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!

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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