On 6/14/2015 9:24 PM, Bruce Schuman wrote:
>> In science and engineering, identity is *never* observable.
>> Similarity is observable, and identity is *always* an inference.
>
> But in what way, and how constructed? (01)
If you think about perception, ask what it would mean to observe
identity. We observe qualities and patterns. We recognize that
some new experience is similar to some previous experience. But
there are no unique ids on them. We just have to rely on our
memories and try to decide (i.e., make inferences) whether two
things are "the same". (02)
> what is the relationship between a "real object" and an "abstract
> object" (a symbolic construction that represents the real object,
> in selected dimensions/aspects that are thought to be significant
> in the present context). (03)
Fundamental distinction (with credit to C. S. Peirce): (04)
1. Reality is what we live in. It's what we perceive and act upon.
Things and processes are chunks of reality that we experience,
analyze, use, and act upon in ways we find desirable. (05)
2. All abstractions are signs. All thoughts are signs. Some signs
refer to parts, aspects, or chunks of reality. Some signs refer
to other signs. And some signs relate signs to signs. The mind
is the totality of all the signs that anyone has experienced and
accumulated over a lifetime (no matter how short or long). (06)
> I want to find the simplest and most generic possible way to build
> up the abstract symbolic model. (07)
Answer by C. S. Peirce: Study the signs. (See ref's below.) (08)
> And to do this -- I think it makes sense to follow the primal
> language of computers -- bits and bytes... (09)
That's one useful kind of sign. But it's just one version of
mathematics, which is essentially a systematic way of analyzing
and constructing signs of signs of signs of signs... (010)
> A few days ago, I was looking at the definition of a set... (011)
That's another kind of mathematical sign system. There are
infinitely many kinds of mathematical systems. They can be fun
to play with (i.e., note the mathematical sign systems called
chess, bridge, go, tic-tac-toe, video games, etc.). And they
can be useful when used to analyze reality. (012)
> Maybe Wolfram has built this kind of math. (013)
Mathematica is a tool for defining and using mathematical systems.
Professional scientists, engineers, statisticians, etc., use it
for doing complex symbolic computations. The many users of
Mathematica have used it to represent and compute with all the
major and huge numbers of minor mathematical theories. (014)
> a bit is something like the lowest-level possible distinction
> in a hierarchy of constructed definitions that build “everything”
> represented as an abstraction... (015)
There are many different "simplest possible things". An empty
set is just as primitive as a bit, but it has different ways
of combining. (016)
> all defined in the absolute simplest/minimalist way. (017)
A point in geometry is another "simplest possible thing". But
Tarski developed a version of geometry in which the "simplest
possible thing" is a sphere. He defined a point as the limit
of an infinite sequence of nested spheres. That theory turns
simplicity on its head: the larger sphere is, in some sense,
"simpler" than the smaller thing nested in it. (018)
> This is the instinct. It’s 100% linear, 100% recursive,
> based on one zero-ambiguity primitive element... (019)
My reaction: it's just one choice among infinitely many
possible starting points. Category theory is a mathematical
approach that tries to avoid making any choice. Instead,
it's a theory about ways of relating theories. (020)
My reaction to category theory: It's nice, and it's very general.
But it's only one choice of a way of relating things. (021)
> I want to mandate an absolute fundamental linearization... (022)
I don't like mandates. They lead to rigid, fragile systems
that fail when they hit another system with a different mandate. (023)
> Objects are identical if they are defined in the same dimensions
> and have the same values in those dimensions. (024)
First point: you can define anything you like, but it won't
eliminate the need for inference to apply those definitions to
determine whether two things are "the same". (025)
Second point: The more rigid you make your definitions, the more
likely they are to fail when confronted with something new.
In an earthquake, softer wooden houses are safer than rigid
stone houses. (026)
Summary: Instead of trying to develop a perfect new system,
look for better ways to relate the immense diversity of imperfect,
but useful systems that people have successfully used and continue
to develop and invent. (027)
John
_________________________________________________________________ (028)
A couple of my articles based on Peircean principles: (029)
http://www.jfsowa.com/pubs/signproc.pdf
Signs, processes, and language games (030)
http://www.jfsowa.com/pubs/rolelog.pdf
The role of logic and ontology in language (031)
A good short book with lots of quotations by Peirce and
references to other useful readings: (032)
de Waal, Cornelis (2013) Peirce: A Guide for the Perplexed,
London: Bloomsbury Academic. (033)
Lectures by Peirce that give a good overview of his methods: (034)
Peirce, Charles Sanders (1898) Reasoning and the Logic of Things,
The Cambridge Conferences Lectures of 1898, ed. by K. L. Ketner,
Cambridge, MA: Harvard University Press, 1992. (035)
Two volumes of his most important writings: (036)
Peirce, Charles Sanders (EP) The Essential Peirce, ed. by N. Houser,
C. Kloesel, and members of the Peirce Edition Project, 2 vols.,
Indiana University Press, Bloomington, 1991-1998. (037)
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