FOM: Complex i.:Questions for Daan Scott
Robert S Tragesser
RTragesser at compuserve.com
Fri Dec 19 09:17:33 EST 1997
Dear Dana,
First, I wanted to thank you for the
extraordinarily insightful explication of
the relationship between algebra and (complex)
geometry. It has given me an understanding how
to handle the problem of this relationship,
pointing to exact senses in which geometric
understanding is mathematically originary.
I am wondering if you'd contribute your views
to some related (I think) inter-related threads:
(1) the sense in which the continuum problem
has an essential geometric (inclusive of fluidity
of flowingness as in Newton and W.R.Hamilton,
Brouwer and in moments Weyl).
(2) your sense of what Goedel called (according
to Wang) the spatial character of sets; I don't
know what he meant, but it suggests an early
view of sets as expressed in the opening chapters
of Hobson of their deepest motivating role being
the representation of geometric continua,
(3) Hobson are also argued that there is no reason
why there cannot be equally sound but conflicting
mathematical representations of intuitive continua.
So I am wondering about your view of the
soundness of Brouwer's mathematical representation
of continua, the sense in which he might be said
to have settled the cobntinuum problem, or, in
general,
(4) your view of sense of a Brouwer like agenda for
solving the continuum problem (which of course would
require a re-statement of it):
(4a) a Bairest restriction of the sets that are
relevant to the analysis of (intuitive) continua,
(4b) or more radically, more like Brouwer, to
associate the continuum problem so deeply with
intuitive and mathematical considerations of geometric
or fluidic continua that a radical revision of the
concept of set is called for in order to solve it.
(5) your view of what I take to be Harvey Friedman's
attitude that no "big picture" (general theory in the
old sense) is likely to settle CH (so that some special
considerations, _such as_ concerning geometric and fluidic
continua are relevant)
cheers, robert tragesser
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