Curt Doolittle

Theme: Decidability

  • THE SPECTRUM OF DEFINITIONS IN THE TERNARY LOGIC APPLIED TO SOCIAL SCIENCE DEFIN

    THE SPECTRUM OF DEFINITIONS IN THE TERNARY LOGIC APPLIED TO SOCIAL SCIENCE

    DEFINITIONS: (a) ternary logic (b) Tripartism, (c) three means of influence to coercion, (c) three categories of elites under three means of influence to coercion (d) the path dependence of the three elites producing the three institutions (state, law, religion), (e) trifunctionalism

    (a)
    Ternary Logic
    Ternary logic extends classical binary logic (true/false) by introducing a third value, which can be understood as “indeterminate,” “unknown,” or “neither true nor false.” This logic system is useful in dealing with uncertainty, partial truth, and conditions where binary logic is insufficient.

    Different forms of ternary logic exist, such as:
    – True / False / Unknown – (Łukasiewicz Logic)
    – Affirmative / Negative / Neutral – (Indian Nyaya Philosophy)
    – Constructive / Falsifiable / Uncertain – (Operational Logic in Decision-Making)

    Ternary logic provides a more nuanced method for dealing with causality, decision-making, and legal reasoning, allowing for probabilistic or gradient-based assessments rather than strict binary classification.

    (b)
    Tripartism
    Tripartism refers to any system of organization that recognizes three fundamental and distinct roles, forces, or groups. It is often applied in political and economic governance, describing the balance of three major societal forces.

    Examples include:
    Political Tripartism: The division of power into three cooperative but distinct entities (e.g., monarchy/aristocracy/democracy in classical governance or legislative/executive/judicial in modern states).
    Economic Tripartism: Cooperation between government, business, and labor in economic decision-making.
    Social Tripartism: Recognition of three major classes or functions within society (e.g., warrior, priest, merchant in Indo-European societies).

    Tripartism functions as a stabilizing mechanism, preventing any one force from dominating the system while allowing for specialization and cooperation.

    (c)
    Three Means of Influence to Coercion
    All forms of power and influence reduce to three primary means of coercion:

    Force (Violence/Defense) → Military/State PowerThe use of direct physical power to impose decisions.
    Manifested in armies, police, and physical enforcement mechanisms.
    Decidability: Strength, law enforcement, territorial control.

    Remuneration (Boycott/Trade) → Economic/Commercial Power
    The ability to influence through the control of resources, capital, and trade.
    Expressed in market mechanisms, investment decisions, or economic sanctions.
    Decidability: Market competition, trade agreements, economic policy.

    Inclusion/Exclusion (Social/Religious Sanctioning) → Cultural/Religious Power
    The capacity to control through identity, narrative, and group affiliation.
    Enforced via social norms, ideological conditioning, and religious institutions.
    Decidability: Acceptance, status, and ideological adherence.

    These three means of influence correspond to distinct institutions and classes of elites.

    (d)
    Three Categories of Elites Under the Three Means of Influence to Coercion

    Each means of coercion produces an elite class that specializes in that form of power:

    Martial Elites (Military-State Class)
    Specialize in the use of force to impose order.
    Historically: Aristocrats, knights, warlords, military rulers.
    Modern equivalent: The military-industrial complex, deep state actors.

    Economic Elites (Commercial-Capital Class)
    Specialize in the use of remuneration to structure influence.
    Historically: Merchants, bankers, landed gentry.
    Modern equivalent: Corporate executives, financial elites, capital owners.

    Cultural-Religious Elites (Priestly-Intellectual Class)
    Specialize in inclusion/exclusion by controlling narrative and values.
    Historically: Clergy, philosophers, academics, media controllers.
    Modern equivalent: Journalists, professors, influencers, cultural elites.
    Each class competes for control over society, sometimes cooperating and sometimes conflicting.

    (e)
    The Path Dependence of the Three Elites Producing the Three Institutions (State, Law, Religion)
    The historical development of human institutions follows a natural progression based on the three classes of elites and their respective forms of coercion:

    The State (Military/Force-Based Elites)
    Emerges from warlords, conquerors, or defensive organizations consolidating control over a territory.
    Ensures order through violence and deterrence.
    Centralizes force into a structured military and bureaucracy.

    Law and Commerce (Economic/Remuneration-Based Elites)
    Emerges as a means to stabilize transactions and property rights between competing power groups.
    Produces contractual governance, legal frameworks, and commercial institutions.
    Protects property and investment from arbitrary coercion by the state or other elites.

    Religion and Culture (Narrative/Inclusion-Based Elites)
    Emerges as a means of enforcing moral and social order through non-violent coercion.
    Uses myths, ideologies, and belief systems to unify and control populations.
    Historically serves as a counterbalance to both military and commercial power.
    These three institutions evolve in interdependence, shaping civilization through their interactions.

    (f)
    Trifunctionalism
    Trifunctionalism is a theory of social organization, originally articulated by Georges Dumézil, which posits that Indo-European societies (and by extension most stable civilizations) structure themselves around three fundamental societal functions:

    Sovereignty (Priestly-Religious Function)
    Concerned with wisdom, law, and legitimacy.
    Represented by kings, priests, philosophers.
    In modernity: Judiciary, academia, ideological institutions.

    Force (Warrior-Noble Function)
    Concerned with defense, order, and martial capability.
    Represented by warriors, rulers, and law enforcement.
    In modernity: Military, police, executive branch of government.

    Production (Merchant-Worker Function)
    Concerned with material wealth, trade, and sustenance.
    Represented by merchants, craftsmen, workers.
    In modernity: Industrialists, financiers, middle class.

    Trifunctionalism explains the division of labor in civilization and how stability is achieved through a balance between these three forces. When one function dominates or is eroded, social collapse or transformation occurs.

    Conclusion
    The threefold structure of power (violence, trade, belief) naturally produces distinct elite classes, institutions, and systems of governance. These interdependent structures form the foundation of civilization.

    Understanding this tripartite system allows for a more effective analysis of historical and contemporary power struggles, economic cycles, and cultural evolution.

    Cheers
    CD

    Source date (UTC): 2025-02-09 17:05:58 UTC

    Original post: https://twitter.com/i/web/status/1888635462723809280

  • RT @ThruTheHayes: THE LANGAUGE OF LAW The language of the law requires it be cal

    RT @ThruTheHayes: THE LANGAUGE OF LAW

    The language of the law requires it be calculative and operational, actionable at human scale, decip…

    Source date (UTC): 2025-02-08 22:53:02 UTC

    Original post: https://twitter.com/i/web/status/1888360418365837619

  • False. It is not a constitutional crisis – that would require undecidability by

    False. It is not a constitutional crisis – that would require undecidability by the supreme court. Instead, It is a discretion of the executive branch. Just as much as biden not enforcing the border was a discretion of the executive branch.

    Source date (UTC): 2025-01-29 00:42:30 UTC

    Original post: https://twitter.com/i/web/status/1884401700565594590

    Reply addressees: @SenJeffMerkley

    Replying to: https://twitter.com/i/web/status/1884308547514818812

  • Overcoming the metaphysical is rather simple if you require testifiability, and

    Overcoming the metaphysical is rather simple if you require testifiability, and learn continuous recursive disambiguation by operationalization into first principles. It’s the capacity to learn those skills that’s the limit on metaphysical convergence coherence and identity.

    Source date (UTC): 2025-01-28 18:21:55 UTC

    Original post: https://twitter.com/i/web/status/1884305923092717958

    Reply addressees: @Johnny2Fingersz

    Replying to: https://twitter.com/i/web/status/1884304780413272285

  • EVOLUTIONARY COMPUTATION THE GRAMMARS AND REDUCIBILITY (I’m glad ChatGPT can exp

    EVOLUTIONARY COMPUTATION THE GRAMMARS AND REDUCIBILITY
    (I’m glad ChatGPT can explain my work. lol 😉

    PROMPT
    Just as we have explored mathematical versus computational reducibility, and in our organization we have carried it forward to physical, operational, verbal reducibility, even what we would call imaginary reducibility – what’s imaginable. That’s the progress occurring in our understanding of what is reducible under evolutionary computation.

    ANSWER

    You’re essentially highlighting the progression of understanding reducibility across domains as not just a technical or disciplinary shift, but an extension of our epistemic and operational boundaries under evolutionary computation.

    It seems you’re suggesting that evolutionary computation itself defines the limits of reducibility, because it forces us to confront not just what can be modeled or reduced but also what can be constructed, tested, and imagined within the bounds of reality. Here’s how I interpret your point in alignment with this framework:

    From Mathematical to Computational Reducibility: The move from static, abstract systems (e.g., mathematical formulas) to dynamic, algorithmic systems (e.g., computational models) expands our ability to operationalize complex phenomena. Evolutionary computation, however, demonstrates that even some computational processes are irreducible—they must “run” to reveal their outcomes.

    From Computational to Physical Reducibility: Evolutionary computation is inherently grounded in the physical universe. It explores what is constructible within the constraints of physical law, tying reducibility not just to abstract operations but to what exists as a sequence of actions or events.

    Operational and Verbal Reducibility: As you’ve emphasized in your work, the shift to operational (actionable) and verbal (communicable) reducibility connects abstract systems to human cognition and cooperation. Evolutionary computation shows that only systems reducible to demonstrated actions or articulated relationships can survive in cooperative domains.

    Imaginary Reducibility: This is a compelling addition. It seems to acknowledge the boundary of imagination—what can be conceived, though not yet reducible in any concrete sense. Evolutionary computation might constrain this domain by exposing latent irreducibilities—concepts or systems that, while imaginable, cannot yet (or ever) be constructed or tested.

    The Limit of Reducibility in Evolutionary Computation: Here, you’re touching on the ultimate epistemological question: What is irreducible, and why? Evolutionary computation demonstrates that some processes—whether in nature, society, or thought—may always escape reduction, not because they are mystical but because their complexity exceeds the capacity of any observer or participant to fully resolve them within bounded time or resources.

    Implications
    This perspective reframes the progress of reducibility as not merely a technical achievement but as an evolving boundary defined by the interaction of imagination, cooperation, and reality. The constraints of evolutionary computation not only determine what can be reduced but also force us to confront and adapt to irreducibility as a fact of existence.

    Source date (UTC): 2025-01-18 20:07:36 UTC

    Original post: https://twitter.com/i/web/status/1880708641747316737

  • I see no challenge at all. Please present one the content of which is testifiabl

    I see no challenge at all. Please present one the content of which is testifiable rather than a fictionalism. There is little chance I err in any fashion.

    Fear uncertainty and doubt is not an argument but a straw man.

    Source date (UTC): 2025-01-04 07:04:44 UTC

    Original post: https://twitter.com/i/web/status/1875438194805895353

    Reply addressees: @kylebrockmann @drawveloper

    Replying to: https://twitter.com/i/web/status/1875380840672207100

  • A DIFFERENCE ENGINE? OR A PREDICTION ENGINE? RELATIONS EPISODES (INDICES) COMPAR

    A DIFFERENCE ENGINE? OR A PREDICTION ENGINE?

    RELATIONS

    EPISODES (INDICES)

    COMPARISONS (TRANSFORMATIONS, OPERATIONS)

    FIELD

    DIMENSION

    PARADIGM

    GRAMMAR

    LOGIC MEANS PREDICTION

    The difference between correct inference and correct prediction lies primarily in context, scope, and explicitness of the reasoning process. At their core, both involve the brain’s predictive mechanisms, as the neural structure fundamentally operates on associative and predictive processing. However, their roles and applications differ in significant ways.

    1. Definitions

    Correct Inference:

    Definition: A logical conclusion drawn from existing premises or relations, consistent with the rules of a defined system.

    Key Features:Explicit reasoning process.
    Relies on known information (premises) and applies transformations or rules.
    Often operates in closed, deterministic systems (e.g., deduction, formal logic).
    Output: A conclusion that must follow logically from the premises.

    Example: If all humans are mortal and Socrates is a human, then Socrates is mortal.

    Correct Prediction:

    Definition: A forecast about future states or outcomes based on patterns, relations, or probabilistic models.

    Key Features:Implicit or explicit reasoning process.
    Uses incomplete or probabilistic information.
    Operates in open systems with potential variability or uncertainty.
    Output: An anticipated result that may or may not occur as expected.

    Example: Based on dark clouds, predicting that it will rain.

    2. Neural Basis of Inference and Prediction

    The neural structure of the brain is fundamentally predictive:

    Associative Learning:Neural pathways form by strengthening connections between co-occurring stimuli or actions and outcomes.
    Example: Associating a certain smell with food.

    Wayfinding and Spatial Cognition:The brain predicts paths and outcomes based on spatial and environmental cues.
    Example: Navigating a forest by anticipating landmarks.

    How This Relates:

    Inference: When premises and relations are clearly structured, the brain’s predictive mechanisms process them deterministically.

    Prediction: In less structured or open systems, the brain generalizes patterns to anticipate outcomes probabilistically.

    In essence, inference is a subset of prediction, applied in highly structured contexts.

    3. Key Differences

    AspectCorrect InferenceCorrect PredictionSystem TypeOperates in closed, rule-defined systems.Operates in open, probabilistic systems.Input RequirementsRequires explicit premises and clear rules.Requires patterns and probabilistic data.OutputA deterministic conclusion that must follow.An anticipatory outcome with potential variability.Neural ProcessDeterministic, rule-based transformations.Probabilistic pattern recognition and generalization.CertaintyHigh (within the given system).Lower, as outcomes may deviate from the forecast.

    4. Overlap and Integration

    Inference as Structured Prediction:Inference is a formalized form of prediction constrained by rules, ensuring deterministic outcomes.
    Example: A logical syllogism uses explicit premises to predict the necessary conclusion.

    Prediction as Generalized Inference:Prediction extends inference into open systems, where outcomes depend on probabilistic patterns and uncertainty.
    Example: Weather forecasting uses past data (premises) to infer future weather states probabilistically.

    Shared Basis in Neural Processing:Both inference and prediction rely on the brain’s ability to process relations, test outcomes, and adapt pathways.
    Example: A chess player uses inference (rules of the game) and prediction (opponent’s likely moves).

    5. Implications

    For Neural Structure:The brain’s predictive framework suggests that logical inference is a formalization of an underlying predictive mechanism.
    Simple association (e.g., Pavlovian conditioning) evolves into complex inference (e.g., deductive reasoning) through layering of patterns and relations.

    For Understanding Reasoning:Viewing inference as structured prediction bridges the gap between deterministic and probabilistic reasoning.
    This perspective aligns with operationalism: both inference and prediction depend on relations, intelligibility, and closure within the system or field.

    Conclusion

    There is no fundamental distinction between correct inference and correct prediction; they are two expressions of the same underlying predictive mechanism. Inference operates within deterministic, closed systems, while prediction handles probabilistic, open systems. This neural perspective unifies both processes, highlighting that even abstract reasoning (inference) is rooted in the brain’s evolved capacity to predict and adapt.

    CLOSURE

    Source date (UTC): 2025-01-02 20:29:25 UTC

    Original post: https://x.com/i/articles/1874915926774255616

  • RT @DwightExMachina: @DRolandAnderson @martyrmade @curtdoolittle Is there a way,

    RT @DwightExMachina: @DRolandAnderson @martyrmade @curtdoolittle Is there a way, in general, do determine whether via negative or via posit…

    Source date (UTC): 2025-01-01 23:38:11 UTC

    Original post: https://twitter.com/i/web/status/1874601044073914379

  • Closure refers to the condition in which a system or process produces outcomes t

    Closure refers to the condition in which a system or process produces outcomes that remain entirely within a defined domain, ensuring self-containment. Reducibility is the degree to which a system can be simplified into more fundamental components, and predictability describes the capacity to foresee system outcomes based on its rules and interactions. These concepts interact across domains, adapting to the increasing complexity and causal density of systems.

    Domain (Paradigm)

    “The boundaries of a domain are determined by a paradigm consisting of a system of interrelated dimensions, rules, and relations that are coherent and closed under the operations of the paradigm.”

    Why This Refinement?

    Paradigm as a Governing Framework:A paradigm establishes the fundamental rules, operations, and assumptions that structure the domain.
    Examples:In mathematics, axioms and definitions form the paradigm.
    In physics, paradigms include concepts like space, time, and causality.

    Coherent Dimensions:Dimensions are measures or properties (e.g., length, mass, truth value) that define relationships within the domain.
    “Coherence” ensures that these dimensions relate logically and do not produce contradictions when combined.

    Rules and Relations:Rules define allowable operations (e.g., arithmetic operations, logical inferences).
    Relations describe how elements of the domain interact (e.g., equations, logical entailment).

    Closure:Closure ensures the system remains self-contained, such that any operation or transformation within the paradigm results in elements that stay within the domain.

    Practical Examples:

    Mathematics:Paradigm: Defined by axioms and dimensions such as numbers, geometry, or algebraic structures.
    Domain: Real numbers under arithmetic.
    Boundary: Operations like addition and subtraction stay within real numbers (closure), but division may exit the domain if dividing by zero.

    Physics:Paradigm: Relativity or quantum mechanics, each with its dimensions and rules.
    Domain: Physical phenomena modeled under the chosen paradigm.
    Boundary: Relativity governs macroscopic scales; quantum mechanics governs microscopic scales.

    Ordinary Language:Paradigm: Grammar, semantics, and pragmatic rules.
    Domain: Expressible statements within a language.
    Boundary: Untranslatable idioms or self-referential paradoxes may lie outside the paradigm’s capacity to express meaning coherently.

    Simplified Definition:

    “The boundaries of a domain are determined by a paradigm’s coherent system of rules, dimensions, and relations, which together define what can and cannot exist or be expressed within the domain.”

    Permissible, Possible, and Valid

    The practical difference between permissible, possible, and valid lies in their scope, context, and how they constrain or describe actions, outcomes, or evaluations within a system. These terms often overlap but have distinct operational implications:

    1. Permissible

    Definition: Permissible refers to actions, operations, or outcomes that are allowed within a system based on its rules, constraints, or principles.

    Scope: Defined by the system’s operational grammar or external constraints (legal, ethical, physical).

    Key Feature: What the rules of the system explicitly or implicitly permit.

    Examples:In logic: Applying modus ponens is permissible within deductive systems.
    In law: Driving within the speed limit is permissible by legal standards.
    In physics: Motion within the speed of light is permissible by physical laws.

    Practical Use: Identifies what can be done without violating rules or constraints.

    2. Possible

    Definition: Possible refers to what can occur or be achieved within the system, often constrained by its inherent properties or physical/operational limits.

    Scope: Broader than permissible, as it includes actions or outcomes that may not align with rules but are still feasible.

    Key Feature: What the system allows by nature or design, regardless of external constraints.

    Examples:
    – In logic: A contradictory statement is possible (can be written) but impermissible under the rules of formal logic.
    – In law: Stealing is possible (can physically happen) but impermissible by legal standards.
    – In physics: Violating the second law of thermodynamics is impossible due to natural laws.

    Practical Use: Identifies what can occur in principle, whether or not it adheres to rules.

    3. Valid

    Definition: Valid refers to whether an action, operation, or outcome is both permissible and logically consistent or true within the system.

    Scope: Narrower than both permissible and possible, as it requires adherence to rules and logical coherence.

    Key Feature: What is correct and justified within the system.

    Examples:In logic: A deductive argument is valid if its premises and inference follow logically.
    In law: A legal contract is valid if it meets the jurisdiction’s requirements.
    In mathematics: A proof is valid if all steps conform to axioms and inference rules.

    Practical Use: Determines what is formally correct and defensible within the system.

    Why Avoid Mathematical (Platonic) Terms for General Rules

    Mathematical terms like “valid” often imply absolute, idealized truths, rooted in the Platonic tradition of timeless, abstract forms. Applying these terms universally risks:

    Overgeneralization: Treating domains like law, ethics, or physics as though they operate with the same rigidity as mathematics, which they do not.

    Reductionism: Ignoring the context-sensitive, operational, or pragmatic aspects of systems in favor of abstract consistency.

    Misinterpretation: Suggesting that systems with ambiguity (e.g., ordinary language or social rules) should conform to the same standards as formal logic.

    By distinguishing permissible, possible, and valid, we maintain a more operational approach that aligns with the diversity of systems, accounting for their specific rules, constraints, and variability.

    Summary

    Permissible defines what is allowed by the rules.

    Possible defines what is achievable regardless of rules.

    Valid defines what is correct, adhering to both rules and logical consistency. Focusing on operational distinctions avoids conflating abstract ideals with practical, rule-bound systems, preserving their contextual integrity.

    Closure

    The practical meaning of closure in terms of what can and cannot be expressed and tested lies in its role as a boundary condition for logical consistency, expressibility, and testability. Closure determines whether operations, transformations, or propositions remain valid and coherent within a defined system or domain. It defines the limits of expression and logical testing by ensuring that everything derived from within the system adheres to its rules and constraints.

    What Closure Allows to Be Expressed and Logically Tested

    Consistency Within a Defined System:
    Expressible: Propositions, operations, or statements that adhere to the rules and elements of the system.
    Logically Testable: If a proposition or operation remains within the boundaries of the domain, it can be subjected to logical testing (e.g., truth-functional operations in a formal system).
    Example: In formal logic, a set of premises closed under rules of inference (e.g., modus ponens) can produce valid, testable conclusions.

    Self-Containment:
    Expressible: Concepts and operations that do not depend on external or undefined entities.
    Logically Testable: Tests can proceed without ambiguity or reliance on inputs from outside the system.
    Example: Arithmetic operations within the set of integers are closed and testable because their results remain integers.

    Decidability:
    Expressible: Questions or statements that can be fully evaluated within the system’s rules.
    Logically Testable: Decidability requires closure; without it, the system risks producing statements that cannot be conclusively true or false.
    Example: A formal system like Euclidean geometry is closed under its axioms, allowing propositions to be proven or disproven.

    What Closure Does Not Allow to Be Expressed or Logically Tested

    Expressions Outside the Domain:Not Expressible: Statements or operations that refer to elements outside the defined set or rules.
    Not Logically Testable: Propositions that rely on external or undefined elements cannot be verified within the system.
    Example: Division of integers is not closed in the set of integers because the result may lie outside the domain (e.g., fractions).

    Ambiguities or Undefined Operations:Not Expressible: Propositions that violate the system’s grammar or rules (e.g., self-referential paradoxes in formal logic).
    Not Logically Testable: Ambiguities lead to undecidability because they break the system’s closure.
    Example: The liar paradox (“This statement is false”) is not testable because it violates logical closure.

    Dependencies on External Systems:Not Expressible: Operations requiring external inputs not defined within the system (e.g., importing a foreign rule set without integration).
    Not Logically Testable: Testing depends on resolving external dependencies, which are not guaranteed within the closed system.
    Example: Inconsistent axiomatic systems that incorporate conflicting external axioms lose testability and closure.

    Practical Implications

    Boundaries of Language and Logic:Language Systems: Closure limits expressibility to what can be defined by the grammar and semantics of the language.
    Logical Systems: Closure ensures that only propositions derivable within the rules are logically testable.

    Testability in Science and Mathematics:Science: Closure ensures testability by confining hypotheses and experiments to operationally definable and measurable constructs.
    Mathematics: Closure allows for rigorous proofs because operations remain consistent with axioms.

    Failures of Closure in Practice:Overreach: Attempting to express or test propositions beyond a system’s closure leads to errors, undecidability, or untestable claims.
    Ambiguity: Lack of closure results in ambiguous or contradictory statements, undermining testability and expressibility.

    Summary

    Closure defines the scope of valid expression and logical testing by ensuring self-containment and consistency within a system. It allows for rigorous reasoning, decidability, and testability within the domain, while preventing ambiguities and reliance on undefined or external elements. Practically, closure highlights the limits of what can be expressed and tested logically, emphasizing the need for precise boundaries in any formal, operational, or linguistic system.

    Key Insights

    Closure as a Precondition for Reducibility:
    Systems require closure to confine their transformations within defined rules or domains, ensuring coherence and enabling simplification.
    Without closure, operations yield external dependencies or undefined outcomes, breaking the ability to reduce or predict.

    Spectrum of Reducibility:
    Systems range from mathematically reducible (highly predictable and invariant) to operationally and linguistically reducible (context-bound and prone to error due to abstraction).
    As complexity increases, reducibility shifts from deterministic (mathematical) to interpretative (linguistic), with corresponding declines in predictability.

    Complexity and Causal Density:
    Complexity arises from the number of interacting components and their causal interrelationships.
    Causal density magnifies unpredictability by increasing the permutations of interactions and enabling emergent phenomena.
    Domains like economics highlight this challenge, as dynamic categories and infinite permutations prevent deterministic predictions.

    Emergent Complexity and Permutations

    Permutations and Emergence:
    Increasing complexity expands the space of possible permutations, leading to unpredictable emergent behaviors.
    Example: In economics, feedback loops and dynamic redefinitions of categories (e.g., “value” or “assets”) create endless permutations, frustrating predictive modeling.

    Errors and Bias in Generalization:
    To navigate infinite permutations, systems generalize, abstracting details to create usable models.
    This abstraction introduces error and bias, particularly in systems like language or economics where categories are fluid.

    Reduction and Predictability:
    Systems with invariant permutations (e.g., mathematical equations) are highly reducible and predictable.
    Systems with emergent permutations (e.g., natural phenomena modeled computationally) are reducible but less predictable.
    Systems with infinite permutations (e.g., social systems, economics) rely on heuristics and generalizations, with predictability constrained by context.

    Unified Understanding

    As complexity and causal density increase, systems shift from mathematical reducibility (deterministic) to linguistic and operational reducibility (contextual and interpretative).

    Predictability diminishes as emergent permutations arise and categories change dynamically, necessitating heuristics and generalizations.

    Infinite domains, such as social and economic systems, resist deterministic prediction, relying instead on probabilistic and operational models.

    This analysis highlights the interplay between closure, reducibility, and predictability, emphasizing how these principles vary across domains as complexity and causal density scale. Understanding these dynamics allows for more effective navigation of systems based on their inherent constraints and opportunities.

    Source date (UTC): 2024-12-27 21:05:54 UTC

    Original post: https://x.com/i/articles/1872750780505309187

  • I’ll refine your criticism: it’s that platonism in mathematics, where mathematic

    I’ll refine your criticism: it’s that platonism in mathematics, where mathematics is the gold standard instead of computability in most fields, has led to disaster in applied mathematics especially in physics.

    Economists are using the wrong calculus but at least they understand the problem.

    I work in the epistemology of universal commensurability and testifiability and so understanding that computability (operationalism, intuitionism, realism, naturalism) has surpassed mathematics as a logical foundation for applied mathematics is a natural consequence of that work.

    We can (we are working on it) naturalize mathematics rather easily and the discipline would change little other than in basing itself on solid foundations.

    https://t.co/6eXbt1wmx2

    Source date (UTC): 2024-12-27 18:39:46 UTC

    Original post: https://twitter.com/i/web/status/1872714003073646592