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As I was musing on the subject of mathematics as a modeling tool
for nature, I realized that some of my wording in this paragraph from a post
this morning (copied in below) is ambiguous:
It makes sense to me that "purely syntactic" expressions of formal
mathematics move into realms which do not exist in nature (like "transfinites,"
or different "sizes" of infinities, for example). Since natural systems are
bound by contextual constraints, any purely syntactical mode of modeling is not
always going to be "congruent". Context is equivalent to "semantics". In
other words, there is meaning/information in the relations created by context.
So when mathematics is bound by the semantics of mathematics it's not a
problem-- it's only when science tries to say that nature is like mathematics
that it becomes a problem. ("We must never forget that number theory is
about numbers.")
The last sentence ought to read: It is only when science tries to
say that nature is like a purely syntactic version of mathematics that it
becomes a problem.
Sorry for the omission!
Judith
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