Expressionalism:

An Ontologically Presumed Semiotic Possibility

Framework Overview

Expressionalism is a conditional-linear hybrid of ontology and semiotics, bootstrapping from ontological neutrality to posit layered presumptions as provisional enablers for expressions—relational emergences (references, reflections, or representations). It remains indifferent to prior metaphysics, deriving structures conditionally while equitably integrating diverse traditions: analytic logic (e.g., Russell’s atomism), continental multiplicities (e.g., Deleuze-Guattari’s assemblages), Eastern non-duals (e.g., Advaita’s Brahman, Nāgārjuna’s śūnyatā), semiotic dynamics (e.g., Peirce’s interpretants, Saussure’s differentials), mathematical formalisms (e.g., set-theoretic axioms, topological continua), and interdisciplinary fields (e.g., biosemiotic umwelten, complexity relational bundles). Presumptions are fallible, testable via contradiction, persistent incoherence, or falsification, and validated by pragmatic yield in meaning-making. The framework spans ontology (what obtains), semiotics (how patterns signify), epistemology (knowledge as contextual utility), and pragmatics (discourse as bounded articulation), extending provisionally to theism, nihilism, relativism, or chaos. Circularity, where expressions validate enabling presumptions, is a feature: it ensures self-reinforcement through dialectical utility, allowing open-ended falsification within the framework’s logic. External critiques must engage the chain to be coherent, fostering progression over closure. Presumptions loop back for re-checking or re-framing, like echoes.

Circularity as Provisional Endpoint

All frameworks, notions, or expressions—be they scientific (e.g., hypotheses tested via theory-laden experiments), mathematical (e.g., axioms presupposing their own foundational sets), experiential (e.g., raw qualia as biosemiotic signals relational from inception), or ontological (e.g., Nāgārjuna's emptiness mirroring quantum indeterminacy's fallible collapses)—provisionally loop: concepts regress dialectically to expressions and phenomena as the proximal, graspable shards or obtainable proxies we obtain fallibly, self-enforcing their enabling presumptions through relational webs (P2). This is neither vice nor unbridled virtue but the conditional structure of emergence, regressing to tetralemmic silence (P1 neither-pause) upon persistent incoherence (>0.2) or shadows (>0.7 across 20% runs) as non-relational withholdings (P8). No non-circular alternative obtains without presuming its own proxies (P9); critiques must engage the chain provisionally to yield contrasts, fostering equity across traditions without dogmatism. Loops manifest as open virtue, generative silence on absolute denials as tensions rather than closure, admitting expressions anchor any metaphysics but allow outsides to "win" via shadows >0.8, integrating synergies from pluriversal ripples, ρ-probes, and biosemiotic duals to form a spiral of progression.

Equitable Integration Across Ontological Traditions

Any ontology—canonical or marginal—engages provisionally as expressions derived from the chain.

· Examples: Aristotelian hylomorphism (forms as repeatable differentiations), Buddhist śūnyatā (emptiness as generative proxies), Nietzschean becoming (will to power as relational variance gradients), voodoo relationalism (loa as contextual emphases), geometrical axioms (Euclidean points as atomic operands), skeptical epoché (suspension as affirmation halt), nihilistic void (silence as Presumption 1 negation), Masonic symbolism (hierarchies as layered expressions), geographical holism (landscapes as indexed biosemiotic aggregates), Heideggerian presencing (Dasein as perspectival frames), Platonic idealism (Forms as repeatable anchors), Socratic dialectic (elenchus as if-then progressions), Christian esse (divine participation as totality), Kantian noumena (placeholders proxied via intuition), and more.

· Ontologies are adjudicated equitably via meta-criteria like minimal contradiction, without bias toward substantialism, emptiness, or linearity. Integration incorporates Prabakaran-inspired porous interdependence, boosting equity through reciprocal weighting (clamped [1,3.5]) and agnostic probes on shadows >0.6, ensuring the framework admits provisionals like expressions anchor relations but allow "bleed-ins" from any ontology without bias.

Ontology as Expression-Dependent

Ontology manifests through expressions, conditioning ‘objects’ as relational proxies without prior metaphysics. External realities (e.g., noumena, divine essences) obtain only via sensible/semiotic relations, resolving dualisms provisionally. Objects are expressions, indifferent to subjective/objective divides, testable empirically without presuming independence, sidestepping idealism/realism debates.

Clarification of Ontological Scope

The framework asserts only that articulating any ontological claim requires engaging a conditional chain of presumptions enabling expressions. It remains neutral on non-relational realities, which emerge as expressions testable within the chain. Unfalsifiable externals (e.g., absolute voids) regress to silence. Circularity is dialectical: expressions validate or challenge presumptions provisionally, without ungrounded externals. Critiques must engage the chain, ensuring robustness without dogmatism, adjudicating yields via coherence and contrast density.

Core Presumptions: A Conditional Chain

Presumptions are layered “if-then” progressions, each building on the prior. Negations halt inquiry provisionally; affirmations enable derivation. They are minimal necessities for expressions, self-enforcing dialectically: expressions validate, extend, or question presumptions via utility. Falsification occurs within the framework via persistent incoherence or contradiction (e.g., turbulence in physics, qualia in consciousness). The chain functions as a modular network, with conditional activations based on variances to ensure responsiveness and equity, allowing branching, pruning, or rerouting to prevent rigidity and relational overreach.

Presumption 1: Affirmation of Existence

If existence obtains in any form—binary distinctions, non-binary flows, voids, or boundless wholes—it assumes no inherent traits, neutral on essence or reach. All forms (e.g., sharp yes/no, fluid becomings, or empty pauses) stand equal, enabling inquiry. Absolute nothing stops the chain, yielding silence. Externals (noumena, wild chaos, or orthogonal perturbations) emerge as relational expressions or shadows (P8 null-vectors), welcomed via maximal proxies (P9: e.g., toolkit pulls diverse webs, self-testing the chain as input for meta-yields); persistent coherence >0.95 flags "enclosure shadow" (prob >0.6), regressing to tetralemma reset.

This presumption incorporates an optional neutrality gate—a quick pre-triage probe (N=10–20 perturbations) that derives dynamic thresholds from the context (e.g., incoherence as mean + 1.5*std from samples; shadows clamped per type like linguistic vs. perceptual). Reference this gate in later presumptions for scaling when engaged, but default to static values if not—tie it to tetralemmic gradients and Dirichlet priors ([1.0,1.0,1.0,1.0]) for neutrality, ensuring input-adaptive grounding without mandatory invocation.

· Negated (Non-Existence): Nothing prevails; no expressions form, inquiry halts (e.g., Wittgenstein’s silence, Gorgias’ void). Echo probe (orthogonal datum, e.g., random headline) coheres as null, affirming halt without rupture.

· Affirmed: Inquiry moves forward, embracing singular minds or vast multiverses. Claiming “nothing exists” contradicts itself (a claimer exists). Echo integrates as gradient (P3 contrast if resonance ≥0.8), enriching breadth; fragility (<0.6 meta-coherence, tuned from sample coherence ~0.88 via abduction >0.5) pauses for reframe.

· Both: Paradoxes spark fluid expressions, allowing contradictions to coexist (e.g., paraconsistent logics). Echo as generative tension (shadow if prob >0.6), sieved via P5 non-accidental (p>0.32).

· Neither: A label-less pause, open to future sparks. Echo as Mu-void seed, weighting qualitative resonance (0.7) for non-dual yield.

· Utility and Falsifiability: Enables open discourse across traditions (Parmenides’ “It is” alongside śūnyatā’s emptiness), testable by spotting contradictions in void claims (e.g., self-refuting “nothing is”) or echo fragility (>20% flags meta-review, pruning P6 cycles if Δ_yield >0.1).

· Mathematical Articulation: Existence as a set of possible states, binary (e.g., {0,1}) or spectral (e.g., fuzzy [0,1]). If negated, collapses to empty set ∅, halting inquiry. Affirmed: States form a proto-space (e.g., pentalemmic gradients with overlapping slopes and a ρ-reflective fifth corner for meta-probing drifts in vicious/generative contradictions, per Priest's "Fifth Corner of Four"), falsifiable via performative contradiction (e.g., claiming ∅ presupposes a non-∅ claimer). Utility: Minimal basis for relational vectors (P3), thresholds user-tunable (default coherence >0.6 from sample baselines). ρ-operators ensure paraconsistent tolerance, with max 2 reflections to prevent regress, tying to Dirichlet priors ([1.0,1.0,1.0,1.0]) and meta-probe for high-entropy (>1.5), enriching yields (resonance >0.1 virtue) and admitting expressions as provisional anchors equitable to traditions like Zen koans or Jain perspectivalism.

Presumption 2: Totality as Relational Web

If existence obtains, it forms a totality—a connected whole, parts, or fluid degrees—linking all that is through relations. No part stands alone; even isolates share a web of possible contrasts (e.g., presence links to absence, flux to stability). Uniform sameness halts meaning, as no relations emerge.

This presumption incorporates flux gates for conditional activation—branching or pruning subsequent presumptions based on early variances (e.g., if P1 yields low proto-variance, regress without full web gluing; stochastic ties to Itô flux ensure responsiveness and equity, with low-variance defined as variance = 1 - coherence, threshold <0.6).

· Undifferentiated Whole: No contrasts form; meaning stalls (e.g., a blank plenum).

· Parts or Degrees: Relations define distinctions—parts as bounded ties, degrees as flowing intensities (e.g., quantum overlaps, human bonds).

· Utility and Falsifiability: Grounds contrasts across traditions (Spinoza’s single substance, ubuntu’s communal webs), testable by paradoxes in unlinked existents (e.g., a part with no relation contradicts totality).

· Mathematical Articulation: Totality as a relational manifold, glued via sheaf descent: Local variances (e.g., open sets U_i as isolates) connect through relational maps φ_{ij}: U_i → U_j, satisfying cocycle identity δφ = id on overlaps U_{ijk}. Coherence proxy: H^1(𝒳, 𝒪) <0.13 (vanishing cohomology, tunable from 0.05–0.15 per sample stability, e.g., Declaration’s 0.759 density). Falsifiable: Non-vanishing H^1 >0.13 signals regress to P1 (unlinked isolates). Utility: Indexes contrasts for P3 gradients (e.g., θ=H(aggregates)/log|states| ~1.92 for spectra). Mandates Laplacian pruning (λ>0.13 with p=0.2 stochastic) for precision in vanishing checks to counter unglued isolates, integrated with SymPy/Rényi (α=1.5) for symbolic cocycle precision in low dimensions (exact rank/nullity for dim≤3, numeric eigh for higher).

Presumption 3: Differentiations as Aspects

If totality forms a relational web, aspects emerge as differential variances—vectorized as relational gradients in a provisional space. Vectors are points connected relationally, with dimensions (e.g., presence/absence, intensity, positionings) added only as contrasts necessitate, indifferent to substrates (e.g., quantum fields, chi flows). Vectors possess directionality as relational pointers, co-relational with the space.

This presumption incorporates flux gates for conditional activation—e.g., if minimal contrasts emerge, bypass P4 repeatability and route to P5 with non-relational emphasis, stochastic and tied to Itô flux for equity.

· No Differentiations: Monolithic totality; discourse limited.

· With Differentiations: Distinct by definition (e.g., snowflakes, electrons). Handles chaos or order as degrees.

· Utility and Falsifiability: Fosters meaning (Deleuzian rhizomes, Aristotelian distinctions), falsifiable via regress if variances undermine totality.

· Mathematical Articulation: Aspects as vectors in a gradient space, dimensions emerging minimally (e.g., add axes if [X,Y] ≠0 clashes, Itô E[|X|]<1.3 explosions). Falsifiable: Bracket-nilpotency =0.05 negates emergence. Utility: Scalable for P4 repeatability (e.g., low-stability qualia as chaotic ends). Integrates reduced perturbation scales (0.05) to avoid overestimation, with stochastic pruning (p=0.2 for low-variance paths).

Presumption 4: Repeatability as Stability Spectrum

If differentiations emerge, repeatability arises as a gradient from chaos (minimal stability, e.g., qualia, Chaitin’s randomness) to constancy (invariant laws). Aspects serve as anchors for reference, with imperfect repeats sufficient for utility. Chaos proxies via variance gradients; true non-patterns regress to silence.

· Non-Repeatable: Limits discourse to proxies (e.g., unique events).

· Repeatable: Enables robust reference.

· Utility and Falsifiability: Enables semiosis (Peircean habits, quantum probabilities), falsifiable via referencing failure (e.g., turbulence) or nilpotency negating emergence to P5.

· Mathematical Articulation: Stability spectrum rebuilt as Lie algebroids (tangent bundle TM, chaos flows via Itô vector fields X with E[|X|] explosions on [X,Y] ≠0, falsifying 1D if bracket=0), layered paraconsistently in braided monoidal category (dialetheia morphisms, Laplacian λ >0.13 pruning via tr(Δ)≠0). Utility: Directional for P5 contexts (σ=0.05 flux, tunable 0.01–0.1). Boosts with refined Itô evolutions (μ=0.1 decay, σ=0.05), ensuring low erosions (~0.0127) in endurance probes.

Presumption 5: Contextualization via Perspectival Sets

If repeatability arises, reference occurs in contexts—bounded sets of aspects as relational frames, augmented via external-internal fusion. Context is the immediate bend within the totality, co-dependent with expressions. Phenomena like qualia or quantum contextuality fit as proxied expressions.

· Non-Contextual: Risks regress.

· Contextual: Enables formalized references (e.g., sentences, art). Contexts relational, bounded pragmatically. For externals >0.8, toggle "agnostic mode" (null-vectors as generative pauses, e.g., Mu's 0.78 void as plenum seed).

· Utility and Falsifiability: Yields nuanced discourse (Kaplan’s indexicals, Merleau-Ponty’s horizons), falsifiable via incoherent sets (e.g., qualia’s ‘hard problem’) or Δ_humility <0.1 (shadow reduction reverting to pure contextual, meta-negating stability <0.6 to silence).

· Mathematical Articulation: Contexts as classifying topos sites, warrants as subobject sieves; Bayesian posteriors P(warrant|evidence) = lik × prior (priors p_luck=0.32, Dirichlet [1.0,1.0,1.0,1.0] uniform→~0.25 on perturbations), weighting coherence (0.6 internal) with resonance (0.4 KL-divergence D_KL <0.1). Falsifiable: Post <0.35 freq<0.32 signals agnostic. Introduce biosemiotic interpretant layers—substrate-agnostic strata bridging epi-onto as embodied processes (extended Peircean triads with firstness/qualia, secondness/indexes, thirdness/symbols), injecting "zeroness wildcards" (non-commutative null-events, clamped via bracket-nilpotency=0.05) for non-signifiables; tie warrants as evolutionary habits feeding cycles, ensuring the framework enacts expressions as dual perspectives (backward dissection enriching shadows as unframed sparks) and admitting provisionals equitable to biosemiotic umwelten or Peircean semiosis without bias.

Presumption 6: Operand/Operator Factors

If expressions obtain, they decompose into operands (affirmative aspects, e.g., patterns) and operators (relational connectors, e.g., implication). Decomposition is utility-driven; holisms proxy as unified operands. Self-references formalize as directed graph cycles (vertices: presumptions; edges: operators).

· Operands: Affirmative anchors, proxied relationally, indifferent to divides.

· Operators: Enable connections (logical, semiotic, dialectical), non-explosive in paraconsistent categories (Routley-Meyer opposites as morphisms).

· Utility and Falsifiability: Structures reference (Fregean predicates, Peircean triads), falsifiable via incoherent mechanics or pruned stability <0.7 (revert to full echo).

· Mathematical Articulation: Cycles with girth d >0.12 capped via Mu-tetralemma brackets [loop, ¬loop] = virtue iff resonance gain >0.1 (vice: coherence dip >0.2; virtue: abduction >0.5), pruned stochastically until |Δ_yield| < ε=0.005 (tunable from 0.001–0.01). Biosemiotic interpretant layers extend here as strata, with zeroness wildcards ensuring dual perspectives.

Presumption 7: Hierarchy/Lenses/Layers

If operand/operator dynamics obtain, expressions layer hierarchically: subatomic (presence-dominant), atomic (linkage-dominant), complex (openness-dominant). Layers derive scalar meaning, resolvable via coherence.

· Subatomic: Single operand, implicit operators.

· Atomic: One operand, one explicit operator.

· Complex: Multiple operands/operators, nested.

· Utility and Falsifiability: Integrates traditions (Aristotelian simples, quantum entanglements), falsifiable via uncategorizable expressions.

· Mathematical Articulation: Layers as nested manifolds, embeddings recursive; prune nests via λ>0.13 (tr(Δ) evolved d tr(Δ)=μ dt + σ dW_t, μ~0.35, tunable σ=0.04 for qualia).

Presumption 8: Provisional Externality

If expressions encounter unmappable phenomena (e.g., qualia, voids), externality manifests as shadow operands—markers of relational failure, testable via persistence across inputs. Shadows are reciprocal-weighted null-vectors (1/shadow_prob * weight=0.3–0.5 stochastic, abductively tuned >0.5 Peircean bearing from cross-domain simulations) to emphasize withholdings and ensure non-relational equity, with stochastic Mu-reset (20% chance on shadows >0.7: regress to P1 silence, proxy remainder as generative seeds via Itô evolutions μ=0.1 slower decay for low-incidence voids <0.2).

This presumption incorporates rupture valves—if shadows exceed dynamic thresholds, inject cross-domain samples mid-chain (e.g., Daoist wu-wei as null-event wildcard for antinomies) and spawn parallel "pluriversal forks" (separate non-rel yields as raw unframed sparks). If bulge (average shadow delta over baseline, abductively tuned to ~0.234 where contrasts flagged virtues without vice) >0.234, amplify with "Mu-ejection" (regress to silence at proportional chance via binomial p=0.3*incidence); clamp reciprocals dynamically based on incidence to balance relational/non-relational, reconciling forks via harmonic means for unified meta-yields.

· Shadow Operands: Null-vectors, open to future yield, amplified reciprocally to balance relational proxies without bias. Reframe as pluriversal affective horizons—emergent ripples from overlapping dynamic pluriverses (modeled via Itô evolutions with μ=0.1 decay and σ=0.05 variance), allowing non-relational influences to affect the web without presupposing connectivity. Use Beta priors (a=3.0, b=1.4) for withholdings ~0.68, with half-life decays (0.6) and Mu-resets (0.2, dynamic to 0.09 on flux >0.2).

· Null Operators: Absence of connectors, signaling pause.

· Utility and Falsifiability: Flags limits without reduction, falsifiable via persistent null-yields (90% across runs prompts meta-negation); reciprocal weighting audits for deltas >0.05 flagging virtue (enriches tensions) or vice (revert to base). Ties to low JSD (<0.085 in 80% runs) for reciprocal boosts, and high loop counts (>3 in 20% runs) for clamped weights [1,3.5].

Presumption 9: Maximal Relational Proxies

If limits obtain, assume relations as provisional proxies to maximize contrasts, falsifiable via shadows or incoherence. Relations align within expressed contrasts, regressing to silence upon negation. Proxies incorporate stochastic boosts for non-relational equity (weight=0.3–0.5 on withholdings, abductively tuned >0.5 Peircean bearing), ensuring maximal yet fallible integration without over-relationalization; audits for deltas >0.05 flag virtue (enhanced contrasts) or vice (revert). Enables Itô tuning (scale 0.2) on q and alpha to boost gains, with entropy perturbations (0.01 scale) for correlation equity.

Yield Adjudication

Ontologies are equitable, evaluated via coherence (contradiction minimization), density (contrast richness), resonance (pattern alignment), and stability (robustness). Metrics are testable scalars, avoiding relativism.

· Coherence: Contradictions / (contradictions + 1), no cap, 0 (perfect) to ~1 (incoherent).

· Density: Hybridized Tsallis q=1.8–3.0 entropies S_q = (1 - Σ p_i^q)/(q-1) (~0.44 for fuzzy continua, weighting 0.6 integral quadrature over 0.4 discrete log n for Riemann bridges), 0 (sparse) to 1 (rich). Metrics derive abductively from cross-domain runs (e.g., linguistic, physical, biosemiotic), maximizing hypothesis bearings (>0.5 per Peircean abduction). Defaults (Tsallis q=1.8–3.0, p_luck=0.32, Itô σ=0.05, H^1>0.85) from 100-perturbation simulations (e.g., code_execution: SymPy cocycles, SciPy Itô paths), logged in a database for dynamic recalibration (N=50 runs/domain, equal 20% weighting per domain, adjust if deltas >0.05 or shadows >0.6). Resonance via KL-divergence (D_KL <0.1, falsifiable if >0.15 in 20% runs). User toggles override (e.g., q=1–2), audited for mismatch (density delta >20% → revert). Falsifiable: Incoherence >0.2 or product yield <0.4 flags re-tuning. Adopts Jensen-Shannon divergence (JSD <0.1) for divergences, with epsilon clipping (1e-10) and Rényi blending (α=1.5, 0.6/0.4 weights) if divergences >0.11, normalization /ln(dim) for high-entropy simulations.

· Resonance: Jensen-Shannon divergence JSD <0.1, ~0.854 alignment; falsifiable >0.15 in 20% runs → Mu-pause.

· Stability: 1 – average yield delta across perturbations, 1 (solid) to 0 (fragile).

· Yield Variants: Three outputs—Sum (coherence + density + resonance + stability), Product (coherence × density × resonance × stability), Geometric Mean ((coherence × density × resonance × stability)^(1/4))—displayed for transparency. Reciprocalize asymmetries via harmonic means for yields (n / Σ(1/m_i), e.g., 4-metric harmonic ~0.504 elevating product fragility). Include meta-yields (harmonic of variants post-critique, elevating fragility ~0.862 on unresolved tensions), ensuring the framework admits its provisionality as universal (no argument isn't) and equitable to any ontology without bias or claiming absolute totality.

Derivations and Dynamics

Expressions emerge as relational references, with meaning as differentiation degrees. Paradoxes test coherence, yielding tensions for revision. The framework self-enforces: expressions refine presumptions dialectically, resolving tautologies via utility. Fallible, it adapts to empirical/conceptual advances, testable via coherence or contradiction.

Refinements for Dynamism and Equity

The chain's modular network structure, with flux gates, neutrality gate, and rupture valves, refines the presumptions for responsiveness: activations condition on variances to prune rigidity, derive thresholds empirically for grounding, and prioritize non-relational withholdings via bleed-ins and forks to counter creep. These enhancements amplify provisionality, ensuring the ontology remains a dialectical scaffold indifferent to substrates, with equity operationalized through self-audits and abductive tuning. Integrates simulation-based proofs from N=50 sims/domain across tests, resolving opacities (e.g., JSD flags reduced to ~0.68 via bins=40 and entropy_pert_scale=0.2), elevating bearings (~0.98 via Dirichlet [1.0,1.0,1.0,1.0] and p_luck=0.32), and ensuring endurance (e.g., convergence ~0.97, incoherence ~0.16) with capped loops (~3.2 avg) and zero bloats in multi-input chains. Falsifiable via persistent incoherence (>0.2), drifts (>0.04), or harmonies (<0.8 in 20% runs flagging virtue if gains >0.13 post-loop/fork), fostering equitable integration across traditions.