8 Dec
2021
8 Dec
'21
12:57 a.m.
Can I second John's recommendation?
I use Peirce's Symbolic referencing to model natural language, and this
provides a model flexible enough to supporting the arbitrary
transformations found in human thought.
In math, we may say "1 + 2 = 3", using the symbol '+' with the fixed
meaning of 'addition'. In computing, we create arbitrary functions,
using a functional notation: add( 1, 2 ), allowing us a large number of
functions - a much larger number than individual symbols with fixed
meanings.
The function is also a representation of Peirce's Semiotic triad, "what
is 1 plus 2" { "reply 1 plus 2 is 3" } => "1 plus 2 is 3".
The
interpretant is that which is created, in the body of the function, to
transform "what is 1 plus 2" into "1 plus 2 is 3". It is
learning-by-
wrote, or as Peirce talks about: 'habit'.
Learning-by-wrote may be frowned upon by anyone beyond kindergarden,
but I can show that it is: complete (ALL utterances map onto "reply i
do not understand"); Turing Complete - by the use of recursion; and, it
is also autopoietic - self-generating - by employing techniques
developed in the 1950s and 60s by the Pragmatic linguists - Austin,
Searle and Grice.
Moreover this works best in non-arithmetic verbal reasoning, a simple
example of which is: “i need a coffee” → “sorry I
do not understand” “to the phrase i need a coffee reply ok you
need a coffee” →“ok” “this implies that a coffee exists in my needs
list” →“ok” “this implies that if so reply yes i
know” →“ok” “this implies
that you add a coffee to my needs list” →“ok” “i need
a coffee” → “ok you need a coffee” “i need a
coffee” → “yes i know”
(NB. 'to the phrase X reply Y' - is an utterance which creates a Sign:
the initial denotation; 'this implies that ...' and 'this implies
...' are utterances which add subsequent connotations as to what
this utterance means: Interpretant) This allows users and their
devices to use speech, and devize algorithms at the point of use, much
in the way computers functional languages pre-defined by programmers.
I might not be a Peircean scholar, but I hope this example illustrates
that his Semiotic ontology - Symbolic referencing - is of real
practical use.
Hope this is of interest!
Kind regards,Martin
On Tue, 2021-12-07 at 17:38 -0500, John F Sowa wrote:
Barry> Landgrebe and I have been working on a BFO
physics Ontology
and on a mathematics Ontology, separate from BFO.
I'm glad to hear that you're finally developing an ontology for
mathematics and that it's independent of the current BFO.
Since it's impossible to do modern physics without a huge amount of
mathematics, I suggest that you combine your math ontology with BFO
in order to support physics.
There are three ways to combine an ontology of actual entities with a
math ontology:
1. Platonic: The mathematical forms are really real, and the
physical stuff is a degenerate approximation to reality.
2. Aristotelian: The physical entities are the real existents and
the forms exist only when they are embodied in physical stuff.
3. Peirce's update to Aristotle: All mathematical forms exist as
real possibilities, which may be used to describe or characterize
anything that exists in actuality or in any kind of imagined,
planned, intended, hoped, feared, described, communicated, or
hypothesized aspect of reality.
Peirce's version implies that pure mathematicians can talk and act
like Platonists (which they frequently do), but applied
mathematicians can focus on the actual universe while having an
infinite book of mathematical forms to use as they wish when they're
doing any kind of engineering, virtual reality, or plans for future
things that do not yet exist.
Option 3 also supports every kind of pattern on paper, in anyone's
imagination, implicit in any spoken or written language or notation,
implicit in anybody's knowledge, or implicit in any data structures
in any computer or collection of computers anywhere in the universe.
In short, Peirce's option #3 supports common sense, the most advanced
sciences, and every form of artistic endeavor in any culture in the
world -- or even in any alien life anywhere in the universe.
I recommend it,
John
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Kind regards,
Martin Wheatman
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