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

On 3/21/25 6:47 PM, olcott wrote:

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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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.
 

You could try, but it can't be done and allow for any reasonable level of power in the logic. You basically need to have a system that can only prove a finite number of facts, so you can check that none of them are inconsistant.