Appendix A. The Root Text

  • Part 1: Things In a general sense, there are three types of objects: everythings, somethings, and nothings. In a universe, there can exist only one everything, many somethings, and exactly zero nothings.

    • Chapter 1.1: Everything Everything means every thing, taken together. Although it may be conceptualized as a single unit, it is best to regard everything as something which is neither singular nor plural (because the concept of singularity requires the concept of plurality).

      • 1.1.1: The Whole Everything cannot be defined.

        • A Definition of Everything Everything occupies every position in all dimensions which are attributed to it.

        • The Properties of Everything Everything neither has properties nor has no properties.

      • 1.1.2: Universes Universes are everything from a particular point of view.

      • 1.1.3: The Integrity of Wholes Wholes, as opposed to collections of parts, are united.

    • Chapter 1.2: Something Something is the result of partitioning a larger thing.

      • 1.2.1: Parts The partition of a thing and the parts of that thing entail one another.

      • 1.2.2: Atoms The smallest thing has no parts.

        • Parts of Reduced Dimensionality Something cannot have a dimensionality less than its parent thing; it occupies a nonzero interval on every dimension which the parent occupies.

      • 1.2.3: Properties The properties of something may be extrinsic or intrinsic. All objects have extrinsic properties except everything, and all objects have intrinsic properties except atoms.

        • Intrinsic Properties Intrinsic properties characterize the parts of a thing.

        • Extrinsic Properties Extrinsic properties characterize the whole of which a thing is a part.

        • Relativistic Properties Properties characterize the relations of a thing.

      • 1.2.4: Dichotomy Dichotomy both collectivizes and dichotomizes, without being intrusive on the dichotomized domain.

        • Sets and Wholes Sets are discrete: they may be divided into their members in only one way. Wholes are continuous: they may be divided into further parts in arbitrary ways.

        • Boundaries A universe has no boundaries

        • Truth, Falsity, and Everything in Between True and false are the essence of categorization.

      • 1.2.5: Dimensions Dimensions are an extension of the concept of dichotomy.

        • Nominal Nominal dimensions have unordered parts.

        • Ordinal Ordinal dimensions are nominal dimensions that have an associated order.

        • Interval Interval dimensions are ordinal dimensions that have an associated measure.

      • 1.2.6: Hierarchy A hierarchy is a structure corresponding to successive partitions of a thing.

        • Ontological Priority As concepts occupy positions in ontological hierarchies with a single root, the notion of ontological priority is introduced.

        • Constructing Dimensions The number of dimensions of a thing is conceptually increased by iterating something along a singleton dimension.

    • Chapter 1.3: Nothing Nothing is a reference which does not refer to something.

      • 1.3.1: Nothing Nothing is the complement of everything

      • 1.3.2: References References form the basis for points of view.

        • Notational and Denotational Equivalence References may differ, even though the things they refer to are the same.

        • Encoding Information References encode small amounts of information about the referenced domain.

      • 1.3.3: Existence Existence refers to the possibility of validly dereferencing concepts.

      • 1.3.4: Identity For two things to be called the same thing implies the notion of identity.

        • Spatial Identity Knowing a thing's identity requires knowing the spatial boundaries of that thing.

        • Temporal Identity Knowing a thing's identity requires knowing the temporal boundaries of that thing.

        • Referential Identity Two references are referentially identical if they have the same referent.

        • Isomorphic Identity A reference has a valid correspondence to a referenced thing if their respective relations in each universe are identical.

  • Part 2: Universes There are three well-known universes: the objective universe, the perceptual universe, and the conceptual universe.

    • Chapter 2.1: The Physical Universe All things are parts of the physical universe.

      • 2.1.1: Dimensions of the Physical Universe The dimensions most commonly attributed to the physical world are the three spatial and the temporal.

        • The Nature of the Physical Dimensions The physical dimensions are most often conceived to be Euclidean.

      • 2.1.2: Parts of the Physical Universe The parts of the physical universe are called objects.

        • Primitives of Reality: Spatial Things versus Events All objects occupy a nonzero interval of time.

      • 2.1.3: The Subjective/Objective Dichotomy The division between the subjective and the objective defines life.

        • 2.1.3.1: The Objective Domain The objective domain consists of those things which are not referential.

          • Causation The actions of lifeless things are determined from the outside.

        • 2.1.3.2: The Subjective Domain The subjective domain consists of those things which, for some individual, refer to things in the physical universe.

          • The Source of Volition Living things are described as having a choice.

    • Chapter 2.2: The Subjective Universe The subjective universe is the part of the physical universe that is directly perceived by a single individual.

      • 2.2.1: Dimensions of the Subjective Universe The most common partition of the subjective universe involves five external and several internal senses, which together form a nominal dimension.

        • External Perception The dimensionality and mapping of the various sensory modalities is sense-specific.

        • Internal Perception Internal perception is responsible for like and dislike.

      • 2.2.2: Parts of the Subjective Universe All of our experience comes to us through our external and internal senses.

        • Perceptual Correspondence Percepts are formed of both objects and concepts.

        • Spatial and Temporal Parts Perception is perception of change.

        • Attention Awareness may be restricted to parts of certain dimensions.

      • 2.2.3: The Conceptual/Perceptual Dichotomy A concept is a reference to a part of subjective experience, or a generalization of percepts.

        • 2.2.3.1: The Perceptual Domain The perceptual domain is composed of perception: it includes sensation, excludes conception, and consists of references to objective reality.

        • 2.2.3.2: The Conceptual Domain The conceptual domain is composed of things called concepts, which are references to percepts.

          • Definition of a Concept Concepts are categories of percepts which are the result of partitioning something.

    • Chapter 2.3: The Conceptual Universe The conceptual universe is the domain of language.

      • 2.3.1: Dimensions of the Conceptual Universe First-order concepts refer to percepts, which refer to objects; they derive their semantic value [meaning] from that which they reference and their relationship to other references.

        • Decision Boundaries Concepts unify the perceptual data on one side of a decision boundary.

        • Intuition A picture is worth a thousand words.

      • 2.3.2: Parts of the Conceptual Universe The parts of the conceptual universe are called concepts.

        • 2.3.2.1: The Sentence The smallest valid reference in the conceptual universe is the sentence.

        • 2.3.2.2: The Noun Phrase The noun phrase identifies the spatial extent of sentences.

          • The First Concepts The primary notion of identity is called self-identity.

          • Self/Other The primary notion of identity is called self-identity.

          • Proper, Mass, and Count Nouns Different types of nouns are abstracted from events in different ways, in virtue of which they require different quantifiers.

          • Ontological Priority of Nouns The abstractness of nouns can be quantified by using the notions of dimensionality and conceptual order.

        • 2.3.2.3: The Verb Phrase The verb phrase is the temporal part of sentences about events.

          • Transitive and Intransitive Verbs Verb phrases may be intransitive, in which case the verbs are semantically complete, or transitive, in which case the verbs require an object.

  • Part 3: References References are relations which are capable of bridging universes.

    • Chapter 3.1: Subjective/Objective References Between the objective domain and the subjective domain are two primary relationships: perception and communication.

      • 3.1.1: Perception Perception is that process by which objects in the objective world are represented by percepts in the subjective world of an individual.

        • Bottom-up Perception Percepts are caused, to some degree, by the objects that they reference.

        • Top-down Perception Percepts are caused, to some degree, by the mind in which they occur.

      • 3.1.2: Communication Communication is that process by which events in the subjective world of an individual are represented in the objective world.

        • Isomorphism of Individual Perception Between referential domains, the only available conditions for identity are those of isomorphism.

    • Chapter 3.2: Perceptual/Conceptual References Between the perceptual domain and the conceptual domain are two primary relationships: conception and naming.

      • 3.2.1: Conception Conception is the process of linking concepts to percepts, such that a set of percepts are identified by some concept.

        • The Stimulus and the Response Conditioning is a popular (extrinsic) model of conception.

        • Neural Networks Neural networks are a popular (intrinsic) model of conception.

      • 3.2.2: Naming Naming is the process of denoting a concept by a percept: the percept, in virtue of this denotation, is called a symbol.

        • Animal Cognition Animal cognition is a part of human cognition.

        • The Modality of Naming Thinking can occur in any modality.

    • Chapter 3.3: Conceptual/Conceptual References Concepts can be formed recursively.

      • 3.3.1: First-Order Concepts First-order concepts refer to percepts that refer to objects; from this reference they derive their semantic value.

      • 3.3.2: Higher-Order Concepts Higher-order concepts refer to percepts-that-refer-to-concepts (i.e. symbols).

        • Paradox Concepts of concepts create the potential for both great understanding and great confusion.