Forms of Thought
The Topology of the Forms of Thought
Topology of Thought
Every system with a top-down component of structure needs some rules by which it is governed.
The simple coherence, and integrity of the system is based on it's adoption of universal rules and structures.
Hence, the model incorporates the of logic of both descriptive and prescriptive methods.
Both inductive creation as well as deductive determination are supported.
The bridge between the form of thought, and the content of language is crossed by symbolic representation.
This is a model of symoblic representation. Or, rather, a meta-model.
This model includes all systems of deductive and inductive logic, as well as conceptual spaces, interpreted by symbolic logical systems.
The classes of compontents to the system:
1. Logic - Grammars - This is the rules governing the logical systems. It defines the process by which sentences, questions and proofs are interpreted.
Grammars represent well-formedness of conceptualization within the model. They also contain the logical process interpretations to evaluate truth statements or procedures.
The logic or grammer class has falls into the Interpretation super-class of core classes. This is because is plays a clarifying or elucidating role.
Other synonyms that relate to the logical layer are : system, network, constraints, meta-model, graph, constraints, rules, game.
As a whole class Logical Rule systems can describe collections including itself. As well, sub-classes of rule systems include Processes and Procedures, that are NOT self-referrential.
The core essence of a logic is that it is desriptive. The core property is well-formedness.
- The next two core classes fall into the type of "Identifiers", since they are involved in the process of naming, and identifying objects as they pertain to the platonic world of forms, or the material.
2. Concept
It represents some "space" projected from some model.
Concepts have internal topologies as well as external topologies and properties within their space.
Other notions of concepts are abstractions, simplifications, generalizations, . Understandings and implications are a sub-class of concepts.
Concepts are used in a bottom-up fashion. They are flexible, unrestricted, ad-hoc, and interpretive.
Their creation process is one of identification. Their nature is determined by their properties.
Concepts refer and may contain objects.
Concept creation is a process, and processes are concepts.
Symbols represent a bridge among concepts, to map and convey higher-order concepts.
Symbols as a technique prepresent the concept of conceptualization or abstraction.
Symbols as a useage however represent the sub-class concept of a grammar.
The concept is interpreted using a Model, a concept can or can not be a Model (Grammar). Some concepts are grammars.
Concepts have properties. Properties are founded on concepts.
The core process of a concept is formulation. Creation. Thought.
The core property is Intangibility. Abstraction. Idea.
3. Object
An Object has the core properties is their name or designation.
Objects serve the process of Identification, Encapsulation, Forming boundaries, Defining, Discriminating, Differentiating.
Objects are Concepts. Objects can be colletions, or atomic. Collections are objects.
A concept is one kind of object.
An object relies on a concept for it's meaning, but also refers to a specific name or designation to connect that meaning to a subspace of a conceptual space.
The object is a label on the map of meaning.
Words are objects. Objects use words as components to identify their scope.
Node, Edge.
In our model, a concept is an object, and an object is a concept.
4. Process - Procedures, that are NOT self-referrential. Role as Verb. Sub-class of Logic.
Procedures are applications of rules.
Proof is a Process. (The proof symbol is a separate object)
Establishment of truth or a result. Returning an answer.
Answer.
Processes enable consistency, compliance,.
Evaluation. Applicaitons.
Processes fall into the super-class of "Interprative Classes".
This is because their purpose is clarification, or elucidation.
Procedures are determinative.
They represent an applications of rules, to symbols that may or may not comply with those rules.
Processes take an abstract rule-bases system, and apply it to a symbol, which is presumably mapped to concepts or objects.
Process is the Action that enables language.
Process Verb. IN grammer a process applies to a subject. The subject of a process of typically a symbol, or space.
Depending on if it is an logical, analytic, algebraic, or graphical process.
In design, Process belongs to the "Structural" super-class.
In usage, Process belongs to the "Interpretation". super-class.
5. Properties. Are Attribues.
COmponents.
Defining Characteristics.
Data Members
Members.
Fields.
Properties can be "natural kinds", or composite properties aggregating concepts.
Every other class has properties.
THe concept of a property is that of characteristics.
The usage of a property is that of identification, or differentiation. Properties can be used to unify objects and concepts, or to divide them.
Properties are objects. (everything is an object)
Properties fall into the interpretation, or clarifying aspect.
Property names are symbols that are used to evaluate the scope of conceptual spaces.
6. Collection.
Resource. Data. Store. Set.
Simple ontology. List + document types.
Document Types are collections of properties.
Experienced through a frame of reference.
May be a conceptual collection which represents a notion.
Structure of Resources. Map of Resources.
Interpretations and Intuitions and Understanding are resources.
Collections are structural.
Collections are objects, contain objects, contain properties, may represent properties.
7. Symbol
Information. Small self-contained units of data. Composed of Nothing. Empty. Irreducable representations.
Representation, Data, Number, Abstraction.
Signal. Sign. Message. Word. Letter.
Names are symbols that designate objects.
Visualization.
Properties of symbols.
Symbols are objects, and make use of the concept of abstract representation.
Symbols have no components. Properties are interpreted, not intrinsic.
8. Relationships consist of a special kind of set or collection.
They consist of objects as well as a property.
THey connect collections to one another and properties.
Colletions (of objects, concepts, sybmols, properties, ...) can be related to one another, or other collections heterogeneous.
An object can be related to an object through a property.
And an object can be related to a property. (through another property)
They are used to signify a property of a collection.
They are enabled by the process of identification.
Connetions. Links. vertex.
Set of pairs with values.
Functions are a Surjective relation.
Relationships are used for "structural intent" or "structural use"
And are comprosed and enabled through "structural process".
9. Use. Meaning, Purpose, Concext.
This refers to how an object from a class is used.
Use is functionally a representation for Meaning.
Behaviour type.
Part of Speech represents a use of a collection of symbols as it relates to the process of relating other symbols.
ACtion. Use is a type of process.
Purpose. Meaning. Concext. Semantic Context.
Essence.
This concluded the core classes that have well-defined properties.
Another core class is that of the user of the language.
10 . The User
The reader, listener, or audience.
Agent. Client. Speaker. Input. Frame. Boundary. Terminus. External Node. Uncertainty. Externality. Limitation. Environment.
Frame. Perspective. Dimension. Vector.
Other supplimentay kinds of class types.
Operatior - Conjuction.
And, or, if , if then , then if, if and only if. else. until.
Perepositions, Postpositions. Related to relationships between objects related to spacial and orientation metrics.
(applied to spacial dimensions.)
Punctuation - Document Type. Model of Well-formedness.
Word - Symbol
Pronoun - Pointer (special kind of symbol that points to a location in space.)
Article (a, the) - identifier that contains the property of context, scope, semantic meaning.
Adjective is a property.
Definition - Core property, Axiom.
Meaning, part of speech, use - Intent, Use
Relation - Set Function, Value
Sentence - Collection Notion thought Resource message
Participant - User
Adverbs - Modifier of process, or meaning, Descriptor of meaning.
that modify verbs - sub process, Meta-process- ex. Process Differently - or Process Descriptively.
that modify adjectives - sub property. meta-property. Ex. Identify Meta-describtively
that modify adverbs - Purposefully Alternatively Descriptively Process
One can see that the adverb plays a special role, and needs further investigation.
Tense
Voice
Aspect
Implicature
Topology of Thought
Every system with a top-down component of structure needs some rules by which it is governed.
The simple coherence, and integrity of the system is based on it's adoption of universal rules and structures.
Hence, the model incorporates the of logic of both descriptive and prescriptive methods.
Both inductive creation as well as deductive determination are supported.
The bridge between the form of thought, and the content of language is crossed by symbolic representation.
This is a model of symoblic representation. Or, rather, a meta-model.
This model includes all systems of deductive and inductive logic, as well as conceptual spaces, interpreted by symbolic logical systems.
The classes of compontents to the system:
1. Logic - Grammars - This is the rules governing the logical systems. It defines the process by which sentences, questions and proofs are interpreted.
Grammars represent well-formedness of conceptualization within the model. They also contain the logical process interpretations to evaluate truth statements or procedures.
The logic or grammer class has falls into the Interpretation super-class of core classes. This is because is plays a clarifying or elucidating role.
Other synonyms that relate to the logical layer are : system, network, constraints, meta-model, graph, constraints, rules, game.
As a whole class Logical Rule systems can describe collections including itself. As well, sub-classes of rule systems include Processes and Procedures, that are NOT self-referrential.
The core essence of a logic is that it is desriptive. The core property is well-formedness.
- The next two core classes fall into the type of "Identifiers", since they are involved in the process of naming, and identifying objects as they pertain to the platonic world of forms, or the material.
2. Concept
It represents some "space" projected from some model.
Concepts have internal topologies as well as external topologies and properties within their space.
Other notions of concepts are abstractions, simplifications, generalizations, . Understandings and implications are a sub-class of concepts.
Concepts are used in a bottom-up fashion. They are flexible, unrestricted, ad-hoc, and interpretive.
Their creation process is one of identification. Their nature is determined by their properties.
Concepts refer and may contain objects.
Concept creation is a process, and processes are concepts.
Symbols represent a bridge among concepts, to map and convey higher-order concepts.
Symbols as a technique prepresent the concept of conceptualization or abstraction.
Symbols as a useage however represent the sub-class concept of a grammar.
The concept is interpreted using a Model, a concept can or can not be a Model (Grammar). Some concepts are grammars.
Concepts have properties. Properties are founded on concepts.
The core process of a concept is formulation. Creation. Thought.
The core property is Intangibility. Abstraction. Idea.
3. Object
An Object has the core properties is their name or designation.
Objects serve the process of Identification, Encapsulation, Forming boundaries, Defining, Discriminating, Differentiating.
Objects are Concepts. Objects can be colletions, or atomic. Collections are objects.
A concept is one kind of object.
An object relies on a concept for it's meaning, but also refers to a specific name or designation to connect that meaning to a subspace of a conceptual space.
The object is a label on the map of meaning.
Words are objects. Objects use words as components to identify their scope.
Node, Edge.
In our model, a concept is an object, and an object is a concept.
4. Process - Procedures, that are NOT self-referrential. Role as Verb. Sub-class of Logic.
Procedures are applications of rules.
Proof is a Process. (The proof symbol is a separate object)
Establishment of truth or a result. Returning an answer.
Answer.
Processes enable consistency, compliance,.
Evaluation. Applicaitons.
Processes fall into the super-class of "Interprative Classes".
This is because their purpose is clarification, or elucidation.
Procedures are determinative.
They represent an applications of rules, to symbols that may or may not comply with those rules.
Processes take an abstract rule-bases system, and apply it to a symbol, which is presumably mapped to concepts or objects.
Process is the Action that enables language.
Process Verb. IN grammer a process applies to a subject. The subject of a process of typically a symbol, or space.
Depending on if it is an logical, analytic, algebraic, or graphical process.
In design, Process belongs to the "Structural" super-class.
In usage, Process belongs to the "Interpretation". super-class.
5. Properties. Are Attribues.
COmponents.
Defining Characteristics.
Data Members
Members.
Fields.
Properties can be "natural kinds", or composite properties aggregating concepts.
Every other class has properties.
THe concept of a property is that of characteristics.
The usage of a property is that of identification, or differentiation. Properties can be used to unify objects and concepts, or to divide them.
Properties are objects. (everything is an object)
Properties fall into the interpretation, or clarifying aspect.
Property names are symbols that are used to evaluate the scope of conceptual spaces.
6. Collection.
Resource. Data. Store. Set.
Simple ontology. List + document types.
Document Types are collections of properties.
Experienced through a frame of reference.
May be a conceptual collection which represents a notion.
Structure of Resources. Map of Resources.
Interpretations and Intuitions and Understanding are resources.
Collections are structural.
Collections are objects, contain objects, contain properties, may represent properties.
7. Symbol
Information. Small self-contained units of data. Composed of Nothing. Empty. Irreducable representations.
Representation, Data, Number, Abstraction.
Signal. Sign. Message. Word. Letter.
Names are symbols that designate objects.
Visualization.
Properties of symbols.
Symbols are objects, and make use of the concept of abstract representation.
Symbols have no components. Properties are interpreted, not intrinsic.
8. Relationships consist of a special kind of set or collection.
They consist of objects as well as a property.
THey connect collections to one another and properties.
Colletions (of objects, concepts, sybmols, properties, ...) can be related to one another, or other collections heterogeneous.
An object can be related to an object through a property.
And an object can be related to a property. (through another property)
They are used to signify a property of a collection.
They are enabled by the process of identification.
Connetions. Links. vertex.
Set of pairs with values.
Functions are a Surjective relation.
Relationships are used for "structural intent" or "structural use"
And are comprosed and enabled through "structural process".
9. Use. Meaning, Purpose, Concext.
This refers to how an object from a class is used.
Use is functionally a representation for Meaning.
Behaviour type.
Part of Speech represents a use of a collection of symbols as it relates to the process of relating other symbols.
ACtion. Use is a type of process.
Purpose. Meaning. Concext. Semantic Context.
Essence.
This concluded the core classes that have well-defined properties.
Another core class is that of the user of the language.
10 . The User
The reader, listener, or audience.
Agent. Client. Speaker. Input. Frame. Boundary. Terminus. External Node. Uncertainty. Externality. Limitation. Environment.
Frame. Perspective. Dimension. Vector.
Other supplimentay kinds of class types.
Operatior - Conjuction.
And, or, if , if then , then if, if and only if. else. until.
Perepositions, Postpositions. Related to relationships between objects related to spacial and orientation metrics.
(applied to spacial dimensions.)
Punctuation - Document Type. Model of Well-formedness.
Word - Symbol
Pronoun - Pointer (special kind of symbol that points to a location in space.)
Article (a, the) - identifier that contains the property of context, scope, semantic meaning.
Adjective is a property.
Definition - Core property, Axiom.
Meaning, part of speech, use - Intent, Use
Relation - Set Function, Value
Sentence - Collection Notion thought Resource message
Participant - User
Adverbs - Modifier of process, or meaning, Descriptor of meaning.
that modify verbs - sub process, Meta-process- ex. Process Differently - or Process Descriptively.
that modify adjectives - sub property. meta-property. Ex. Identify Meta-describtively
that modify adverbs - Purposefully Alternatively Descriptively Process
One can see that the adverb plays a special role, and needs further investigation.
Tense
Voice
Aspect
Implicature
posted by Matthew Robson at
10:51 AM
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