they only had chocolate so I bought
a slice of Pizza instead" in arithmetic?

You could Godel encode it to a number. (I Think this is the basic description of the method)
Assign natural numbers to the each of the letters or punction marks
We then define p[i] to be the ith prime number
If the nth symbol has the value m[n] then we take the product over all positions of p[m[n]] ** p[n]
This will give you a unique number for every possible sentence, and allows you to add new items to the list (giving them high values for m) without needing to re-encode the rest of the list, and that number can be "easily" converted back into the original statement from the list of symbol encodings and the list of prime numbers, via a simple factoring exercise.

 

What it does not have is a set of truth preserving
operations from basic facts to a truth value of TRUE.
Is the Goldbach Conjecture known to be True? No.

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But the question is NOT "is it KNOWN to be True?" but "is it True?"
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 Then the answer is "no one knows".
The answer to the question: "What time is it (yes or no)?"
is that question is rejected as incorrect.

Which isn't a valid answer for a truth predicate,

 

Thus, you demonstrate that your whole argument is based on the FRAUD of a STRAWMAN, and that you are just too stupid to understand the difference between TRUTH and KNOWLEDGE.
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 I don't think that you are too stupid to know that you are lying.
You are certainly not stupid.
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but you are.
I have pointed out in DETAIL why you are wrong, and you have yet to point out an error in what I say, the best you do is try to ask for proof of something I say, that has actually be proven in the literature, something you are just too stupid to understand.