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.