Cactus Language • Preliminaries 1
• https://inquiryintoinquiry.com/2025/03/30/cactus-language-preliminaries-1/
❝Picture two different configurations of such an irregular shape,
superimposed on each other in space, like a double exposure photograph.
Of the two images, the only part which coincides is the body. The two
different sets of quills stick out into very different regions of space.
The objective reality we see from within the first position, seemingly
so full and spherical, actually agrees with the shifted reality only in
the body of common knowledge. In every direction in which we look at all
deeply, the realm of discovered scientific truth could be quite different.
Yet in each of those two different situations, we would have thought the
world complete, firmly known, and rather round in its penetration of the
space of possible knowledge.❞
— Herbert J. Bernstein • “Idols of Modern Science”
The task before us is to describe the syntax of a family of formal languages
intended for use as a sentential calculus, and thus interpreted for the purpose
of reasoning about propositions and their logical relations.
To carry out our discussion we need a way of referring to signs as if they
were objects like any others, in other words, as the sorts of things which
can be named, indicated, described, discussed, and renamed if necessary,
which can be placed, arranged, and rearranged within a suitable medium of
expression — or else manipulated in the mind — which can be articulated and
decomposed into their elementary signs, and which can be strung together in
sequences to form complex signs.
Signs having signs as their objects are known as “higher order signs”,
a topic which demands an adequate level of formalization, but in due time.
The present discussion needs a quicker way to get into the subject, even if
it settles for informal means which cannot be rendered absolutely precise.
Resources —
Cactus Language • Preliminaries
• https://oeis.org/wiki/Cactus_Language_%E2%80%A2_Part_1#Cactus_Language_.E2.…
Survey of Animated Logical Graphs
• https://inquiryintoinquiry.com/2024/03/18/survey-of-animated-logical-graphs…
Survey of Theme One Program
• https://inquiryintoinquiry.com/2024/02/26/survey-of-theme-one-program-6/
Regards,
Jon
As before, I often have conflicts on Wednesdays. But when I got back, I went through some of my backlog of notes that raise important issues. This is about a note from October 2024 that I had intended to comment on, but it got buried long ago.
As Mihai Nadin wrote below, C. S. Peirce made important comments about the issues discussed in these notes. He represented them in graphs about graphs, and the modern term is 'metalanguage'.
Farther below, Hans Polzer wrote "We tend to overlook the enormous amount of information we humans create about things that don’t actually exist in the natural world, at least not in the sense of material objects.... The physical properties of such representations bear no inherent relationship to the things they represent, such as the deed to a piece of property or a movie (which itself may represent something that doesn’t actually exist in the natural world)."
The fact that these things don't "exist" in some sense does not mean that we can ignore them. Money, for example, is just a number. You can say that it refers in some complex way to some gold bars in some distant place, but the connection is so remote that it's ignored by every computer program that processes numbers about money.
Similar principles apply to everything in our computer systems. Nothing physical is ever stored in transistors or transmitted across wires, thin air, or the vacuum of outer space. All of it is language about something. And a large amount of that "something" is more language about something else.
In the bottom note below, Alex talks about higher order logic. That's not quite right. It's more accurate to say that it is related to terms and terminology about physical things. The word 'metalanguage' is more appropriate.
And there is no limit to the number and kinds of metalanguage that anyone might want or need to say about something. A bank, a grocery store, a stock broker, and their customers all talk about money, but they say very different things for very different reasons.
As usual, there is a huge amount of commentary that could be debated about these issues. And by the way, the question whether any of these words are mapped to and from some formal notation is irrelevant to the fundamental problems of interpreting the symbols in some program.
John
----------------------------------------
From: "Nadin, Mihai" <nadin(a)utdallas.edu>
This is the semiotics of the subject. Discussed many times by our Forum. Indeed, without referencing C.S. Peirce on the matter we will not make progress. In this vein: syntax and semantics are important. But sign processes are driven by the pragmatics: representations have a purpose or can be associated with purposes. Mihai Nadiin
From: hpolzer via ontolog-forum <ontolog-forum(a)googlegroups.com>
Understood, Ravi. I was just trying to illustrate with some examples of what I meant by the virtual world created by humans in addition to the natural world that John was referring to in his email. We tend to overlook the enormous amount of information we humans create about things that don’t actually exist in the natural world, at least not in the sense of material objects. Of course, we often create physical representations of some types of such things, but even there many of those representations have been reduced to bit patterns on some digital storage media, aka, “the cloud”. The physical properties of such representations bear no inherent relationship to the things they represent, such as the deed to a piece of property or a movie (which itself may represent something that doesn’t actually exist in the natural world). That general problem was one of the big challenges faced by Sagan and crew when working on the Voyager plaque/disk.
Hans
From: ontolog-forum(a)googlegroups.com <ontolog-forum(a)googlegroups.com> On Behalf Of Ravi Sharma
Hans
Human made markers have been in use for a long time but used to operate in their own small areas of applications.
For example Ujjain India Meridian is where their astronomers calculated time for a millennia or two.
When they tried to apply this in today's context they found that both US and India will be split by the dateline.
Some strange results like metric - US (old British) units' lack of conversion led to space missions failures.
But hope we can correct all such aberrations going forward!
Staying with as close to reality as you suggest, I support.
Regards
Thanks.
Ravi
On Thu, Oct 10, 2024 at 10:43 AM deddy <deddy(a)davideddy.com>
For a natural language, almost every word has a continuous range of meanings.
And this is only for "natural" language.
See classic George Miller "Ambiguous Words"
13 simple Robert Frost words offer 3.6 TRILLION combinations.
https://www.thekurzweillibrary.com/ambiguous-words
So far no acknowledgement at all of the existance of "unnatural language."
Unnatural language being the strings / labels / terms used INSIDE software applications. Many universes of written but minimally spoken terminology that AFAIK is entirely ignored in the current interest in AI & ontologies.
For those who expect "meaning" from statistics... long, long, long ago I encountered an insurance company that had found 70 different "names" for the concept "policy number."
AI LLMs / ontologies address this ... how?
David Eddy
> -------Original Message-------
> From: John F Sowa <sowa(a)bestweb.net>
>
> Alex,
>
> There are two very different issues: (1) Syntactic translation from
> one notation to another; (2) Semantic interpretation of the source or
> target notations.
>
> For a formally defined notation, such as FOL or any notation that is
> defined by its mapping to FOL, there is a single very precise
> definition of its meaning.
>
> For a natural language, almost every word has a continuous range of
> meanings. The only words (or phrases) that have a precise meaning are
> technical terms from some branch of science or engineering. Examples:
> hydrogen, oxygen, volt, ampere, gram, meter...
>
> If you translate a sentence from a natural language to formal
> language, that might narrow down the meaning in the target language,
> But that very precise meaning may be very differentt from what the
> original author had intended.
>
> Summary: Translation is not magic. It cannot make a vague sentence
> precise.
>
> John
> _______________________________________
>
> FROM: "Alex Shkotin" <alex.shkotin(a)gmail.com>
>
> John,
>
> Let me clarify what I meant by "English is HOL" by example.
>
> Sentence: "I see a blue jay drinking out of the birdbath."
>
> HOL-structure: (I see ((a (blue jay)) (drinking (out of)) (the
> birdbath)))
>
> where
>
> "of" is an unary operator used in postfix form, applied to "out" being
> an argument. As a result we get "(out of)" an expression or term.
>
> But this term is itself an unary operator used in postfix form,
> applied to "drinking" to create a term "(drinking (out of))", being
> binary operator in infix form being applied to two arguments: left
> one: "(a (blue jay))", and right one: "(the birdbath)".
>
> As a result we have a proposition which is a right argument for
> another binary operator in infix form "see", which has the left
> argument "I".
>
> And we are talking here not about Logic, but about Language.
>
> In every syntactically correct phrase, words are combined: one word is
> applied to another. The result is something like molecules, but in the
> World of Words.
>
> How to get this structure from a chain of words? How to work with
> these structures to get what? Some pictures? True|false value?
>
> This is the question
>
> Alex.
