The Formal Law: Logics

( … )

 

LOGICS

AND;

(How can we observe what those words refer to)

  • Observable, Empirical, Empiricism: .
    • Sensory Observation(Input): The direct observation of phenomena using the human senses (sight, hearing, touch, taste, smell, disambiguation, and prediction(modeling)) to gather information about the environment. Despite its limitations in scope and precision, sensory observation remains a fundamental aspect of empirical inquiry, serving as the basis for forming initial hypotheses and for direct experiences of phenomena.
    • Intuitionistic Observation (Consistency/Non): “All comparisons must eventually reduce to tests of consistency and coherence by our intuition.” The application of intuition upon the results of sensory, physical, and logical instrumentation to test the consistency and coherence of the totality of sensory, physical, and logical information. It functions across the epistemic spectrum from hypothesis generation, theory development, and testing by the evaluation of logical and empirical consistency and coherence.
    • Physical Instrumentation (Observation ): the use of tools and instruments to extend the range and precision of human senses, enabling the detection, measurement, and analysis of phenomena that are beyond the direct reach of our senses. When phenomena are reduced to a system of measurement of any kind, instrumentation allows for reduction to an analogy to experience where our sense, perception, and intuition can indirectly ‘sense and perceive and compare’ physical aspects of the universe impossible without such instrumentation.
    • Logical Instrumentation (Competition): The use of logic and logical frameworks, mathematical models, and computational methods to understand and predict phenomena that are not immediately accessible to sensory or instrumental observation. Logical instrumentation operates through the construction and manipulation of abstract concepts and relationships, facilitating the exploration of theoretical domains and the formulation of hypotheses and theories, whether to falsify, justify, or test for survival.
  • Empirical Access (Observable): Both entities and their identities are accessible through empirical means. However, defining an entity involves observing its existence and behavior, while defining its identity involves observing its properties and relations.

Summary:

|Empirical Observation Spectrum|: Sensory Observation (Input) > Intuitionistic Observation (Consistency/Non) > Physical Instrumentation (Observation) > Logical Instrumentation.
The spectrum of empirical observation methods, starting with direct sensory input and progressing through intuitionistic evaluation, enhanced by physical instrumentation, and culminating in abstract logical analysis. Each step signifies a deeper layer of observation and understanding, from direct physical experiences to the abstract interpretation and theoretical modeling of phenomena

AND;

Learning, Knowledge (Epistemology):

  • Problem -> Theory -> Test -> Survival:  ( … )

AND;

Reasoning (Testing):

  • Via Positiva (Justification): a referent exists by the set of its properties. “A sculptor adds clay.”
  • Via Negativa (Falsification): a referent exists by the set of what properties it lacks. “A sculptor removes stone”
  • Via Adversaria (Competition, Survival): a referent exists by the competition between the set of its properties and the set of properties it lacks. “Markets compete for survival.”

AND;

Decidability: (End of route, conclusion, exit, complete?) ( … )

  • Agreement: ( … ) 
    • comprehensible/incomprehensible, consistent/inconsistent, correspondent/non-correspondent, true/false, good/bad, agree/disagree … the dimensions that humans can testify to if reduced to analogy to experience that is in turn subjectively comparable and testable.
  • Decidability: ( … )
  • Testifiability (Truth): ( … )

=== Section Expression ===

AND;

How do we express our observations?

Collections of relations. (whole value and purpose of language)
language as necessary for reason and calculation.

(say what the next steps are?)

 

 

GIVEN;

(What Words Refer To)
Universal Grammar: ( … )
   “… unambiguously clarify the means and methods of human expression (and the means of speaking of the universe’s means of expression at all scales”

To create clarity across disciplines and emphasize the transition from abstract to concrete and from static to dynamic:

  • Referrer (Actor, Observer, Origin) The observer that initiates the process of constructing references.
  • Reference (Symbol, Name, Noun) acts as the linguistic or symbolic link.
    • Referent (Concept/Category,Term) The tangible objects, people, abstract concepts, events, or phenomena the reference refers to. Usage: Linguistics, Semiotics.
    • Identity (Set of Properties): Refers to that set of properties  that disambiguate one referent or set of referents from another.
    • Entity (Instance) Refers to Referents and Identities that have distinct existence, whether concrete or abstract, physical, experiential, or metaphysical. It allows for the inclusion of both things that exist in the external world (existential), constructs created through human action or thought (constructable and expressible), mental phenomena (imaginable), and even those aspects of reality that might transcend our current understanding or capacity for expression (metaphysical). The term maintains a level of ontological neutrality, not inherently biasing towards physicalism, idealism, or dualism, which makes it suitable for cross-disciplinary use.
      • System: All Entities consist of Relations between their constituent causes that together produce Attributes(Properties), Behavior(Methods), and Interactions (cooperation). Nothing is static over a long enough time frame. Everything is dynamic (changing) over a long enough time frame. The change is determined by the acquisition of energy faster or slower than the relations that constitution the system can decay in the face of entropy.
        • Relations, Stable Relations, Constant Relations (Constitution, Construction, Set, Noun): All systems consist of a set of constant(stable) relations. 
        • Attributes (Properties, Noun||Verb) the static qualities or characteristics of entities.
        • Behavior (Methods(process, procedure), Actions, Verb) the actions or functions entities can perform when conditions are met.
        • Interactions (“Externalizations”, Exchanges(messages), Verb) the interactions between entities, influenced by their attributes and behaviors.
    • Object (Tangible) refers to a distinct entity with tangibility—meaning it can be directly perceived by the senses—or a well-defined conceptual focus. In the physical sense, objects are entities that occupy space and have mass. In more abstract domains, such as programming, objects are instances of classes that encapsulate data and functions, suggesting a structured conceptual focus rather than physical tangibility.

Summary: The progression from “referrer” to “object” outlines a conceptual hierarchy that starts with the act of denotation and moves towards the specificity and tangibility of existence.

  • Referrer initiates the denotation process, acting as the agent (person, system, or mechanism) that points or refers to something else. It is the starting point of reference, where the intention to denote or communicate about something is first manifested.
  • Reference serves as the intermediary linguistic or symbolic link, the means through which a referrer denotes or points to something. It embodies the act of referring itself, bridging the gap between the abstract intention of the referrer and the conceptualization of what is being referred to.
  • Referent represents the cognitive leap from abstract reference to the conceptualization of what is being referred to. It is the conceptual or real-world entity that a reference aims to denote, encompassing both tangible and intangible existences.
  • Identity further specifies the referent by delineating its distinguishing characteristics or attributes. It is what makes a referent distinct, providing a set of defining features that allow for recognition and differentiation.
  • Entity broadens the scope to include any form of existence, both abstract and concrete. It is an umbrella term that captures everything that can be considered to have a distinct existence, serving as the foundation for further specification into more tangible or well-defined concepts.
  • Object narrows down the concept of an entity by emphasizing physical tangibility or a well-defined conceptual focus. Objects are entities with a clearly defined structure, applicability, and, in some cases, measurability, making them the most concrete expression in this conceptual hierarchy.

|Semantic Continuum|: Referring (Referrer > Reference) > Conceptualization(Referent) > Specification(Identity) > Broad Existence (Entity) > Specific Existence (Object)
This hierarchy describes the sequence from the act of referring (referrer and reference) through conceptualization (referent), specification (identity), broad existence (entity), and finally to the tangible or well-defined existence (object). Each step represents a further clarification and specification in the process of denoting and understanding the world, both abstractly and concretely.

 

THEREFORE;

  • |??? “Grammatical something”|: Referrer (actor) > Reference (symbol) > Referent (category, concept) > Identity(Properties) > Entity(Instantiation) > {Attributes, Behavior, Interactions}: the progression from the initiation of a reference to the dynamic interaction of entities within systems.

AND;

How we disambiguate, compare, contrast, and organize terms (references, terms) by some common principle, behavior, or property.

 

Disambiguation 1: ( spectrum into measures ):Measurement (Disambiguation of the term):

  • Measurement: ( … ) (and why it matters (comparison is impossible otherwise)
  • Dimension, Dimensions: A property or set of properties of an identity (reference > referent > identity > entity) that can function as a measurement of that property internal to entities and across entities. As such all entities consist of one or more properties that themselves can be measured on one or more dimensions.
  • Order: Organization by one or more organizing principles (causality): criteria for organizing while retaining consistency and coherence with the organizing principle or principles across entities, phenomena, or processes. Most commonly the arrangement of references from less to more, or from center or neutral to more or less, but can also include Hierarchies, Trees, and Graphs in n-dimensions.
    • Methods of Ordering: A Progression of concepts that can be interpreted as increasingly complex ways of understanding and organizing information or phenomena.
      • Cardinal (Numbered)
        Definition: In mathematics, cardinal numbers (or cardinality) represent the quantity of items in a set, describing “how many” there are of something. It’s about counting without concern for order or arrangement.
        Application: This is the most fundamental way of understanding quantity, serving as the basis for much of arithmetic and measurement.
      • Ordinal (Indexed): Refers to position or rank in a sequence, showing the order of items but not the relative difference between them. It’s about sequencing elements in a linear progression.
      • Natural (By Natural Properties): Refers to natural numbers in mathematics (positive integers starting from 1) and can extend to mean arrangements or sequences that follow an inherent, expected, or “natural” progression based on intrinsic properties.
      • Adversarial (Triangulation): Triangulation by comparison by sets of properties that may or may not be the same, but can be compared (less vs more) by some method even if only by preference) and subject to conflict or competition, where entities interact in opposition. Example: Art.
      • Evolutionary (Consequential Over Time): Refers to processes that unfold or develop over time, leading to changes or adaptations as a result of cumulative consequences, interactions, and selections. 
    • Limits: ( … ) (limits necessary for a dimension)

AND;

Disambiguation 2: ( Measures into states ): How disambiguate the reference by organizing static and dynamic properties.

Weights and Measures of The States of Dimensions ( … )

  • State: ( … )
  • ( … ) (Noun, Verb, Agreement, dimensions, as measures.) 

AND;

Disambiguation 3: ( relationships between states ): How we relate those measurements to each other.

Syntax (Weights and Measures ): ( … ) (equations, transaction, description, terms, phrases, sentences, stories)

  • Cognitive Syntax|: Referrer (actor) > Reference (symbol) > Referent (category, concept) > Identity (Properties) > Entity (Instantiation) > {Attributes, Behavior, Interactions}: This progression outlines the cognitive syntax from the initiation of a reference to the dynamic interaction of entities within systems, highlighting the cognitive and communicative structure that facilitates understanding and interaction across various domains.

AND;

 

Logic: ( … )

The consistency coherence and correspondence of those relations between states.

  • ( … ) Properties of logic. (consistency and coherence)

 

AND;

Logical First Causes (Foundations, Baselines, Beginnings)

  • First Principle (Universal Discovered, Irreducible, Invariant):
    • First principles are the fundamental, foundational truths or assumptions that form the basis of a system of thought or inquiry.
    • These principles are considered to be self-evident, irreducible, and cannot be deduced from other propositions or assumptions.
    • In philosophy, first principles are used as the starting points for reasoning and building arguments.
    • Examples of first principles include Aristotle’s law of non-contradiction and Descartes’ cogito ergo sum (“I think, therefore I am”).
  • Axiom (Logic, Declared, Invariant in context):
    • An axiom is a statement or proposition that is considered to be self-evident or universally accepted as true within a particular domain or system of logic.
    • In mathematics, axioms serve as the foundational assumptions upon which a theory is built. They are not proven but are accepted as the starting points for deriving other truths through logical reasoning.
    • Examples include the axioms of Euclidean geometry, such as “parallel lines never intersect” and “a straight line can be drawn between any two points.”
  • Law (Science, Discovered, Reducible, Invariant at some scale or context):
    • In the context of natural sciences, a law refers to a well-established, universal principle that describes the fundamental behavior of natural phenomena. Laws are based on empirical evidence and are considered to be true within the limits of current scientific understanding.
    • Examples include Newton’s laws of motion, the laws of thermodynamics, and the law of conservation of energy.
  • Rule (Authority or Agreement, Invented, Invariant in context):
    • A rule is a specific guideline, regulation, or principle that governs behavior or procedure within a particular context.
    • Rules are often established by authority, custom, or agreement and are meant to be followed to maintain order, consistency, or achieve a desired outcome.
    • In contrast to laws, axioms, and first principles, rules are generally more narrow in scope and can vary depending on the context or system in which they are applied.
    • Examples of rules include grammatical rules in language, rules of a game, or rules of conduct in a professional setting.

AND;

The limits of the logic within the set of permissible dimensions of measurement included in the terms (references, measurements,  states).

Systems of Measurement(Paradigm):

  • ( … ) Sciences, paradigms (vocabulary, logic, grammar, syntax)  (Measurements within some limited set of dimensions)

AND;

Grammar (Method): “Rules of continuous, recursive, disambiguation within the limits of a paradigm”  ( …) (???? Answer: What are you doing with grammar – converting it into a formula that is testable for comprehensibility and agreement/disagreement.)

  • Continuous: Identity formation, whether of linguistic units (words, phrases) or entities (individuals, objects), is not static but evolves over time. It adapts in response to changing contexts, interactions, and understandings. This continuous aspect underscores that identity is not a fixed attribute but a fluid characteristic that undergoes constant negotiation and redefinition.
  • Recursive: The repetition of a process where the output of one iteration becomes the input for the next. In the context of identity and grammar, this implies that the determination of identity (or meaning) is built upon previous iterations of identification and differentiation. Each act of identification refines or revises the understanding of the entity or concept in question, contributing to a deeper, more nuanced comprehension.
  • Disambiguation: Resolving ambiguity, making clear distinctions where there might be inflation, deflation, or conflation. Or loading, framing, obscuring, fictioning or fictionalism. In grammar, it involves clarifying the meaning of words or structures based on syntax, semantics, and context. In the formation of identity, disambiguation involves distinguishing an entity or concept from others.
  • Summary: The first principle of Continuous Recursive Disambiguation is applicable across linguistic, physical, personal, social, and ontological domains – and is synonymous with with not only grammar we use to describe the universe, but Evolutionary Computation as the first principle of the universe, and Evolution as the result.
  • Algorithm: “While ambiguous add information until agreement or disagreement (consistency, correspondence) on an identity.”

Universal Decidability:

To claim that a logical system that satisfies a truth claim under realism, naturalism, identity, consistency, correspondence, and coherence, we must incorporate a combination of logical first causes that ensure the system adheres to these limits on testifiability:

  1. First Principles:
    • Include first principles that establish the foundational assumptions of your logical system, such as the principle of non-contradiction (a statement cannot be both true and false at the same time) and the principle of sufficient reason (every fact or claim must have a sufficient explanation or reason for its existence or truth).
    • Ensure that these first principles are consistent with the tenets of realism and naturalism, acknowledging the existence of an objective, mind-independent reality that can be studied through empirical means.
  2. Axioms:
    • Develop a set of axioms that are self-evident truths within your logical system, serving as the starting points for logical reasoning and the development of theories.
    • Ensure that these axioms are consistent with your first principles and with each other, adhering to the principle of consistency.
    • Make sure that your axioms correspond to the fundamental aspects of reality as understood through realism and naturalism, satisfying the principle of correspondence.
  3. Laws:
    • Identify the universal principles or laws that govern the behavior of the phenomena within the scope of your logical system.
    • These laws should be derived from the logical consequences of your axioms and first principles, ensuring a coherent and consistent framework.
    • The laws should accurately describe the observed patterns and regularities in the natural world, aligning with the principles of correspondence and naturalism.
  4. Rules:
    • Establish a set of rules or guidelines that specify how the logical system should be applied in specific contexts or domains.
    • These rules should be derived from and consistent with your laws, axioms, and first principles, maintaining the overall coherence and consistency of the system.
    • The rules should be applicable to real-world scenarios and provide practical guidance for reasoning, decision-making, or problem-solving within the relevant domains.
  5. Definitions and Identity:
    • Clearly define the terms, concepts, and entities within your logical system, ensuring that each has a unique and unambiguous identity.
    • These definitions should be consistent with your first principles, axioms, laws, and rules, and should accurately capture the essential properties or characteristics of the defined entities, aligning with the principle of identity.

By incorporating this combination of logical first causes – first principles, axioms, laws, rules, and clear definitions – and ensuring their alignment with the principles of realism, naturalism, identity, consistency, correspondence, and coherence, you can claim to have produced a logical system that satisfies a truth claim under these philosophical frameworks.

 

AND;

( … ) ? Title?

  • Subjectivity: Man is the Measure for Man (“Vitruvianism“) (Protagoras)
    • Human Faculties ( … )
  • Meaning:  ( ) the significance or relevance attributed to entities, concepts, actions, and interactions based on their relations and functions within one or more paradigms.
    • Relational Significance: Meaning arises from the constant relations between entities, whether they are sense perceptions, properties, references, or actions. The way entities relate to each other within a system or framework contributes to their significance.
    • Cognitive Recognition: Meaning is what human cognition attributes to entities and phenomena based on their identity (names), the internal consistency of their properties, and their place within the language (sets) that describes them.
    • Empirical Correspondence: In the realm of science (observations), meaning is associated with the empirical relationships between theories, concepts, or references and observable reality. It’s the extent to which scientific observations correspond with and accurately describe the external world.
    • Practical Application: Operationally, meaning is tied to the feasibility and implications of actions within the context of reality over time. It concerns the causation and consequences of actions, emphasizing their operational consistency and possible impact.
    • Decision-Making Context: Meaning also involves the rational incentives behind choices and the reciprocal incentives that drive cooperation. In this sense, meaning is related to the reasons, motivations, and expected outcomes that inform rational decision-making and cooperative behavior.
    • Communicative Function: Through language, meaning encompasses the conveyance of ideas, emotions, intentions, and information between individuals, facilitating understanding and interaction.

AND

Empirical Realism (Actions, Actionable, Interaction):

  • Testifiability: ( … ) (these are testifiable, disambiguating the existential from imaginary)
  •  
  • Cause and Consequence: ( … )
  • ( … )
  • Realism: 
    • The External World: The universe and all in it exists independently of our sensory experiences or conceptual paradigms. Even if we can imagine more than exists or can exist in the universe other than in our imaginations.
    • Correctness and Correspondence: The properties of the universe can be discovered and are determined by how accurately our thoughts correspond to the external reality.
    • Discoverability of Reality: Through observation, reason, and measurement, humans can gain knowledge about existential reality.
  • Physicalism: All of reality (existence) can be (eventually) reduced to physical cause and consequence, even if externally beyond our natural ability to sense and perceive, or internal beyond our ability to introspectively sense and perceive – even if there remains a difference between individual experience (Qualia) and the explanation of that experience using language. Because language consists of information compressed into general symbols that evoke information in the mind of the audience rather than the totality of information perceived by the author or the audience.
  • Naturalism: All cause and consequence in reality ( … )
  • Existence of External Reality: The universe and all within it exists independently of human perception, auto-association, imagination, prediction, thoughts, or linguistic constructs.
  • Empirical Accessibility: The belief that this external reality is accessible to us through sensory experience and empirical investigation using physical and logical instrumentation that reduces information imperceivable by our senses to analogy to experience that is testable by our senses.
  • Causality and Natural Laws: Natural laws govern the behavior of entities within reality, and that causal relationships can be discovered and understood through observation and reasoning.
  • Physicalist Ontology (to a large extent in naturalism and variably in realism): A tendency towards understanding reality in terms of physical entities and processes, with some forms of realism being more open to non-physical entities as long as they have an objective existence.

AND;

  • Symbolic Notation (-,+,=): A simplified representation of the process where recombination (symbolized by “+”) leads to new entities or systems that are equal to or greater than the sum of their parts (“=”). This underscores the idea that the merging of different elements or systems can result in new forms with added or enhanced functionalities.
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