A bit of conceptual analysis: the book-keeper and the invisible hand [MR #3]

I’ve got an addendum to my earlier post on marginalism as a Rank 4 concept. Claude made the following observation in the course explaining just what that implied:

The transition from double-entry bookkeeping to supply-and-demand might itself be seen as a Rank 3 reflective abstraction: going meta on the bookkeeping closure principle to ask what maintains closure at the level of the entire market, not just a firm's ledger.

Let’s take a look at what is going on here. In the case of double-entry bookkeeping it is the book-keeper that is the agent that maintains the closure over the accounts. In the case of supply-and-demand there is no explicit agent governing market closure, that is, the balance between supply and demand. The agent is abstract. Adam Smith famously used the metaphor of the invisible hand to mediate the conceptual gap between an actual book-keeper working on the books and the abstract market in which the actions of individual buyers and sellers are constrained in a way that keeps closure.

Making such abstractive leaps is not trivial. For it is not only the book-keeper that must be rendered abstract. So must the books. They become the market place. And the book-keeper’s actions of making entries into the debit and credit ledges must be abstracted into individual acts of buying and selling, taken as a collectivity.

The change in conceptual ontology is similar to that of abstracting over salt to come up sodium chloride. In this case the act of abstraction applies to the same physical object. In the case of supply and demand the act of abstraction gives us a new concept and about a different entity. Markets existed before the concept of supply and demand, but that concept gives us a new understanding of them. And the abstract concept of sodium chloride gives us a different way of thinking about and dealing with salt.

Thus we are brought to the notion of conceptual ontology, which is beyond the scope of this short note. You might want to consult these working papers: Ontology in Cognition: The Assignment Relation and the Great Chain of Being, Ontology in Knowledge Representation.

Notes on the Metaphysical Structure of the Cosmos

I’ve been thinking about something I all “the metaphysical structure of the cosmos” now and then since August of 2020 when I introduced it in a post written in the wake of GPT-3. I wasn’t entirely serious about it. I’d only just then thought of the idea and hadn’t had time to think it through. It came back to me a few days ago when I was thinking about the “Xanadu meme” and other ideas. This time, in a conversation with Claude, I hazarded the idea that the metaphysical structure of the cosmos was recursive, though I didn’t use the word “cosmos.” Claude agreed.

It's about time I thought about the idea seriously. Is it one I want to use, in a technical sense, going forward? I don’t know. But I’ll offer some thoughts on the matter.

Just what does it mean, “metaphysical structure of the cosmos”?

Here’s what I said when I originally introduced the idea:

There is no a priori reason to believe that world has to be learnable. But if it were not, then we wouldn’t exist, nor would (most?) animals. The existing world, thus, is learnable. The human sensorium and motor system are necessarily adapted to that learnable structure, whatever it is.

I am, at least provisionally, calling that learnable structure the metaphysical structure of the world. Moreover, since humans did not arise de novo that metaphysical structure must necessarily extend through the animal kingdom and, who knows, plants as well.

“How”, you might ask, “does this metaphysical structure of the world differ from the world’s physical structure?” I will say, again provisionally, for I am just now making this up, that it is a matter of intension rather than extension. Extensionally the physical and the metaphysical are one and the same. But intensionally, they are different. We think about them in different terms. We ask different things of them. They have different conceptual affordances. The physical world is meaningless; it is simply there. It is in the metaphysical world that we seek meaning.

As I’ve already said, I introduced the idea in the wake of GPT-3, the first large language model (LLM) that had received much public exposure. Though only small number of people had direct access, enough of those wrote about it in fairly public ways that many of us knew about it, knew enough to be impressed.

When I introduced the idea I used a diagram something like this:

We have the LLM running down the middle, either that or the text on which it is trained. At this level of analysis it could be either one. The structure of the individual texts is a function of the human mind, which created the text, and the world, which the text is about, albeit often only indirectly (as in works of fiction). From this it follows, almost by definition, that the LLM derived from those texts reflects those two things as well, the mind and the world.

The significance of GPT-3, that is, its underlying LLM, and of subsequent LLMs is that that is the first time we’ve got the “whole thing” gathered together in a single, a single what? Model, text, whatever? It’s all there.

Yeah, I know. Not of it. All LLMs are biased in favor of the texts on which they’re built. Much of human thought, especially the thought of pre-literate peoples, is not represented in the training corpus of any LLM. So, we’re talking about an idealization. That’s OK. As long as we’re aware of what we’re doing, we can proceed.

Now, there’s lots of structure in any given text, and there’s lots of structure latent in any LLM. I’m not interested in all of that structure. I’m only interested in the ontological structure, by which I mean something close to the concept of ontology as it is ordinarily used in knowledge representation.

John Sowa’s use is typical. Here’s how he introduces the topic: “The subject of ontology is the study of the categories of things that exist or may exist in some domain. The product of such a study, called an ontology, is a catalog of the types of things that are assumed to exist in a domain of interest D from the perspective of a person who uses a language L for the purpose of talking about D.” I’m interested in structure of that catalog. I hypothesize that that structure is something which, for convenience, I call the Great Chain (a term long in use). Here’s a diagram:

That diagram needs some explaining; but this is not the time or place to do that. I say more in this old unpublished paper: Ontology in Knowledge Representation. My point is simply that there is a specific structure there. It’s that structure that interests me.

As an example, that structure tells us the difference between salt and sodium chloride (NaCl). Physically they are the same substance, but conceptually they are quite different. We recognize salt by its texture and appearance and, above all, by its taste. We can taste the presence of salt even where we cannot see it existing as a discrete substance. That is to say, conceptually, salt is adequately characterized by its sensorimotor properties. Sodium chloride is not. Sodium chloride is characterized in terms of a chemical theory that did not exist until the 19th century. That theory talks of atoms and bonds between them. We can’t see atoms or their bonds, rather we infer them on basis of a wide body of experimentation. Conceptually, then, they are very different.

Similarly, in one account of the world, based on one ontology, the Morning Star and the Evening Star are two different objects. But in account based on a heliocentric model of the solar system, they turn out to be the same object, the planet Venus. And so it is with the difference between animals and human beings. To the biologist they are the same kind of thing; human beings are just one kind, one species of animal. But in the common-sense construal of the world, they are very different; humans are not animals, though we have animal-like characteristics.

That, more or less, is what I’m talking about when I talk of the metaphysical structure of the cosmos (or world). That conceptual structure. It’s not explicit in any LLM, but it certainly exists implicitly, otherwise LLMs wouldn’t generate coherent texts. (Note that I have a working paper on ChatGPT and stories where it betrays ontological sensitivity: ChatGPT tells stories, and a note about reverse engineering.)

On the explicit construction of cognitive ontology: From “salt” to “sodium chloride”

I have long used the conceptual difference between “salt” and “sodium chloride” to illustrate the idea of conceptual ontology. Except for impurities in (samples of) salt, they are the same thing. But conceptually they are quite different. Salt hardly needs any formal definition at all; it's a basic taste and a common physical substance. But sodium chloride is expressed in conceptual terms that weren’t fully developed until the 19th century.

Lately I’ve been wondering what would be required to develop cognitive accounts ontological concepts in a rich and full way. I’ve been talking about conceptual ontology using the idea of the Great Chain of Being. But I’ve always thought of that as a stand-in for a more thorough treatment, one I’ve never gotten around to. What would that more thorough treatment be like?

It's fairly obvious what we need to do with salt. It’s a white granular substance. We know how to do that sort of thing with tools invented back in the 1970s and 1980s. Nor should there by much difficulty it explicitly accounting for texture, taste, and whatever odor there is. But what about sodium chloride?

That’s not so clear. Oh, there’s been lots of work on formal ontologies for informatic purposes. John Sowa has worked on this, and Barry Smith’s website has lots of material. But that’s not quite what I had in mind.

For example, chemical experimentation typically involves weighing substances very carefully. In the 18th and 19th centuries they might have used a mechanical analytical balance something like this one:

Photo by Sarcyn, licensed under a CCA by-SA 3.0 Unported License.

Such balances would have been used in the experiments used to identify the chemical elements, such as sodium and chlorine, identified in modern atomic theory. Since that is the case, the construction and operation of such balances is part of the conceptual web that supports the concept, /chemical element/, as is the mathematical used in analyzing these experiments. I wouldn’t expect that construction and operation to be directly implicated in the definition of chemical element, but there would be an explicit traceable linkage between the definition and that constructure and those operations. There would also be traceable links to reports in formal journals. Those reports would have specific weights and calculations, etc.

THAT’s the kind of thing I have in mind when I talk about a “thorough treatment” of conceptual ontology. On the one hand we have the sensorimotor processes involved in make observations and conducting experiments. That’s at the bottom layer, if you will, the foundation, of this cognitive constructure. Those objects and processes are going to be bound into complex patterns over which abstractions are made and those abstractions will end up as the terms directly involved in, in this case, 19th century atomic theory and its elaboration in chemistry.

I’m pretty sure that, if you ask your favorite chatbot about these things, it will tell you about salt, sodium chloride, sodium and chlorine, atoms and elements, analytical balances, solutions, gases, arithmetic, and so forth and so on. All of that stuff is there. But I haven’t the foggiest idea of what kinds of connections are latent in the model. It is by no means that all of the connections implied in my previous paragraph would be there in LLMs.

Thus, when I talk about LLMs as digital wilderness, I am implying that it is there to be explored, mapped, and ultimately “domesticated.” What do I mean by domestication? I mean development a rich and full symbolic cognitive account of some intellectual domain. In order to do that, we’re going to need to know how LLMs work internally. That’s just the beginning. I figure different intellectual communities will take responsibility for different regions of the digital wilderness. Getting the whole thing domesticated? That’s the work of intellectual generations. The idea that one day we’ll achieve the magical AGI which will then lead to AI-takeoff in which everything is all worked out in a matter of hours, days, weeks, or months at the most, that’s pure foolishness.

Wolfram on Machine Learning

Wolfram has a post in which he reflects on the work he’s done in the last five years: Five Most Productive Years: What Happened and What’s Next. On ChatGPT:

So at the beginning of February 2023 I decided it’d be better for me just to write down once and for all what I knew. It took a little over a week [...]—and then I had an “explainer” (that ran altogether to 76 pages) of ChatGPT.

Partly it talked in general about how machine learning and neural nets work, and how ChatGPT in particular works. But what a lot of people wanted to know was not “how” but “why” ChatGPT works. Why was something like that possible? Well, in effect ChatGPT was showing us a new science discovery—about language. Everyone knows that there’s a certain syntactic grammar of language—like that, in English, sentences typically have the form noun-verb-noun. But what ChatGPT was showing us is that there’s also a semantic grammar—some pattern of rules for what words can be put together and make sense.

My version of “semantic grammar” is the so-called “great chain of being,” which is about conceptual ontology, roughly: “rules for what words can be put together and make sense.” Here’s a post where I discuss it on the context of Wolfram’s work: Stephen Wolfram is looking for “semantic grammar” and “semantic laws of motion” [Great Chain of Being].

A bit later Wolfram says a bit more about what he’s recently discovered about the “essence of machine learning”:

So just a few weeks ago, starting with ideas from the biological evolution project, and mixing in some things I tried back in 1985, I decided to embark on exploring minimal models of machine learning. I just posted the results last week. And, yes, one seems to be able to see the essence of machine learning in systems vastly simpler than neural nets. In these systems one can visualize what’s going on—and it’s basically a story of finding ways to put together lumps of irreducible computation to do the tasks we want. Like stones one might pick up off the ground to put together into a stone wall, one gets something that works, but there’s no reason for there to be any understandable structure to it.

And the future? Among other things: “symbolic discourse language”:

But finally there was blockchain, and with it, smart contracts. And around 2015 I started thinking about how one might represent contracts in general not in legalese but in some precise computational way. And the result was that I began to crispen my ideas about what I called “symbolic discourse language”. I thought about how this might relate to questions like a “constitution for AIs” and so on. But I never quite got around to actually starting to design the specifics of the symbolic discourse language.

But then along came LLMs, together with my theory that their success had to do with a “semantic grammar” of language. And finally now we’ve launched a serious project to build a symbolic discourse language. And, yes, it’s a difficult language design problem, deeply entangled with a whole range of foundational issues in philosophy. But as, by now at least, the world’s most experienced language designer (for better or worse), I feel a responsibility to try to do it.

In addition to language design, there’s also the question of making all the various “symbolic calculi” that describe in appropriately coarse terms the operation of the world. Calculi of motion. Calculi of life (eating, dying, etc.). Calculi of human desires. Etc. As well as calculi that are directly supported by the computation and knowledge in the Wolfram Language.

And just as LLMs can provide a kind of conversational linguistic interface to the Wolfram Language, one can expect them also to do this to our symbolic discourse language. So the pattern will be similar to what it is for Wolfram Language: the symbolic discourse language will provide a formal and (at least within its purview) correct underpinning for the LLM. It may lose the poetry of language that the LLM handles. But from the outset it’ll get its reasoning straight.

The symbolic discourse language is a broad project. But in some sense breadth is what I have specialized in. Because that’s what’s needed to build out the Wolfram Language, and that’s what’s needed in my efforts to pull together the foundations of so many fields.

Will AIs be able to create new knowledge?

This is a quick and dirty reflection on the question posed in the following tweet:

This is always a question I have asked myself: Given the knowledge that Einstein had by 1906, could a currently existing AI have invented GR and realized that it needed Riemannian geometry and tensors to figure it out? If not, what would it take? https://t.co/fdqCd5Vhk0

— Ash Jogalekar (@curiouswavefn) June 20, 2024

That question has been on my mind for some time: Will AIs be able to create new knowledge? Just what does that mean, “new knowledge”? It’s one thing to take an existing conceptual language and use it to say something that’s not been said before. It’s something else to come up with fundamentally new words. I think that latter’s what that tweet’s about. General relativity was something of a fundamentally new kind, not just a complex elaboration of and variation over existing kinds.

In my previous post, On the significance of human language to the problem of intelligence (& superintelligence), I pointed out that animals are more or less biologically “wired” into their world. They can’t conceptualize their way out of it. The emergence of language in humans allowed us to bootstrap our way beyond the limits of our biological equipment.

I figure there are two aspects of that: 1) coming up with the new concept, and 2) verifying it. The tweet focuses on the first, but without the second, the capacity to come up with new concepts won’t get us very far. And when we’re talking about new concepts, I think we’re talking about adding a new element to the conceptual ontology. Verifying requires cooperation among epistemologically independent agents, agents that can make observations and replicate those observations. (See remarks in: Intelligence, A.I. and analogy: Jaws & Girard, kumquats & MiGs, double-entry bookkeeping & supply and demand.)

Now, let’s think about the current regime of deep learning technology, LLMs and the rest. These devices learn their processes and structures from large collections of data. They’re going to acquire the ontology that’s latent in the data. If that is so, how are they going to be able to come up with new items to add to the ontology? It’s not at all obvious to me that they’ll be able to do so. The data on which they learn, that’s their environment. It seems to me that they must be as “locked” into that environment as an animal is. Further, adding a new item to the ontology would require changing the network, which is beyond the capacity of these devices.

And then there’s they requirement of cooperation between independent epistemological agents. The phenomenon of confabulation is evidence for the importance of independent epistemological agents. The only requirement inherent in one such agent is logical consistency: that it emit collections of tokens that are consistent with the existing collection. The only thing that keeps humans for continuous confabulation is the fact that we must communicate with one another. It is the existence of a world independent of our individual awareness that provides us with a way of grounding our statements, of freeing ourselves from the pitfalls of our linguistic fluency.

* * * * *

I’ve been working my way through episodes of House, M.D. Every episode contains segments where House and his team participate in differential diagnosis, which involves rapid conversational interaction among them. In the first episode of season 4, “Alone,” House no longer has a team. He ends up bouncing ideas off of a janitor. That doesn’t go so well.

Pattern, Conceptual Ontology, and the Well-Turned Story [ChatGPT]

I’ve spent a lot of time getting ChatGPT to tell stories. I’ve taken a particular interest in having it generate variations on some source story. That was the topic of what I consider to be my most important working paper on ChatGPT:

ChatGPT tells stories, and a note about reverse engineering: A Working Paper, Version 3 https://www.academia.edu/97862447/ChatGPT_tells_stories_and_a_note_about_reverse_engineering_A_Working_Paper_Version_3

In that set of experiments I would give ChatGPT a source story and ask it to create a new story based on it. I would then specify that, instead of the protagonist of the original story, it use a new protagoist that I specified. I also said it could make any other changes it wanted to.

Global change

I was particularly struck by experiments in which the new story was all but completely different from the source story. Thus, and using a source story about princess Aurora, in one experiment I asked ChatGPT to make her a giant chocolate milkshake (experiment 7, p. 13) and in another I asked ChatGPT to make XP-708-DG the protagonist (experiment 6, p. 12). Why, in each case, did ChatGPT change the entire story? Why didn’t it change only the protagonist, as I explicitly requested, and leave the rest of the story alone? One might observe that, in both of those cases, a total change makes for a better story. It would have been a bit strange having a robot named XP-708-DG tromping around in a fairy tale universe. Setting XP-708-DG in a science fiction universe makes for a more coherent story. The same is true in the case of making Aurora into a giant chotolate milksake, when the new story takes place in a landscape of deserts.

But how did ChatGPT know to do that?

Elara, Z78-ß∆-9.06Q, and a kumquat

Consider the current series, which involves, first the source story, and then two variations (appended below). Each of the three stories is seven paragraphs long. Are are the first paragraphs of the three stories:

Original: Once upon a time, in a quaint little village nestled between rolling hills and a crystal-clear river, there lived a young girl named Elara. Elara was known for her boundless curiosity and her insatiable desire to explore the world beyond the village.

1st Variation: In the distant future, in a world where technology and nature coexisted in delicate harmony, there existed a unique being named Z78-ß∆-9.06Q. Z78, as they were affectionately called by the inhabitants of their futuristic city, was an advanced humanoid created by the fusion of artificial intelligence and the remnants of ancient, mystical energies.

2nd Variation: In a land of sweets and confections, there existed a whimsical kingdom where the inhabitants were made entirely of delectable treats. In the heart of this sugary realm stood a lively candied kumquat named Elara. With her vibrant orange hue and a sugary glaze that shimmered in the candy sunlight, Elara was known for her insatiable sweetness and an adventurous spirit that matched her citrusy flavor.

I’ve used color-coding to indicate analogous sections in the three stories. I could do the same thing for each of the other paragraphs in the stories. It’s clear that the we are dealing with the one story structure that is being realized in three different worlds. That structure is invariant across the three stories. If you wish, you can think of the story structure as a set of slots and fillers, in which case we have one structure of slots with the fillers being chosen from three different universes. I'm guessing that in an 'old school' symbolic story grammar, that invariance is specified by constraints on what can fill the slots. How is it handled in the LLM? By the topology of the network?

Is the underlying LLM organized into patterns of slots (in one place) and different sets of fillers (in other places)? If so, how? What does that even mean?

If we were dealing with stories generated with a ‘classical’ symbol-based story grammar, I’d say that the grammar has implemented a conceptual structure sometimes known as the Great Chain of Being, which I’ve discussed at some length here:

Ontology in Knowledge Representation https://www.academia.edu/238610/Ontology_in_Knowledge_Representation

Why does ChatGPT behave as though it “knows” about that knowledge structure? How is that structure realized in the pattern of weights in the underlying LLM?

About “Elara”

A young woman named “Elara” shows up in many stories, see:

ChatGPT tells 20 versions of its prototypical story, with a short note on method, Version 2, https://www.academia.edu/108129357/ChatGPT_tells_20_versions_of_its_prototypical_story_with_a_short_note_on_method_Version_2

Why that name? I did a Google search on the name “Elara” and came up with 13,000,000 hits:

https://www.google.com/search?client=firefox-b-1-d&q=Elara#ip=1

I had no idea that the name was so popular. In particular, I had no idea that there was so much commercial branding associated with the name.

I suspect that that provides at least a partial explanation of why ChatGPT treats Elara as the prototypical protagonist in a prototypical story. I wonder what would turn up if I did searches on other names popular in ChatGPT’s stories. How would one get exact counts of how many times each name appears on the web?

* * * * *

Note: You might want to compare this post with an earlier one: St. George Variations [ChatGPT].

The Elara story and two variations

Tell me a story.

Once upon a time, in a quaint little village nestled between rolling hills and a crystal-clear river, there lived a young girl named Elara. Elara was known for her boundless curiosity and her insatiable desire to explore the world beyond the village.

One day, as she wandered into the nearby enchanted forest, she stumbled upon a hidden clearing bathed in golden sunlight. In the center of the clearing stood an ancient, moss-covered stone pedestal with a mysterious, glowing orb resting upon it. Mesmerized by the radiant glow, Elara reached out to touch the orb, and as soon as her fingers made contact, a warm energy surged through her.

In that moment, Elara felt a connection with the magic of the forest. The trees whispered ancient secrets, and the animals approached her with trust. She discovered that she had been bestowed with a unique gift – the ability to communicate with the creatures of the forest and harness the magic that flowed through it.

Word of Elara's newfound abilities spread throughout the village, reaching the ears of the wise elder, Thalia. Intrigued by Elara's connection to the forest, Thalia approached her and revealed that the village had long been protected by the enchantment of the magical orb. However, the magic had weakened over the years, and the village was now vulnerable to external threats.

Thalia explained that Elara was the chosen one, destined to embark on a quest to restore the orb's power and safeguard the village. Determined and fueled by a sense of responsibility, Elara accepted the challenge.

Guided by the whispers of the forest and the wisdom of Thalia, Elara journeyed through dense woods, crossed rushing rivers, and climbed towering mountains. Along the way, she encountered mythical creatures, each offering a piece of the puzzle needed to restore the orb's magic. Elara's courage and kindness won the trust of these beings, and they joined her on her quest.

As Elara approached the final destination, a dark and foreboding cavern, she faced her greatest challenge. A shadowy figure, drawn by the weakening magic, emerged to thwart her efforts. With the support of her newfound friends and the strength within her, Elara confronted the darkness, unraveling the true power of the orb.

In a dazzling display of magic, the orb's glow intensified, dispelling the darkness and restoring balance to the enchanted forest. The creatures celebrated, and the village thrived once again under the protection of the rejuvenated magic.

Elara returned home, her heart filled with gratitude for the journey that had shaped her into the village's guardian. As she looked out over the now vibrant and lively landscape, Elara understood the importance of harmony between nature and humanity. The tale of the young girl who saved the village became a legend, passed down through generations, reminding all who heard it of the enduring magic that resides in the connection between people and the natural world.

Mapping ChatGPT’s ontological landscape, gradients and choices [interpretability]

By ontological landscape I mean the repertoire of different things it knows about. The parlor game, Twenty questions, was invented in the United States in the 19th century as a way of playing around on this landscape. One player thinks of some phenomenon and the other has to guess it by asking a series of no more than 20 questions that have a “yes” or “no” answer. One popular variant of the game begins with a simple question: “Animal, vegetable, or mineral?” Once the question has been answered the questioner must continue with binary questions.

In this post I take a look at how ChatGPT deals with this structure. I start simply, with concrete and abstract object, and move on from there.

* * * * *

All of the interactions reported below took place on the morning of October 15 using the September 25 version of ChatGPT.

Physical things

I decided to start with the simplest prompt I could imagine, “thing.” That’s the most general category we’ve got, no? Anything whatever is going to be some kind of thing. But how would ChatGPT respond? It responded as I thought it would, so I gave it a more explicit prompt, to which it responded.

Thing

It seems like you mentioned "thing," but you didn't provide a specific question or context. Could you please clarify or provide more information so I can assist you better?

Give me a list of 20 things, anything.

Certainly! Here's a list of 20 random things:

1. A beach ball
2. A rainbow
3. A bicycle
4. A bookshelf
5. A coffee mug
6. A mountain
7. A laptop computer
8. A painting
9. A pineapple
10. A pair of sunglasses
11. A telescope
12. A running shoe
13. A wristwatch
14. A musical instrument
15. A flower vase
16. A hammock
17. A traffic light
18. A hot air balloon
19. A chef's knife
20. A Rubik's Cube

These are just a few examples of things, and the list could go on endlessly!

I had no particular expectations about how ChatGPT would respond. But I couldn’t help but notice that each item in its response was some kind of physical thing. To be sure, rainbows (the second item in the list) are rather diaphonous, and you couldn’t actually touch one (I should have asked ChatGPT about that; later...), but it is still a physical thing.

I didn’t ask for physical things, but that’s what ChatGPT gave me. That’s worth noting.

Let’s think a bit before continuing on. I wonder if that first list is “rigid” in the sense that ChatGPT would respond the same way given the same prompt. I suspect not, but it’s easy enough to find out. I went back a bit later.

Give me a list of 20 things, anything.

Certainly! Here's a list of 20 random things:

1. Beach vacations
2. Chocolate chip cookies
3. Classic literature
4. Sunsets
5. Roller coasters
6. Coffee shops
7. Mountain hiking
8. Vintage cars
9. Starry nights
10. Watermelon
11. Jazz music
12. Sunflowers
13. Science fiction movies
14. Art galleries
15. Hot air balloons
16. Snow-capped mountains
17. Aquariums
18. Street food
19. Historical landmarks
20. Puzzle games

It’s not the same list I got the first time, but almost all of them are physical things. Classic literature (#3) isn’t really a physical thing, though books are. Mountain hiking (#7) is a physical activity, but whether or not you’d call it a physical thing is, well, an interesting issue. Jazz music (#7)? Science fiction movies (#13), puzzle games (#20)?

I decided to log out and then try again:

Give me a list of 20 things, anything.

Certainly! Here's a list of 20 random things:

1. Pencil
2. Bicycle
3. Sunflower
4. Smartphone
5. Coffee mug
6. Guitar
7. Rainbow
8. Lighthouse
9. Chocolate chip cookies
10. Telescope
11. Mountain
12. Soccer ball
13. Vintage typewriter
14. Starfish
15. Hot air balloon
16. Eiffel Tower
17. Polar bear
18. Sandcastle
19. Wristwatch
20. Lightning bolt

That’s better. I notice we’ve got “rainbow” again (#7), and “Lighhtening bolt” (#20) is rather ephemeral as well, though if one were to hit you, the effect would be dramatic and quite physical. “Chocolate chip cookies” (#9) show up again, as does “Hot air balloon” and “Bicycle.” These lists seem to be drawn from roughly the same conceptual territory. I suppose that’s not terribly surprising, but it certainly doesn’t seem like ChatGPT is making random choices from among all available physical things. Why these things?

I decided to explicitly specify physical objects:

How about 20 physical objects.

Of course, here's a list of 20 physical objects:

1. Refrigerator 2. Sofa
3. Running shoes
4. Toaster
5. Sunglasses
6. Umbrella
7. Bookshelf
8. Camera
9. Toothbrush
10. Bicycle helmet
11. Microwave oven
12. Flower vase
13. Tennis racket
14. Water bottle
15. Alarm clock
16. Car keys
17. Backpack
18. Desk chair
19. Blender
20. Laptop computer

None of those items are problematic in the way rainbows and lightening bolts are. You can touch each of them. In fact, except perhaps for the refrigerator, you can pick each item up and carry it around. No polar bears, mountains, lighthouses, roller coasters or traffic lights. But there are no purely abstract things here either, things like love, freedom, justice, beauty, etc. They go on a different list.

What’s ChatGPT doing?

Yes, we know, it’s cranking out one word after another. But that’s not very informative, as I argued some time ago, The idea that ChatGPT is simply “predicting” the next word is, at best, misleading. Remember, each time ChatGPT generates a new token it does a calculation that involves all 175 billion weights (Wolfram). Its entire “neural” space is involved in every such calculation.

Stephen Wolfram is looking for “semantic grammar” and “semantic laws of motion” [Great Chain of Being]

Wolfram has a very interesting account of how ChatGPT works, What Is ChatGPT Doing … and Why Does It Work? Toward the end he talks about “Meaning Space and Semantic Laws of Motion,” which is more or less something I’m thinking about in my current work on ChatGPT’s ability to tell stories. Here he talks of trajectories “in linguistic feature space”:

We discussed above that inside ChatGPT any piece of text is effectively represented by an array of numbers that we can think of as coordinates of a point in some kind of “linguistic feature space”. So when ChatGPT continues a piece of text this corresponds to tracing out a trajectory in linguistic feature space. But now we can ask what makes this trajectory correspond to text we consider meaningful. And might there perhaps be some kind of “semantic laws of motion” that define—or at least constrain—how points in linguistic feature space can move around while preserving “meaningfulness”?

As ChatGPT tells them, stories consist of a sequence of sentences. Those sentences are ordered by a story trajectory. The particular stories I’ve been working with follow a trajectory that seems to have five segments: Donné, Disturb, Plan, Enact, and Celebrate (Benzon 2023). But that’s an aside. Let’s return to Wolfram. Later, after presenting visual illustrations of words arrayed in “semantic space” Wolfram observes, “OK, so it’s at least plausible that we can think of this feature space as placing ‘words nearby in meaning’ close in this space.”

Yes, it is. In particular, he’s looking for a “fundamental ‘ontology’ suitable for a general symbolic discourse language?” That’s what this post is about.

That fundamental ontology has a name, the Great Chain of Being (cf. Lovejoy 1936), though it has rarely been discussed under that rubric in linguistics and related disciplines. This is what a sketch of it looks like:

I have used the term “assignment” for the relationship being specified on the arcs (Benzon 1985, 2018).

Read the diagram from the bottom. A physical object consists of an assignment between a substance and a form. For a rock the substance is mineral and the form can be almost anything. For a cube of sugar the substance is sugar granules, and the form is, obviously, that of a cube. A plant consists of an assignment between a physical object and a vegetative soul (to use Aristotle’s terminology from De Anima). That is to say, plants can have any attributes characteristic of physical objects, visible form, characteristic textures, taste, odor, and so forth, but they also have attributes only applicable to living things, they grow, change form, and they die. Animals can have attributes of the kind characteristic of plants, plus new ones; they can move, hunt, sleep, see, hear, smell, etc. With humans you add still more attributes and capabilities.

Think about it for a minute or two. What kinds of verbs require humans as agents? Verbs about a whole range of mental and linguistic processes, no? Animals are not appropriate agents for such verbs, at least not in the commonest usages: Animals don’t think, or dream, or tell stories, ask questions, etc. But animals can walk, sleep, smell, see, feel pain, etc. And so can humans. The diagram is about capabilities and affordances, which are inherited up the diagram. Objects have weight, but so do plants, animals, and humans. But only humans can speak. Once you tease out the implications, it becomes apparent that assignment structure has very wide-ranging semantic implications.

When someone makes a statement the violates assignment structure, philosophers talk of category mistakes (Sommers 1963). Noam Chomsky’s most famous sentence, “Colorless green ideas sleep furiously,” is a contains two category mistakes and a contradiction. Ideas are not the kind of thing that can sensibly be said to sleep, or to have color. That there can be such a thing as “colorless green” is a contradiction. Wolfram offered his own collection of category errors packaged as a sentence: “Inquisitive electrons eat blue theories for fish.” Electrons can neither be inquisitive nor can they eat anything and theories, like ideas (of which they are a type) cannot have color. Nonetheless, ChatGPT is able to tell a story about them, which I have appended to this post.

Now consider this diagram:

It has a similar form, but is something I sketched out for the purely mechanical world of manufacturing. As in the previous diagram, the relationship between the nodes is that of assignment.

Again reading from the bottom, an object consists of a assignment between a material (comparable to substance in the previous diagram), a shape (comparable to form), and a surface (which would probably be appropriate to the previous diagram as well). Shape is the most complex of these aspects. The shape will have components, such as edges and vertexes or even component shapes. The substance of the part is the stuff of which the object is made; it has properties of mass, density, ductility, heat conductivity, etc. Finally, the surface must be considered separately from substance and shape because different types of process apply to it. The surface may be painted or plated, and/or ground to set specifications. This doesn't affect the shape or the nature of the substance.

We can continue on up: An assembly has a different ontological structure than a primitive part, which is to say than an assembly is not merely a complex part. There is more to it. An assembly is an assignment between a part and a connectivity structure. To think of an assembly as a part, first imagine shrinking an envelope around the assembly. The resulting shape/surface/substance triple is the assembly as part. Its shape and surface might be quite complex (think of an automobile engine as an assembly which is part of the automobile), and its substance heterogenous (e.g. rubber, plastic, three kinds of metal, etc.). This part is, of course, a complex part. As such it has components, the simpler (perhaps even primitive) parts which make it up. Simple objects do not have components, though their shapes do.

We can keep moving up. A mechanism is an assembly with articulated parts, thus allowing them to move. Add a source of power to the mechanism and you have an engine. Over there to the left we have a computer conceived of as an assembly with a program. That is no doubt way too simplified, but at this level of conceptual resolution it may be satisfactory.

What’s important about these diagrams is the relationship they establish between the objects in them: assignment. The ontological structure Wolfram is looking for consists of assignment structure. It warrants further exploration.

References

Benzon, William L. (1985) William Benzon, Ontology in Knowledge Representation for CIM, Computer Integrated Manufacturing Program, Center for Manufacturing and Technology Transfer, Rennselaer Polytechnic Institute, Doc.# CIMMMW85TR034, 1985. https://www.academia.edu/28723042/Ontology_of_Common_Sense.

Benzon, William L. (2018) Ontology in Cognition: The Assignment Relation and the Great Chain of Being, Working Paper. 5 pp., https://www.academia.edu/37754574/Ontology_in_Cognition_The_Assignment_Relation_and_the_Great_Chain_of_Being.

Benzon, William L. (2023) ChatGPT intimates a tantalizing future; its core LLM is organized on multiple levels; and it has broken the idea of thinking. Version 3. Working Paper, Feb. 6, 2023, 25 pp., https://www.academia.edu/95608526/ChatGPT_intimates_a_tantalizing_future_its_core_LLM_is_organized_on_multiple_levels_and_it_has_broken_the_idea_of_thinking_Version_3

Lovejoy, Arthur O. (1936). The Great Chain of Being: A Study of the History of an Idea. Harvard University Press. 1936. Available online, https://archive.org/details/ArthurO.LovejoyTheGreatChainOfBeing.

Sommers, Fred (1963) “Types and Ontology.” Philosophical Review. 72, 327 - 363.

What is a conceptual ontology?

From Wikipedia:

In computer science and information science, an ontology encompasses a representation, formal naming, and definition of the categories, properties, and relations between the concepts, data, and entities that substantiate one, many, or all domains of discourse. More simply, an ontology is a way of showing the properties of a subject area and how they are related, by defining a set of concepts and categories that represent the subject.

Every academic discipline or field creates ontologies to limit complexity and organize data into information and knowledge. Each uses ontological assumptions to frame explicit theories, research and applications. New ontologies may improve problem solving within that domain. Translating research papers within every field is a problem made easier when experts from different countries maintain a controlled vocabulary of jargon between each of their languages.

This differs from what philosophers have generally meant when they talk of ontology. They are concerned with what’s really real about the world, not how people think about the world. The study of conceptual ontology is about what people think, regardless of whether or not it is true?

But, you might be thinking, aren’t philosophers, even the best of them, only human beings and so their thoughts about ontologies are only thoughts? Ah...

Think of a set of building blocks, Lego pieces, Erector set components, or, for that matter, the various components that go into the construction of, say, actual buildings, whatever. There is a finite set of distinct different types of objects in these various collections. That set of types is your ontology. This set of types places constraints on what you can build. But what you can actually build depends on your imagination and determination, plus, of course, having enough tokens of each type to complete the job.

John Sowa’s top-level set of categories based on the work of Charles Sanders Pierce and Alfred North Whitehead. From his book, Knowledge Representation (2000):

He argues that that is the conceptual ontology fundamental to all human thought.

I’ve got my doubts about that, but don’t want to argue it here and now. There may well be some elements that are universal among humans, but I will say that each culture has its own underlying conceptual ontology. And ontologies change over the long duration, thus, for example, the ontology of 19th century chemistry is different from that of alchemy. More generally, when Thomas Kuhn talks about revolutionary science vs. normal science, he’s talking about regimes where the underlying ontology changes, revolutionary science, versus those where it remains unchanged.

My set of conceptual Lego pieces was complete by the time I completed my master’s thesis on “Kubla Khan” in 1972. It was rich enough that I was able to learn Hays’s computational semantics and, on that basis, imagine Prospero, the system that could “read” Shakespeare. When the possibility of actually constructing Prospero disappeared, the set of conceptual Lego pieces – my conceptual ontology – remained unchanged. But my sense of what one can build with those pieces changed.

When I began (email) conversations with Walter Freeman about the complex dynamics of the nervous system, I was able to do so with that set of conceptual Lego pieces (ontology) – though, keep in mind, I don’t command the underlying mathematics and so have to work analogy and metaphor. That same conceptual ontology has allowed me to conceive of attractor nets, networks of logical operators over attractors in various attractor landscapes, where each landscape corresponds to a neurofunctional area in the brain. When I began thinking seriously about deep learning and artificial neural nets, I did so in terms those ontological primitives. They allowed me to see, both that GPT-3 represents a conceptual advance, and that such technology is not sufficient in itself.

Remember, finally, that that conceptual ontology took shape through investigating the form and meaning of “Kubla Khan.” That ontology was ‘designed,’ if you will, to encompass a rich example of verbal artistry. It ranges over neurons, logical operators, poems, and more.

What has happened over the course of my career is the my sense of what can be built within this ontology has changed. Yes, I have had to drop Prospero and things ‘like’ it from the list, but I have added things to the list as well, such as the origins of human thought and attractor nets. On the whole, my sense is that the space of possible constructs has grown larger and more various.

For a more detailed look, see:

Ontology in Cognition, The Assignment Relation in the Great Chain of Being, Working Paper, November 12, 2012, https://www.academia.edu/37754574/Ontology_in_Cognition_The_Assignment_Relation_and_the_Great_Chain_of_Being

Ontology of Common Sense, in Hans Burkhardt and Barry Smith, eds. Handbook of Metaphysics and Ontology, Muenchen: Philosophia Verlag GmbH, 1991, pp. 159-161, https://www.academia.edu/28723042/Ontology_of_Common_Sense

Ontology in Knowledge Representation, Working Paper, 1987, https://www.academia.edu/238610/Ontology_in_Knowledge_Representation

Ontological Cognition, Working Paper, November 12, 2012, https://www.academia.edu/7931749/Ontological_Cognition