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Paul Grobstein's picture

formal systems and infinities

Point well taken.  One may be "disinterested in" rather than "threatened" or "afraid" of formal systems.   Part of the objective on my mind is to make the case that formal systems are actually quite interesting, whoever one is.  The problem here, I think is how they are taught/talked about, as if they were a special activity of significance only in a specialized world and accessible only to those trained in that world.  Instead, they should be talked about as  a significant component of all of us, one we all use all of the time.  And better understanding them, both their strengths and their limitations, can be not only interesting but empowering for everyone.  It is through an appreciation of formal systems that we gain the ability to identify and transcend our own presumptions at any given time. 

Very much agree that the connection of formal systems to "mindless"/"mindful" and "soulless"/"soulful" is worth exploring further.  And expect that to be a significant component of the next, Turing/computers phase of our conversations.  To anticipate a bit, I'll almost certainly argue that the "mindless"/"soulful" state you describe is indeed "absolutely present" but is not actually "absolutely bountiful.  Unbounded.  Infinite."  It has a lot to be said for it (cf interconnected vastness, oceanic feeling, the taoist story teller), but there is lots beyond it, worlds/universes/states of being that can't be reached next except via skepticism and thinking.  Trees and computers are "absolutely present."  And limited, relative to the human brain, as a result.  Formal systems provide a way of transcending those limitations.  Piece wise, never absolutely.  All infinities, as per Cantor, are embedded in still larger infinities; none are "unbounded."  

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