ONT Re: Signs Of Pragmata
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SOP. Note 4
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There is a point here that I am still struggling to express/explain on several
of my other lists, about the diference between the way that most mathematicians
think and the way that some logicians and some philosophers think (I probably
mean analytic not existentialist philosophers here). Mat has this sense of
due proportion about Plato's heaven that tells him how inexhaustible it is,
and that he is darn lucky to grasp this or that tiny patch of it at a time.
So when Mat says "universe" he always means "universe of discourse", or
"object (= space) in a category of related objects (= spaces)", always
a thing well-bounded by the frame of some venn diagram or category.
So it's always local and relative to the discussion in progress.
Growing out of this there's a type of "polymorphism", where the
number 1, at first sight an instance of constant value, 1 : U,
is also the constant function 1 : U -> U, where 1(x) = 1.
When you are reading "1" as the logical value "true", then
1 : U -> B = {0, 1} is the proposition "it's all good",
that is, the predicate that is true of every-thing in U.
This 1 is what presides at the top of the lattice of
functions (propositions, predicates) on U, and so
some people call it T = Top = Thing, but we start
getting into Big Trouble here, as now we are
ontologizing it (= ossifying it) and losing
the good senses of its local, relative,
polymorphic meanings. It lead to big
trouble in set theory once to think
that what's a thing in one context
is a Thing in all contexts.
Phil, in contrast, seems to think that it's within his grasp
to say many useful things about the literal universe, if not,
indeed, all possible universes. Mat thinks that sheer hubris.
Jon Awbrey
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http://www.cs.bsu.edu/homepages/mighty/history.html
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