When working with Ontologica, you should assume the following.
Axiom 1
"There are things."
Sub-axioms
The world is made of things.
Every thing is a thing.
Anything that can be talked about is a thing.
There is nothing that is not a thing.
Justification
It is primary.
All roads lead to Rome. Any process of stripping things back will often lead to this most general of object categories.
It is parsimonious.
It is minimalistic. We want to start with as little as we have to.
It is hard to deny.
Imagine if someone denied that there are actually things, on the ground that the experience of recognizable things in the world around us is a product of our cognitive systems that chunk unorganized, continuous experience into discrete, patterned units. From this, they claim that "outside of the human mind" (Kant's phenomena), those things do not in fact exist.
Imagine that, when pressed, that person were asked, "What then does exist?" If they said, "The only thing that exists are atoms moving around", we might say, "Not so - modern physics says it is in fact subatomic particles". They might say, "Ok, yes - well, whatever modern physics tells us is the actual lowest level building blocks of reality." Even if that is the case, then there are still things. Therefore, this axiom woudl be compatible with such a worldview.
But take it further. Claim that in fact, quantum mechanics says the universe is not locally real. There are not stable, conscribed things of "physical stuff" occupying volumes. Things come and go, they don't require consistency of identity, etc. No matter - then what is the system you describe? "Well, it's quantum wavefunctions; particles aren't so much waves as they are clouds of probability". Then so be it: what actually exists are probability clouds and wave functions; the rest is human fancy / fantasy / illusion.
But say we take it further, and say, "But everything must be made of something". Max Tegmark says that as yo go further down, the whole notion of "physilac" disappears, and we are left mroe with something informational, even virtual. No matter: then what exists are certain formal laws or systems that control the evolution of some virtual bits of information: then that is what actually exists. And those are things.
It is unavoidable.
Imagine trying to deny this and subsequently buildling any sort of formal ontology theory. The only idea in mind would be a world of continuous, boundariless entities, perhaps without fixed identity either. Nonetheless, it would be highly experimental
It is uncontroversial.
It accords with human's "natural attitude" about the world.
Husserl, cross culturally, etc.
It is just a seed to be refined later.
Commentary
It should not be understood that this axiom is 'self-evident'. These statements are not self-evident.
First of all, it is not clear what they mean.
When one says "Every thing is a thing", are they saying something that is true-by-definition, i.e. the Identity Law that for all x, x is x? That each thing is itself? Or that if something has type thing, then it has type thing - the reflexive implication law?
Or are they using the word "thing" as a type of thing?
And if so, is it still tautological, or are they using the word thing in two ways: the first, "every object of reference", the second, "of some type I am hereby introducing, called "thing"? This woudl take the form in first-order logic, forall x . Thing(x), whereupon it becomes clear it is not tautological in the sense of (1) (the previous interpretation).
It is not clear what they mean. However, they are hard to deny; and they are also inevitable.
Imagine if someone were to claim that things exist only in our minds.
Therefore, most attempts at descriptions of the world will include the category of "things", except for highly experimental ones.
Assertions vs. Observations
Implicit Meaning
A recurrent topic in this document will be human's relationship to meaning. It is often difficult to give a good definition for a given word, yet this belies the inarticulable way in which we feel meaning intuitively, experientially, and subconciously. It is often much easier to pinpoint the meaning of something by "unfolding" it into a large pile of empirical data, so we can see hidden structures become apparent.
Therefore, they are inoffensive as assumptions: we are free to assert things we do not fully understand, in this framework, because we can always later backtrack when we discover there to be a problem.
- they are a minimum / modicum of (ontological) commitment
(- it doesn tmater because our onotlogy grows and coherentizes itself, so,m we can always go back and revise past stataemtns)
these statemenst are not necessarily self evident nor free from ambigutiy. i..e, (talk about differne interpretaions).
on the other hand, they are extremely rudiemntary and simple.
Thing should not be understood in a more restricted sense like "inanimate object", "physical object", or "concrete entity". Thing does not impose qualitative constraints on what a thing can be like. It can be used to talk about vaguely-defined things, or things whose existence we are unsure of.
as we will see later, we will often move between grammaticla categories. the example: is red the same as redness? is "run" the same as "running"? thi sis why thing encompasses even what i will call "non-thing-like-things".
we can even genreat snetnces with formal grammars.
history of theories of meaning: equivalence classes of sentences.
It is the first assertion in this theory because of its fundamentality.
Thing is the universal category. In the sense of model theory, Thing is our domain of discourse.
Axiom 2
There are things about things.
This notion has also been called "predicates" or "relations". Its essence is the observation that, for some given thing, one can ask something about that thing. For example, given a car, I can ask, "What is its color?", or, "Who are its friends?" A thing about a spoon is its size. A thing about the concept of democracy is its definition.
i like to call this an aboutness. similar to haskell currys term "functive", it combines functions and relations into something that requires something else. it is also similar to dependent entities in BFO, as well as depednent types in MLTT.
There will be some more dialectical puzzles to work out, regarding predicates. Some things I have been considering:
When we ask, "What is a thing about cars?", why does it seem we can answer that question either talking about the values it takes under certain predicates, versus the predicates which are defined for it?
What if we collapsed the distinction between things and predicates and used a single universal binary operation where any Thing can act in the predicate role? Would it be illuminating or be poorly defined?
...
Anyway, for now, we are assuming there is a kind of extra-linguistic, mathematical operation which, unfortunately, we simply cannot question (at least not yet). We can choose to take a predicate, a thing, and a thing, and consider them as a little "unit" - a Cartesian triple. It is important to reflect on the properties of such a "triple". Mathmatically, it is a composite object: it can be talked about as a single thing, yet we can also reach inside and grab the internal things it is made of (its subject, predicate, and object).
For the time being, we basically just assume that mathematical idea I just stated.
These are the two most important ideas in the foundations of Ontologica.
Unlike in some other formal conceptions of the world, in Ontologica, a predicate is also a thing. At the risk of becoming redundant, I may frequently invoke the dictum that "every thing is a thing", as a reminder of this principle.
The rest of the theory I am still working on, so the following is a bit more tentative.
There will probably be a fundamental notion I introduce called an action.
Conventionally, it is a well-established idea that you can take a predicate and "apply" it to some atomic entity, to form some unit of meaning, like, "likesPickles()" applied to a certain person, "Jimmy", formed a statement analogous to saying "Jimmy likes Pickles".
My current issue is that I believe there are multiple ways to compose such elements into some new element, so I want to be very careful in how I define this.
Interlude on Functions and Acts of Creation
We should think about the idea of "taking a subject, a predicate, and an object, and creating a statement from them" very carefully.
The abstract conception of an ontology, in Ontologica, is more or less using set theory. Your ontology consists of some collection of things. However, your ontology exists in time - like you do. When I ask (myself, or someone else), "Is so-and-so in my ontology?", the question is with regards to what is in my ontology right now.
Ontologies are meant to be changed. We change them by adding new entries to them. Sometimes we might want to remove entires, or modify some of the ones we added. But abstractly, despite that the ontology is meant to carry so much complex meaning, in a way, we can reduce all questions about the ontology to questions of existence. To ask, "Does Jim like peaches?" with regards to the ontology is more literally to ask, "Does the fact "Jim likes peaches" exist in this ontology (right now)?"
lets consoldiate what weve asserted so far:
(the motto, lists of sentneces)
there are things
there are things about things
there are knds of things
thing about a thing is akindof thing
having as kind has as kind thing about A thing
etc
show how man languages it can be tranlsated into, i.e. most langauges have some words like htis
the notion of "reference", i wanted to use a bianry opeation, but it didnt work. i.e. "as to perosn, the netit name is..
perahps we can surmise a primitive ontolgoical framework cross cutrlaly, idk
i.e. mention how some philsophers have no clue what is outside the human mind
but if there were not things, even then, the world wou ldhave to be made of htings at the bototm,w ouudl it not? even if not physicla things, i.e. subaotmic partiles, then its math. eevn if its quantum.a t some point, it becomes impossible to say that there are in fact not things.
linguistic normalizioant of verbs. every sentence in this document about ontolgoic acan be conveted to a triple by an ai, but we estbalished like a style guide in that verbs should be changed to their subjunctve, not declaratvei form.
List of statements, like, ontology genreation form.
Ontologica is based on the idea that there are "things".
Ontologica is (etc.)
Therefore, the formal model of Ontologica is roughly:
An ontology is a collection of things.
There are two fundamental kinds of things: things, and aboutnesses.
(A thing can have multiple kinds.)
An aboutness is also a thing.
An ontology is a model of a world. It does not have to be true, or conform, in its intepretation, to "the real world / the thing around us".
An ontology is generally created by a human (or, someone sentient). The human can decide and judge what things they want to add or exclude from their ontology.
Of course, a human may often wish their ontology to try to accurately describe "the world", or, the world as they experience it, as they judge it to be.
The human arbiter / creator can change their ontology by adding or remove things from it.
There are two equivalent ways of things about "changing your ontology": one is that the old ontology is gone, and a new one has been created. The other is that the same ontology is still here, but "something about it" has changed. If "something about it" has changed, that can also be viewed as a change in quality of a thing (i.e., the vlaue a predicate takes), or it can be seen as the deletion of a statement-thing from the ontology (that that predicate holds true for that object) and teh addition of a new one.
"Change" for thing sof stable entty across time can also be re-viewed as the creation or destructio of static, unchagning things. but that woudl imply that we are in a changing context (the ontology itself). but even that we can get rid of if we think reality is created anew every mment in time, for example. idk.
on the other hand, how mgiht we move from the sense of something being added or deleted, to something just "changing"? need to think about it.
That means that in orde to explain why it is taht we can create triples
a new document
the problem with triples
The problem with triples.
Assuming the mental (not "formal", just "intuitive") notion of "a collection of things, different kinds of things, and things that can be said about them" is well and clear, we need to try to explain what it means to not just add some arbitrary new element and assert things about it (we could take that route, though. Maybe that should be it???), ...
Different points of view
"Predicates are such that there is a semantically clear operation which constructs a precise kind of thing from a predicate, subject, and object."
The idea here is
I have 3 things here; I know what kind of thing they are; and I can choose
to apply a construction operation I know. VOILA.
I took the three things, and put them together.
This has created a new thing: the result of applying that construction.
The problem
The problem is that there is arguably pretty strong reason to believe, there is not one way to put these three things together. Equivalently, there are multiple "creational actions/processes which can take in these three things and create something from them - just as I couldl take peanut butter and jelly and bread, and make a peanut butter and jelly sandwich; but i could also blend them and make a peanut butter and jelly smoothie. In both cases, the final product seems, ontologically and mereologically, to clearly "be made of" the three things we used to make it, such that it can even be relationally decomposed into those things. Hence, there are different ways to put things together.
The next problem
should there be a neutral backgroun didea of "putting things together but without having specified in what way, what kidn of trhing was intended tob eproduced"? a downside with this is, it forces us to choose some kind of pre-type. maybe its. apradox, we wanted to avoid "neutarl operations", but we ended up creating one anywya. its like positing an "intermeidary stage" that doesnt realy eixst, doesn tactualy make sense.
instead, we coudl say, there is an infintue of such dependent entiteis. but ther ies no "neutral" one. it isup to you to defien wha tkidn of creative action it is. we mighte ven have a rule from dpeendnt type theory on creatin such entites. hence, you acnnot just assume "we can make soemthing", you have ot show specifiaclly how to construct it. ?
solution 1:
abandonign creativ actions. you never "bind 3 elements". you only add whatever you want, say, a fact, and include that it relates, via intenral predicates, to othe entities?
So maybe.... instead of functions and actions, we have dependent entities. like we make a rule that you can construct a thing of type statement from a subject predicate and object. but you can have many things with the same function singautre. also, you dont have to include it as a new type on teh hgihest level. instead, a constrution rule could be, you just create a "dependent thing", plus you add the perdicate "has as kind". maybe this is all it tkaes....
the mathematics of it, maybe...
Other, more tentative axioms.
There are kinds of things.
A Thing About A Thing is a kind of thing.
has as kind has as kind
A Thing About A Thing.
By introducing the (internal) predicate "has as kind", we can make use of one of the most common ontological structural principles, which are types, classes, etc., whatever you want to name it.
We can now begin to track what kinds of things we have in our ontology so far, based on what we've mentioned.
x has as kind Thing
this ontology
Item 2
Item 3
x has as kind Things about things
has as kind
Item 2
Item 3
X has as kind the kind "kind"
Item 1
Item 2
Item 3
in the event anyone is reading htis, i decided to move towrds trying to strictly formaliez this in MLTT, so now im exploring if i can write it in Agda.