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LauLuna
Posts:
177
From:
Siles, Jaén, Spain
Registered:
5/29/06


Re: Skepticism, mysticism, Jewish mathematics
Posted:
Jul 30, 2006 5:27 AM


david petry wrote:
>It seems clear to our skeptic that if we are to believe that >the formal theorems in our formalism should be accepted as compelling >arguments, then at the very least it must be the case that we already >believe that our formalism is consistent, and hence, no possible formal >proof within that formalism could be considered to be the evidence that >compels us to believe that the formalism is consistent. And our skeptic >asks, is that not already the essential content of Godel's theorem?
You are conflating two meanings of "prove": proving as proving someting true (let's say "PROVE") and proving as generating as string of symbols the way a formal system could do (let's say "prove"). And, consequently, you confuse two meanings of "sentence": sentence as "formal sentence" and sentence as the proposition resulting from some interpretation of some formal sentence.
Gödel PROVED that some formal systems don't prove some formal sentences, while your skeptic PROVES that those systems don't PROVE some interpretations of those sentences.
Regards



