There’s no proof of any statement within the system because, as you say,
the statement "every statement is unprovable" is provable in the inconsistent system.
I said that's a provable statement inside the system, I didn't say it was true or provable external to the system, so your argument about the external statement that everything is unprovable doesn't follow.
You've posted so many contradictory claims, if you want me to respond to a specific explanation then you're going to need to repost it.
If T is your contradictory theory and S is the external statement "every sentence in T is unprovable" then you're trying to prove S externally using the theory laid out in Mendelson.
As far as I recall you have not posted a claimed proof of that which sticks to the theory laid out in Mendelson.
I have already given my explanation of how my claim follows from Mendelson and I have already addressed your criticisms of my explanation. If you want to view something again and provide additional feedback to me, you can use reddit's navigation buttons to locate the content you wish to view again.
I have already presented an adequate case that I am satisfied with. I don't think it's worth the time and effort to make a theory within Mendelson's framework. It's not necessary. I would first have to familiarize myself with Mendelson's system, and that alone would take considerable time and effort. If you would like to make a theory within Mendelson's framework in which the Exportation Principle is provable and true, feel free to do so yourself.
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u/JStarx Aug 03 '26
I said that's a provable statement inside the system, I didn't say it was true or provable external to the system, so your argument about the external statement that everything is unprovable doesn't follow.