>But then for > Foy any F such that > F entails Theorem V applies to S, F > is an even bigger > (stronger) assumption about S.
I'm confused by this. It seems that you are responding to yourself. The original quote (at the top of your post) isn't mine. It is something you said. I'm somewhat tired so maybe I'm just lost here.
moving on...
> > Of course there may be a whole gradation of weaker, > stronger, and not > comparable assumptions to make about an arbitray > system S.
But the fully general thm assumes very little.
And > whatever is entailed about systems that satisfy > stronger assumptions > holds for systems that satisfy weaker assumptions.
but conditions 1 & 2 are weaker.
> And for particular > systems, we can prove that certain of those > properties hold for the > particular system. Yet in all of that I don't see any > problem with > Godel's remark about generality nor with our ability > to carry out the > generality theorem rigorously and routinely.
and this process results in a thm that it weaker then godel's thm and does not entail it.
