On 8/22/2018 10:55 AM, Stephen Curtiss Rose wrote:
Reality is anything, all, totality, the sum of semiotic existence.
Thus if I say Mello Rolls (something from my long ago childhood) in
the year 2099, it is real, Reality does not depend on the faculties
of the body or mind.
That is one possible way of using the word 'reality'. And it is
one of the main reasons why I did not use the word 'reality'.
For modal logic, Peirce adopted the words possibility,
actuality, and necessity and defined them as three distinct
universes.
I adopted his definitions and related them to a puzzle that has
plagued the philosophy of mathematics for centuries: When
you say "there exists an x" about some x in a mathematical
theory, where does that x exist?
Since many mathematical structures, including the integers,
form an infinite set, They can't exist in a finite universe.
One could say that they exist in a Platonic heaven, but then
you have to explain how that heaven relates to our ordinary
universe.
My proposal is the one I stated in my previous note to Ontolog
Forum (copy below). That universe of possibilities is big
enough to contain all semiotic types. Any marks and tokens
of those types would exist in our physical universe.
John
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From a previous note in this thread:
The definition I stated is absolutely precise. To emphasize
the precision, I'll restate it in 4-D coordinates -- but it
remains just as precise when you translate it to 3-D plus time:
1. Pure mathematics is the study of possibilities. Every
possible structure or process can be described by some
theory of pure mathematics, but no structure or process
of pure mathematics exists in actuality.
2. Everything in the universe that is actual is either a
4-dimensional region of space-time or it is wholly
contained within some 4-D region of space-time.
3. Applied mathematics is the practice of selecting structures
specified by one or more theories of pure mathematics and
using them to describe something contained within some 4-D
region of space-time. The descriptions of applied mathematics
are rarely, if ever, absolutely true. But it's often possible
to estimate the expected errors in measurement or prediction.
The distinction between #1 and #2 is precise. All the errors
and vague intermediate cases result from difficulties in #3.
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