A symbolic object or concept held in the mind or represented by symbols (alphabets, numbers) in some medium like a computer or a piece of paper.

initial exploratory hypothesis

"abstract objects are represented by and composed of synthetic dimensions"

• the meaning of the term (object) is defined by values in dimensions
• the word (object) itself is constructed from dimensions

see meaning triangle

"abstract" could mean both "symbolic" and "conceptual"

Real or reality -- at the point or level where action occurs (??)

Actual number line as opposed to "real" number line

Uncertainty created by an open interval which can be interpreted in alternative ways

The open interval has a range of values and we don't know which one it is

Two things are alike or similar in some regards (some dimensions) but not all

The doctrine according to which there are no universals or types in reality, but only individuals and particulars

How can we best understand the dimensionality of comparison?

What are the dimensions of apples and what are the dimensions of oranges? How are they similar, how are they different, how can we refine that understanding to a high degree of accuracy?

Fan-in path for constructing a composite object in linear/sequential order

Trusting or assuming that something is true without scientific certainty

Understanding that something is true without being able to measure it

In this framework, we want to explore how we can construct definitions of all terms and concepts from semantic ontology in a common language, following a common method.

Objects are defined by their boundary values (highest and lowest) in their defining dimensions.

We are defining a "boundary value" as a minimum or maximum value of some variable inherent in the definition of some abstract object.

We are asserting that the method of boundary values is highly suited to this task, and expect to describe the universality of this method in high detail.

Abstract objects are defined by a range of boundary values, in an n-dimensional envelope that functions like a container.

This seems to be a recurring theme -- fundamental concepts in the definition of an "interval" that have many different names in different contexts -- but are in some general sense "the same thing"

1. boundary value
2. end point
3. starting point
4. highest (maximum) value
5. lowest (minimum) value
6. cut (as i define it)
7. distinction
8. slice

   what is the relationship between these ideas an the concept of the interval from 0 to 1 -- the "unit interval

   it has cut point at 0 and 1

   those can be ambiguous, hard to define -- does the cut have "thickness

   is it based on euclidean geometry

   can it be reprosed in the real world -- the "actual" world

   now

   that that problem seems to be solved with the closed lop circular model

   it may be that what we want to do is -- insist that we are not concerned with idealized mathematics, purely conceptual mathematics (??) but only with engineering math -- the primary issue being that we are dealing with concrete measurement, and numbers that can be represented by digital values contained in cells and represented in on/off 1/0 bits.

It seems these terms are all more or less equivalent. Google lists them as synonyms for the word "type"

1. kind
2. sort
3. variety
4. class
5. category
6. classification
7. group
8. set,
9. bracket
10. genre
11. genus
12. species
13. family
14. order
15. breed
16. race
17. strain
18. style
19. description
20. designation
21. condition
22. quality
23. nature
24. manner
25. design
26. shape
27. form
28. pattern
29. rank
30. brand
31. make
32. model
33. line
34. mark
35. generation
36. vintage
37. stamp
38. ilk
39. kidney
40. cast
41. grain
42. mold
43. stripe

Certainty relates to knowledge and our capacity to measure something

If we can measure something -- in any kind of dimensions -- we begin to have knowledge of it and our degree of "control" increases

a feature or quality belonging typically to a person, place, or thing and serving to identify it. "inherited characteristics such as blood groups" Similar: attribute feature quality essential quality property trait

A "class" is a list of objects brought together by something (some value in a defining dimension) they all share.

If the objects in that class can be ordered by values in one of its defining dimensions, it is isomorphic to -- it "is" -- a dimension.

• "A dimension is an ordered class of values"
• A genus is a class
• A species is a class --- a "subclass of that genus"
• There may be (are) defining boundary value ranges that define "what is in the class" and "what is outside the class"
• So its defining dimensions function as boundary values

The classical theory of concepts is one of the five primary theories of concepts, the other four being prototype or exemplar theories, atomistic theories, theory-theories, and neoclassical theories. The classical theory implies that every complex concept has a classical analysis, where a classical analysis of a concept is a proposition giving metaphysically necessary and jointly sufficient conditions for being in the extension across possible worlds for that concept.

https://iep.utm.edu/conc-cl/

We are developing ways to define the concept of "comparison" in terms of dimensionality and values in dimensions. As possible, we want to define fundamental mathematical and arithmetic/algebraic operations in these same terms.

Forms of comparison to be defined in dimensional terms:

• Equality ("two things are equal to each other")
• Identity ("two things are identical")
• Similarity ("two things are similar")
• Difference ("two things are different")
• Metaphor ("two things are similar or identical in some dimensions")
• Analogy ("one thing is like some other thing")
• Also - simile, parable, other intuitive forms of comparison

What are these "things"? We are using the term "object", at several different levels.

The idea that word meaning is often compositional or composite, and that broader concepts "contain" implicitly nested sub-elements.

In this project, we want to define all semantic objects in terms of structures composed of primitives.

In our approach, those primitives are not "simple concepts" as might be seen in more traditional philosophic systems. They are raw primal "distinctions defined in dimensionaity" that are combined for form semantic objects. These structures are generally defined by stipulation -- they are made to mean something intended

Something motivates the emergence of a codified distinction

For example, the definition of a new species within some genus

A variety of anti-realism consisting in a doctrine to the effect that entities conceptualized in the same way have nothing in common but the fact that they are so conceptualized

Something actually "out there" -- actual, something physical, with boundaries and properties that can be described. A planet, a house, a rock, a person, an automobile, a tree

(the boundaries are symbolic and assigned by a thinker. does a rock have a "boundary"? obviously yes. where does that boundary exist? it's defined in abstractions)

Sowa's meaning triangle calls this the referent

We are exploring the idea that "consciousness" is best understood through a notion of structure -- essentially composed of ideas, which form a composite often described by such terms as "world view".

The "consciousness" that preceded the discovery that the Earth revolves around the sun held an entirely different world view.

Consciousness and awareness depend on articulate structures, that become increasingly accurate and meaningful as human spiritual/cognitive evolution continues to evolve.

Example from Wikipedia

Deductive reasoning, also deductive logic, is the process of reasoning from one or more statements (premises) to reach a logical conclusion.

Deductive reasoning goes in the same direction as that of the conditionals, and links premises with conclusions. If all premises are true, the terms are clear, and the rules of deductive logic are followed, then the conclusion reached is necessarily true.

Deductive reasoning ("top-down logic") contrasts with inductive reasoning ("bottom-up logic"): in deductive reasoning, a conclusion is reached reductively by applying general rules which hold over the entirety of a closed domain of discourse, narrowing the range under consideration until only the conclusion(s) remains. In deductive reasoning there is no epistemic uncertainty. In inductive reasoning, the conclusion is reached by generalizing or extrapolating from specific cases to general rules resulting in a conclusion that has epistemic uncertainty.[

The inductive reasoning is not the same as induction used in mathematical proofs – mathematical induction is actually a form of deductive reasoning.

Deductive reasoning differs from abductive reasoning by the direction of the reasoning relative to the conditionals. The idea of "deduction" popularized in Sherlock Holmes stories is technically abduction, rather than deductive reasoning. Deductive reasoning goes in the same direction as that of the conditionals, whereas abductive reasoning goes in the direction contrary to that of the conditionals.

What is a dimension? Why and how does it makes sense to talk about dimensions of something as its properties or attributes?

How is a dimension an attribute, and how does that interpretation relate to the traditional definition of dimension as a fundamental element of measurement?

Google's definition:

• a measurable extent of some kind, such as length, breadth, depth, or height.

• an aspect or feature of a situation, problem, or thing.
  • aspect
  • feature (Smith and Medin say a feature is a ---)
  • element
  • facet
  • side
  • characteristic
  • property
  • attribute

These are all properties of -- what? Models? Concepts? "Composite dimensional structures"? "A situation, problem or thing"

How do we construct a "thing" out of dimensions?

How do we construct a "situation" out of dimensions?

We have to follow the general Sowa law of picking aspects that are interesting to us for some reason.

We don't "construct the entire object". We abstractly represent aspects of the object ("dimensions of the object") that are interesting to us.

**

Poperties and attribute are composite/hollstic/assembled objects with internal structure

Is a dimension a cut or a distinction? If it is a property or attribute, how would that be true?

I used to define a dimension as an "ordered class"

So the notion of "opposite" might be generalized to define this range of variation, with a lowest and highest value in some defining attribute -- the way we might order the members of a "species" by a value in one of their defining attributes

***

"a difference between two similar things"

https://dictionary.cambridge.org/us/dictionary/english/distinction

I like this definition -- because it pulls the two objects together

similarity and difference -- the primary distinctions defined by Linnaeus

difference, contrast, dissimilarity, dissimilitude, divergence, variance, variation; division, separation, differentiation, contradistinction, discrimination, segregation, dividing line, gulf, gap, chasm

dividing line

boundary

the best phrase here is "dividing line"

or "cut"

"words slice up the world"

What is the domain and range of a property? How does these concepts relate to boundary values

Empirical, actual, "sensori-motor", quantitative

measurable, physical, real, concrete

tension between form and content

If A = B, are A and B "identical"?

Does a definition of a term amount to the use of equals?

A distinctive attribute or aspect of something

Google: a distinctive attribute or aspect of something. "safety features like dual air bags" Similar: characteristic attribute quality property trait mark hallmark trademark aspect facet side point detail factor ingredient component constituent element theme peculiarity idiosyncrasy quirk

Something cuts -- something is cut. One is figure, one is ground

One is active ("yang") -- one is passive ("yin")

That which cuts is active -- that which is cut is passive

to cut is to divide -- one is divided into two

the divided become "units" -- or can be defined that way

Is this related to similarity / difference? I am guessing yes.

Ambiguity of value in some definition -- a bounded range. Related to error tolerance and uncertainty. Has meaning in various contexts, such as "fuzzy logic". Related to ambiguity and uncertainty.

In this framework, we generally want to talk about boundary values and intervals, where the range across the interval involves an undefined span which may be understood as fuzzy.

There are types of variables where the values are inherently fuzzy, such as temperature defined in terms like "very cold", "cold", "cool" "average", "warm", "hot", "very hot".

The meaning of those values in precise measurement can be stipulated by agreement.

A fuzzy concept is a concept of which the boundaries of application can vary considerably according to context or conditions, instead of being fixed once and for all.[1] This means the concept is vague in some way, lacking a fixed, precise meaning, without however being unclear or meaningless altogether.[2] It has a definite meaning, which can be made more precise only through further elaboration and specification - including a closer definition of the context in which the concept is used. The study of the characteristics of fuzzy concepts and fuzzy language is called fuzzy semantics.[3] The inverse of a "fuzzy concept" is a "crisp concept" (i.e. a precise concept).

A fuzzy concept is understood by scientists as a concept which is "to an extent applicable" in a situation. That means the concept has gradations of significance or unsharp (variable) boundaries of application. A fuzzy statement is a statement which is true "to some extent", and that extent can often be represented by a scaled value. The best known example of a fuzzy concept around the world is an amber traffic light, and indeed fuzzy concepts are widely used in traffic control systems.[4] The term is also used these days in a more general, popular sense - in contrast to its technical meaning - to refer to a concept which is "rather vague" for any kind of reason.

In the past, the very idea of reasoning with fuzzy concepts faced considerable resistance from academic elites. They did not want to endorse the use of imprecise concepts in research or argumentation. Yet although people might not be aware of it, the use of fuzzy concepts has risen gigantically in all walks of life from the 1970s onward. That is mainly due to advances in electronic engineering, fuzzy mathematics and digital computer programming. The new technology allows very complex inferences about "variations on a theme" to be anticipated and fixed in a program.[5]

New neuro-fuzzy computational methods make it possible to identify, measure and respond to fine gradations of significance with great precision.[6] It means that practically useful concepts can be coded and applied to all kinds of tasks, even if ordinarily these concepts are never precisely defined. Nowadays engineers, statisticians and programmers often represent fuzzy concepts mathematically, using fuzzy logic, fuzzy values, fuzzy variables and fuzzy sets.[7]

https://en.wikipedia.org/wiki/Fuzzy_concept

Term for class in taxonomy

Sometimes generalized as "taxon" or "taxa"

Hierarchy is a basic organizational principle, and concepts can be organized in a hierarchy. The prime example is a taxonomy, which categorizes types and classes of objects in the world in terms of a hierarchy of categories.

There are many examples of hierarchical organization in the real world, across a wide array of subject areas.

In philosophy, idealism is a diverse group of metaphysical views which all assert that "reality" is in some way indistinguishable or inseparable from human perception and/or understanding, that it is in some sense mentally constructed, or that it is otherwise closely connected to ideas.[1] In contemporary scholarship, traditional idealist views are generally divided into two groups. Subjective idealism takes as its starting point that objects only exist to the extent that they are perceived by someone.

https://en.wikipedia.org/wiki/Idealism

"An interpretation is an assignment of meaning to the symbols of a formal language. Many formal languages used in mathematics, logic, and theoretical computer science are defined in solely syntactic terms, and as such do not have any meaning until they are given some interpretation. The general study of interpretations of formal languages is called formal semantics."

https://en.wikipedia.org/wiki/Interpretation_(logic)

This project is "linear". It's about "order", and we make the claim that in the end, "all order is linear" (ie,. it is sequential)

But of course, most representations of the world ar highly abstract and holistic. But we are "decompositionalists" -- and we say that these holistic objects always have an intended linear decomposition that we can track down to their absolute foundation in terms of pixels, fonts, states of a medium, and in general terms to dimensions.

"Everything is made out of dimensions, and dimensions are linear"

Mathematics

• Sequence, an ordered list of elements, especially one of infinite length
• Tuple, an ordered list of finite length
• Multiset, a list/set of elements which can have multiplicity different than 1

Computing

• List (abstract data type), sometimes called a sequence
• Comma-separated values, sometimes character-separated values, a file type that stores tabular data in plain-text form

A fundamental form in being and existence, which defines the fundamental properties of "the Whole".

Logos contains logic and all rationality, and outlines "the form of the whole", within which we want to embed all our thoughts relative to the whole

Symbolically coded intention

The meaning of a word is its definition

The objective is to "make a point"

Define this concept at a series of levels

• Meaning of part of a word (sound, letter, syllable)
• Meaning of a word
• Meaning of a statement
• Meaning of a question

How do these principles combine around the concept of "making a point" (ie, of defining/bounding a point in x synthetic dimensions) -- thee dimensions defined with error tolerance and fuzziness in every dimension, which can be reduced through drill-down

What is a model? How does a model represent the reality it purports to describe? What is the correspondence between the model and the reality? What is the relationship between "the map" and "the territory"?

In some way, we establish an isomophism (a one-to-one correspondence) between the abstract model and the "real" reality it describes.

The model exists in an abstract symbolic medium -- such as a computer -- describing something "real". We choose aspects of the reality to include in our model because they are important for something we are doing, and ignore aspects that are insignificant.

We are defining "object" in various ways, and these definition go to the concept of model -- what is the relationship between the map and the territory

A variety of anti-realism consisting of a doctrine to the effect that entities labeled by the same term -- this bonobo or that bonobo have nothing in common but their name

the doctrine that universals or general ideas are mere names without any corresponding reality, and that only particular objects exist; properties, numbers, and sets are thought of as merely features of the way of considering the things that exist. Important in medieval scholastic thought, nominalism is associated particularly with William of Occam.

We want to drive the definition of number by a criteria of optimal conformity to the overall containing matrix of the Closed Loop, and the simple representation of a number on "the strip"

As per Wikipedia

• Count
• Measure
• Label

"What are the dimensions of number?"

We want to work on three levels of defining an object, and develop terminology that keeps them distinct

• a "real" object -- something concrete and actual and physical in the world (referent)
• a "mental" object - an image or word or idea in the mind (concept)
• a "representational" or "symbolic" object defined in some medium like a computer or a map or a piece of paper (symbol)

Wikipedia lists a series of definitions: https://en.wikipedia.org/wiki/Object

Examples:

• an item (word, term) in a list can be an "object" -- that would be a symbolic (fix, make consistent)
• the representation of that item in a computer would be (?)
• the "actual object in the real world that this term refers to" would be a concrete object

This applies to many areas and disciplines, including

• philosophy
• computing
• mathematics
• physics

Don't use the word "subject" or "subjective". The word "real" may also be misleading, because the symbolic representation in a medium (computer, piece of paper) has an actual concrete existence. This series of definition-levels is inherent in the concept of model.

The "meaning triangle" expresses this idea and Sowa cites it

https://en.wikipedia.org/wiki/Triangle_of_reference

• Symbol
• Thought or reference ("concept")
• Referent

Do these terms point to the same "three levels"

real, representational, mental

Objective idealism is an idealistic metaphysics that postulates that there is in an important sense only one perceiver, and that this perceiver is one with that which is perceived. One important advocate of such a metaphysics, Josiah Royce (the founder of American idealism),[1] wrote that he was indifferent "whether anybody calls all this Theism or Pantheism". It is distinct from the subjective idealism of George Berkeley, and it abandons the thing-in-itself of Kant's dualism.

https://en.wikipedia.org/wiki/Objective_idealism

Monism attributes oneness or singleness (Greek: ?????) to a concept e.g., existence. Various kinds of monism can be distinguished:

Priority monism states that all existing things go back to a source that is distinct from them; e.g., in Neoplatonism everything is derived from The One.[1] In this view only one thing is ontologically basic or prior to everything else. Existence monism posits that, strictly speaking, there exists only a single thing, the universe, which can only be artificially and arbitrarily divided into many things.[2] Substance monism asserts that a variety of existing things can be explained in terms of a single reality or substance.[3] Substance monism posits that only one kind of stuff exists, although many things may be made up of this stuff, e.g., matter or mind. Dual-aspect monism is the view that the mental and the physical are two aspects of, or perspectives on, the same substance.

Is every dimension a range of "opposites"?

It cuts a unit into two similar units that are "different" with respect to that dimension.

"Opposite" is too simple -- it implies binary opposition across a range of values

Multiple meanings, including several meanings in mathematics

Only the physical is real

Abstract objects exist objectively and outside the human mind

What is a "primitive"? How are "composite holistic integral abstract" categories composed from ('built out of") independent lower-level elements, the way other constructed objects are "built out of parts"?

Basic claim:

• primitives must be atomic -- ie, they are "indivisible units"
• word meaning at an abstract level must be built from primitives
• symbolic representation in a computer is built from primitive elements, like "bits"

We are exploring this question.

Drive the notion of fundamental constructive object to its lowest possible level

Build every abstract object out of distinctions

Every category or concept or class is defined by nested distinctions

How does this issue change or varying depending on "the type of object" we are constructing?

I probably need to firm up these definitions of "object"

is a "category" an "object"?

is a "term" or a "type" an "object"?

probably yes to all

Wikipedia says "a property may have properties"

We are trying to address that complexity through the use of synthetic dimensions

prototype or exemplar theories

Abstract dimensionality

Range of some function or variable

What is meant by real? How does "real" relate to "actual"?

Various meanings

• That a concrete object/item in the world is "real" - e.g., "that concrete wall over there"
• Or -- that abstractions and "universals" are "real" - e.g., "there are such things as concrete walls"

the doctrine according to which scientific theories are broadly true of reality

In mathematics, a set is a collection of distinct elements. The elements that make up a set can be any kind of things: people, letters of the alphabet, numbers, points in space, lines, other geometrical shapes, variables, or even other sets. Two sets are equal if and only if they have precisely the same elements.

a form of comparison

A taxa -- a class

Stipulation is a process of assigning specific meaning to a term by intentional affirmation. The user of a word or term can stipulate its meaning. Sometimes call "fiat".

In a dialogue/conversation process, stipulation can remove all ambiguity from the meaning of a term by "drilling down" until an acceptable definition is negotiated.

n philosophy, idealism is a diverse group of metaphysical views which all assert that "reality" is in some way indistinguishable or inseparable from human perception and/or understanding, that it is in some sense mentally constructed, or that it is otherwise closely connected to ideas.

Subjective idealism, or empirical idealism, is a form of philosophical monism that holds that only minds and mental contents exist. It entails and is generally identified or associated with immaterialism, the doctrine that material things do not exist. Subjective idealism rejects dualism, neutral monism, and materialism; indeed, it is the contrary of eliminative materialism, the doctrine that all or some classes of mental phenomena (such as emotions, beliefs, or desires) do not exist, but are sheer illusions.

https://en.wikipedia.org/wiki/Subjective_idealism https://en.wikipedia.org/wiki/Idealism

A physical representation of an abstract object -- like a word in a database cell

see meaning triangle

This is a major item of study

A synthetic dimension is

• An ordered class -- meaning a set of distinct objects or elements that can be place in an unambiguous serial order base on some criteria possess by all the objects in the set

https://en.wikipedia.org/wiki/Property_(philosophy)

The meaning of terms are defined in relativistic ways, based on foundational principles. In stand-alone ways, there is no absolute meaning to a term like "class" or "concept" or "category" or "type".

To maintain commensurateness across processes and vocabularies, those fundamental terms must be defined relative to one another, in a constructive/additive process that builds from a common foundation following a common method.

In this project, we are constructing a method to derive all dimensions and terms common to ontology and epistemology from a common universal foundation, where the properties of that foundation are absolute simplicity and consistency.

A cascade of nested distinctions ranging across levels of abstraction.

A "species" is a distinction nested within a "genus"

A symbolic object or concept held in the mind or represented by symbols (alphabets, numbers) in some medium like a computer or a piece of paper. initial exploratory hypothesis "abstract objects are represented by and composed of synthetic dimensions"

Type is a synonym for category that is assigned specific meaning in a specific system context. Google search for the word "type" returns the following:

a category of things having common characteristics.

synonyms: kind, sort, variety, class, category, classification, group, set, bracket, genre, genus, species, family, order, breed, race, strain; style, description, designation, condition, quality, nature, manner, design, shape, form, pattern, rank; brand, make, model, line, mark, generation, vintage; stamp, ilk, kidney, cast, grain, mold; stripe

Like ambiguity, an open undefined range between defined and known cut points

Uncertainty and continuity are closely related -- there is always a space between known/measurable cut points

Ontologies for scientific purposes should be constructed such that their terms are referring to ""universals" or "types" He is using these two terms to describe the difference between an individual concrete object and a category that contains or describes it -- in a "is-a" relationship I think