Scientific Representation

Syntactic approaches in the philosophy of science, which are based on formalizations in predicate logic, are often considered in principle inferior to semantic approaches, which are based on formalizations with the help of structures. To compare the two kinds of approach, I identify some ambiguities in common semantic accounts and explicate the concept of a structure in a way that avoids hidden references to a specific vocabulary. From there, I argue that contrary to common opinion (i) unintended models do not (...) pose a significant problem for syntactic approaches to scientific theories, (ii) syntactic approaches can be at least as language-independent as semantic ones, and (iii) in syntactic approaches, scientific theories can be as well connected to the world as in semantic ones. Based on these results, I argue that syntactic and semantic approaches fare equally well when it comes to (iv) ease of application, (v) accommodating the use of models in the sciences, and (vi) capturing the theory-observation relation. (shrink)

Planck's constant h and Boltzmann's constant kB conventionally connect spectral frequency to energy and energy to temperature. Recent analysis of blackbody spectral relations in the frequency domain revealed an unexpected result. Unlike conventional physical constants, which typically appear in the slopes of individual relations as local scaling factors, the ratio h/kB does not appear in any individual relation. Instead, different relations between spectral observables and temperature fail to close, and h/kB emerges as the intercept residual of that non-closure. This suggests (...) that h/kB acts as a global consistency factor required to reconcile the different mappings. This observation raises a deeper question. If h/kB appears neither in the spectral observables nor in temperature itself, but only in the mapping between them, is it describing the empirical structure being observed, or the mapping used to represent it? More generally, are physical constants merely scaling factors between equivalent domains of description, or do they connect fundamentally different domains? We explore this question by distinguishing between an empirical domain of directly measurable spectral quantities such as frequency, phase, and linewidth, and a representational domain of abstract constructs used to represent those observations, including temperature, energy, entropy, and spatial parametrizations. Within this framework, physical constants are interpreted as quantities introduced to achieve internal consistency among different representations of the same empirical structure. We develop this perspective through the concept of Domain Projection and discuss its implications for the interpretation of physical constants, physical laws, and the foundations of scientific description. (shrink)

Modern science relies on representational models that organize empirical observations through constructs such as electrons, energy levels, spacetime, wavefunction and causal mechanisms. While these models achieved extraordinary predictive success, they also led to an implicit inversion in which these unobservable theoretical constructs are treated as explanatory ground and observable spectral regularities as derivative. Recent large-scale analyses of atomic spectra reveal that diverse physical measurements exhibit unexpectedly low-dimensional and relational organization recoverable directly through frequency-domain relations, without introducing hidden entities or theoretical (...) assumptions. These results show that classification, compression, generalization, and prediction emerge naturally from intrinsic spectral structure prior to representational interpretation. The paper argues that representation reorganizes empirical structure rather than generates it and becomes methodologically secondary once observable relations exhibit predictive closure. The persistent demand for additional mechanistic explanation arises not from deficiencies in empirical structure, but from the expectation that physical understanding must ultimately be translated into narratives of localized objects, linear causality, and particle interactions. Once representational constructs acquire explanatory authority beyond their empirical origin, they tend to stabilize and reify, expanding the theoretical apparatus to accommodate inconsistencies. This motivates the concept of representational debt, whereby additional abstract layers accumulate beyond empirical necessity, increasing descriptive complexity and delaying the discovery of simpler organizing principles. More broadly, the analysis motivates Foundational Science, a discipline concerned not with ontological entities or local causal mechanisms, but with invariant relations, scaling laws, and structural constraints. The Spectral Framework is presented as an empirical realization of this methodological perspective, illustrating how scientific explanation may be re-grounded in simple organizational principles already present in measurements. (shrink)

This article critically evaluates Itzhak Gilboa, Andrew Postlewaite, Larry Samuelson, and David Schmeidler’s account of economic models. First, it gives a selective overview of their argument, highlighting its emphasis on similarity and their oversight of the role of idealizations in economics. Second, it proposes a sketch of an account of models as arguments and argumentative devices. This account not only sheds light on Gilboa et al.’s approach, including its shortcomings, but also identifies key challenges in model-based inference, suggesting a fresh (...) perspective on the uses of models in economics for diverse objectives. (shrink)

Quantum mechanics contains a single category error: it treats mechanical registration as if it were Observer‑level recognition. A detector click, pointer position, or classical record is a trace (T), not an outcome. The definite outcome arises only when a meaning‑bearing Observer performs the recognition step (Jo) and commits to a specific interpretation (C). Because QM models the physical evolution of systems and the production of traces but does not model recognition and commitment, it collapses two distinct steps into one and (...) generates the measurement problem, Schrödinger‑type paradoxes, Wigner’s Friend, decoherence confusion, and the entire interpretational landscape. -/- This paper extends the ongoing development of the Universal Principle of Collapse (UPC), presenting a focused analysis of its bridge to quantum mechanics. UPC is a formal, domain‑general operator chain: PO → MO → s → LO → Jo → C → T, that makes the missing structure explicit. It is not metaphysics, psychology, or interpretation; it is a structural architecture, and isomorphic with the measurement sequence that QM already uses. We show that QM is a special case of this universal sequence: it formalizes the device‑side operators and silently assumes the observer‑side operators. -/- Using a pocket calculator, a 1920s mechanical cash register, and a laboratory measurement, we demonstrate that only observers perform recognition and collapse. Once Jo is restored, collapse becomes semantic rather than physical, decoherence is no longer mistaken for collapse, and the paradoxes disappear. UPC reveals the full architecture that quantum mechanics has always relied on but never formalized. -/- Quantum experiments are classical–quantum–classical chains: classical apparatus prepares and detects, a microscopic quantum transition occurs, and the detector amplifies that imperceptible transition into a classical trace. The outcome is not in the device; the trace has no meaning on its own. The Observer recognizes the trace and commits to its meaning. -/- Note: This paper distinguishes physical traces from recognized outcomes. Quantum mechanics models the former (T), not the latter (Jo → C). UPC does not modify or alter QM; it clarifies the structural step QM presupposes when speaking of an “outcome.” The UPC framework is a structural operator chain, not an interpretation or metaphysical claim. A fuller reader’s guide appears at the end of the Introduction and in Appendix A7. May 26, 2026 -/- Authored by Eloy Escagedo Gutierrez as part of The Universal Principle of Collapse (UPC) Research Project. (shrink)

Quantum mechanics provides a complete mathematical description of physical potential and correlation formation, but it does not specify the structural components required for articulated outcomes. The theory lacks a definition of an Observer, a distinction between physical registration and interpretive collapse, a mechanism for outcome indexing, and a structural basis for consensus. These omissions generate the measurement problem and its associated paradoxes. The Universal Principle of Collapse (UPC) supplies the missing architecture. It defines (1) a potential domain (PO), (2) observer (...) models (MO) that partition potential, (3) articulation operators (LO) that produce observer‑indexed outcomes, (4) a strength function corresponding to the Born rule, (5) mechanical registration as a purely physical process, (6) meaning collapse as an interpretive act performed by human observers, and (7) consensus layers that determine the stability and shareability of outcomes. Mapping this architecture onto the quantum measurement chain shows that quantum mechanics describes the evolution of potential and the formation of physical correlations, while UPC describes the articulation of outcomes by observers. This reveals the structural boundary of the quantum domain: quantum mechanics charts the physical evolution of potential, but not the interpretive domain in which outcomes become actual for observers. Once this boundary is made explicit and the missing distinctions are restored, the measurement problem is completed rather than solved. The paradoxes dissolve because the conditions that generate them no longer exist. Quantum mechanics remains physically intact; UPC completes the conceptual structure surrounding it. March 21, 2026. (shrink)

The cosmological constant problem remains one of the deepest paradoxes in modern physics: quantum field theory predicts a vacuum energy density (~10^120) times larger than the value inferred from cosmological observations. This hierarchy mismatch, together with debates over anthropic reasoning and dynamical dark energy, highlights persistent inconsistencies across scales and observer frames. This paper applies the Universal Principle of Collapse (UPC) as a cross‑scale audit axiom, linking quantum, relativistic, and cosmological domains through recognition and collapse. UPC dissolves the paradox not (...) by introducing new physics but by exposing linguistic and conceptual inconsistencies: the assumption of a static vacuum energy, the neglect of observer‑dependent recognition in cosmological inference, and the concealment of recognition as a relational construct. By enforcing recognition consistency across scales, UPC reframes dark energy as a context-dependent entity rather than a paradoxical constant, continuing the dissolution of foundational contradictions established in prior UPC work (Escagedo Gutierrez, 2025a–d). The paper unfolds through Background, UPC Framework, Audit, Resolution, and Philosophical Framing, guiding the reader step by step to clarity. December 2025. (shrink)

This paper asks why particle vocabulary is so effective in scientific practice: why terms such as “electron” function as generic, repeatable, shareable kinds across laboratories despite the absence of direct access to intrinsic particle individuality. I propose a representational explanation based on two constraints. First, scientific objectivity requires publication, understood as stabilization of a public record suitable for intersubjective coordination. Second, publication is bounded by representability: only a limited set of distinctions can be made separable and trackable in the public (...) record at once. Together these constraints force tokenization into a finite public vocabulary, and the resulting mapping from richer underlying variation to public tokens induces stable equivalence classes. Under standard objectivity requirements (cross-observer repeatability, robustness under changes of experimental context, and portability across modelling and intervention), these equivalence classes have the functional profile of particle kinds: fungible tokens with stable invariant labels. A toy mapping illustrates the mechanism, and I briefly connect it to decoherence-based accounts of objectivity and the distinguishability–visibility tradeoff in quantum foundations. The proposal is intended as a philosophy-of-science contribution about scientific representation and objectivity, adjacent to debates on indistinguishability and structural realism. (shrink)

In the philosophy of science, increasing attention has been given to the methodological novelties associated with the study of complex systems. However, there is little agreement on exactly what complex systems are. Although many characterizations of complex systems are available, they tend to be either impressionistic or overly formal. Formal definitions rely primarily on ideas from the study of computational complexity, but the relation between these formal ideas and the messy world of empirical phenomena is unclear. Here, I give a (...) definition of complex systems that draws on algorithmic complexity theory, but also provides a way of interpreting the formal idea in an empirical setting. I then use the definition to show that two canonical forms of scientific idealization are empirically inadequate when applied to complex systems. The inadequacy of these forms of idealization is shown to be the primary reason that complex systems require novel methods. Moreover, this demand for novel methods helps explain the rise of complex systems science as an autonomous discipline. (shrink)

We argue that quantum mechanics is not an ontological description of microscopic reality but a frame-dependent epistemic structure. Building upon the Aperture Stack architecture, we interpret quantum formalism as a topology of observational constraint rather than a reflection of physical entities. Wavefunction collapse, uncertainty, and measurement are reframed as structural transformations within epistemic geometry. Interpretations of QM are thus slices of frame geometry, not metaphysical claims. We further explore a structural homology between quantum formalism and reflexive cognitive architectures, suggesting a (...) deep alignment between knowing and being. (shrink)

A wide range of persistent philosophical disputes may originate from a common inferential transition. Structures introduced to represent empirical systems gradually begin to function as if they directly specified the ontology of those systems. What begins as representation becomes ontology. This paper reconstructs that transition and formalizes it as the ontologization of the descriptive layer. The central claim is that descriptive success alone does not license ontological identification. A successful framework may preserve relevant relational structure while remaining ontologically distinct from (...) the system it represents. The analysis develops this claim through the Descriptive Non-Identity Lemma, according to which structural correspondence underdetermines ontological identity. Building on this result, the paper introduces two methodological diagnostics: the Ontologization Test, which identifies transitions from representation to unsupported ontological commitment, and the Operational Emergence Test, which distinguishes ontological inflation from higher-order structures that become operationally significant by stabilizing constraints within system dynamics. The argument is developed through discussions of scientific representation, model theory, underdetermination, mathematical platonism, gauge theory, and emergence. The resulting framework separates representational success, operational organization, and ontological commitment without collapsing into either eliminative reductionism or unrestricted ontological realism. (shrink)

The quantum wavefunction has been debated for a century without convergence not because philosophers are insufficiently clever, but because the debate has been attempting classification of a target that is not yet in a condition to be classified. Dark matter is the same situation at cosmological scale: four independent lines of evidence converge on a structural role that nothing with a substrate-stable identity has been found to fill. These are not hard cases for scientific realism. They are the debate's most (...) precise results—accurate expressions of what tracking looks like when a target resists ontological completion while continuing to constrain everything inquiry does with it. This paper argues that the scientific realism debate's persistent instability has a structural source that no argument within the debate can address: it begins too late, presupposing science as a first given and truth as primarily ontological, while the conditions under which scientific targets remain answerable have already been decided before the ontological question is raised. Many of the debate's most recalcitrant targets are neither stable substances nor merely instrumental constructions. Their scientific reality lies not in substrate-stable identity but in repeatable re-enterability, constraint-bearing role, and resistance to arbitrary revision across transformations of model, context, and realization. I call these apermanent structural targets. They do not merely resist classification; they generate the debate's constitutive antinomy by simultaneously activating the realist demand for answerability and the anti-realist demand for revisability. The debate has not failed to resolve this antinomy because the arguments are bad. It has failed because the targets themselves make resolution at the first-order level structurally unavailable. On this basis, I distinguish ontological truth within science from the existential truth of science itself—whether science still stands in a mode of occurrence open to being revised by reality rather than merely processing what its current admissible interfaces allow through. Nine familiar repair strategies, from structural realism to stance pluralization, can be read as attempts to protect one of three legitimacy conditions—object-answerability, process-fallback, debate-sustainability—by displacing load onto another. None preserves all three simultaneously. The paper therefore proposes neither a new mandatory doctrine nor an anti-realist retreat, but a permissive tracking-stance: a methodological permission to hold the diagnostic question open at a pre-classificatory level, without forcing an immediate choice between heavy ontology and instrumental deflation. At most, the paper offers a partial fallback. The wavefunction's century of unresolved interpretation and dark matter's four decades without a substrate identity are not embarrassments to be eventually overcome. They are what the debate looks like when it is working correctly at the right level. (shrink)

Let ξ(s) = ½s(s−1)π^(−s/2)Γ(s/2)ζ(s) be the completed Riemann zeta function and let {γ_ρ} denote the positive imaginary parts of its nontrivial zeros. We first prove a universal product formula: for all s∈ℂ (under the Riemann Hypothesis), ξ(s)/ξ(½) = ∏_{γ_ρ>0} (1 + (s−½)²/γ_ρ²), expressing the ratio ξ(s)/ξ(½) as a product over the Riemann zeros with coupling a(s) = |s−½|. The formula has two regimes: for real s each factor exceeds 1 so ξ(s) ≥ ξ(½) (the completed zeta function is minimized at (...) the critical interface); on the critical line s = ½+it the sign reversal gives ξ(½+it)/ξ(½) = ∏(1−t²/γ_ρ²), the exact sine-product analogue with the Riemann zeros replacing the integers. We then apply this to a physically motivated family. For integers k≥1, N≥2, define the shadow coupling a_{N,k} = |k+N−2kN|/(2(k+N)) = |kN/(k+N) − ½|, which is always a nonzero rational number. The Shadow Euler Identity is the specialization to the glueball evaluation points: ξ(kN/(k+N))/ξ(½) = ∏_{γ_ρ>0} (1 + a_{N,k}²/γ_ρ²). The proof rests on two ingredients: the classical Hadamard product theorem for ξ, and an algebraic identity showing that the relevant numerator factors as a perfect square for every pair (k,N). Two forms of the identity are distinguished. The unconditional form expresses the ratio as a product over zero-pairs {ρ, 1−ρ̄} with factors (4ρ(1−ρ)−Δ₁(2−Δ₁))/(4ρ(1−ρ)−1). The RH-conditional form uses ρ(1−ρ) = ¼+γ_ρ², which holds if and only if Re(ρ) = ½ (the Riemann Hypothesis). Assuming RH, the perfect-square algebraic identity shows that a_{N,k} = (k+N−2kN)/(2(k+N)) is rational for every (k,N). The novelty lies in the evaluation point: within the shadow framework, the argument kN/(k+N) is the arithmetic coordinate of the first glueball celestial weight of pure SU(N) Yang–Mills theory at Kac–Moody level k. The identity thus evaluates the completed zeta function at a physically distinguished spectral datum as a product over the Riemann zeros. The SU(3), k=1 master identity is the cleanest: ξ(3/4)/ξ(1/2) = ∏_{γ_ρ>0}(1 + 1/(16γ_ρ²)). The family is verified numerically for nine combinations of (k,N). Special cases include the k=1 principal series, the level-equals-rank diagonal k=N, and the large-N limit which recovers ξ(0)/ξ(½) = ∏_{γ_ρ}(1+1/(4γ_ρ²)). (shrink)

In this paper I argue against a deflationist view that as representational vehicles symbols and models do their jobs in essentially the same way. I argue that symbols are conventional vehicles whose chief function is denotation while models are epistemic vehicles whose chief function is showing what their targets are like in the relevant aspects. It is further pointed out that models usually do not rely on similarity or some such relations to relate to their targets. For that referential relation (...) they reply instead on symbols (names and labels) given to them and their parts. And a Goodmanian view on pictures of fictional characters reveals the distinction between symbolic and model representations. (shrink)

Apparently modally laden terms and relations figure in scientific models, especially though not only possibility. There is an old empiricist tension between measurements as returning actual values, and stronger forms of modality. How could we measure what didn't happen, or use measurement to distinguish what didn't happen but could have, from that which did not happen and could not have? I offer several pragmatist points in the context of modeling and possibility specifically, by which to see this tension as a (...) fruitful one. Peirce offers a view of positive possibility, where it prior to and required for actuality, and which can be differentiated from merely in-principle possibility. He also offers a view of doubt where it requires one suspend use of a belief and initiate an inquiry; views of possibility like those in Humean accounts, even pragmatic Humean views, are offering what amounts to a doubt about models that do not represent these, and only represent positive possibilities. This leads to a distinction by Price between e-representation and irepresentation, where some representation is constrained externally by the environment, and some constrained internally by inferential connections. Putting these together provides a better way to understand how models can represent modality such as positive possibility, and how models can be used in ways that settle direction of fit. (shrink)

This chapter examines the relationship between cognitive maps and episodic memory, and the tensions that arise when we aim to integrate these capacities. I trace the evolution of cognitive maps from Tolman's behavioral studies through the discoveries of place cells, head direction cells, and grid cells, examining how understanding cognitive maps was guided by the type of computations required for physical navigation. I then review how philosophers have sought to explain cognitive maps and spatial representations as computational structures required to (...) encode and retrieve information about the past. However, I show that despite shared neural architecture in the hippocampal formation, mechanistic decomposition reveals tensions between cognitive maps and episodic memory: either episodic memory requires mechanistic components beyond traditional memory circuits, or cognitive maps contribute only partially to memory function. This suggests we must either recharacterize episodic memory or limit cognitive maps' explanatory use for understanding episodic memory. (shrink)

I argue that normative formal epistemology (NFE) is best understood as modelling, in the sense that this is the reconstruction of its methodology on which NFE is doing best. I focus on Bayesianism and show that it has the characteristics of modelling. But modelling is a scientific enterprise, while NFE is normative. I thus develop an account of normative models on which they are idealised representations put to normative purposes. Normative assumptions, such as the transitivity of comparative credence, are characterised (...) as modelling idealisations motivated normatively. I then survey the landscape of methodological options: what might formal epistemologists be up to? I argue the choice is essentially binary: modelling or theorising. If NFE is theorising it is doing very poorly: generating false claims with no clear methodology for separating out what is to be taken seriously. Modelling, by contrast, is a successful methodology precisely suited to the management of useful falsehoods. Regarding NFE as modelling is not costless, however. First, our normative inferences are less direct and are muddied by the presence of descriptive idealisations. Second, our models are purpose-specific and limited in their scope. I close with suggestions for how to adapt our practice. (shrink)

In contrast to the syntactic conception of scientific theories, the semantic conception holds that theories are not statements about the world, but families of models. Recent debates have tended to blur the differences between these two views. Practice-oriented philosophers of science have also challenged both views on the ground that models are central to science, but autonomous from theories. However, they have not proposed any alternative. This article is an attempt to sharpen the challenges faced by the semantic view in (...) order to pave the way for a truly pragmatic conception of theories. I examine different ways in which a focus on models could make the semantic view different from the syntactic view. In the end, they share the same resources to individuate theories, they account just as well for different layers of interpretation, and they face the same issues regarding the relation between formal representation and informal experience. I argue that the only relevant contrast lies not between linguistic and non-linguistic representation, but between descriptive and schematic representation, but this ultimately favours a pragmatic view by implying a role for context in theoretical interpretation. I sketch an account of schematic representation that could serve as a basis for a pragmatic conception of theories. (shrink)

If large language models (LLMs) are models, what do they represent exactly? I address this question by applying the various conceptions of epistemic representation that have been entertained by philosophers of science to this case. After discarding the idea that they would represent the structure of natural languages, I argue that LLMs do not directly represent the world by linguistic means either, but rather a certain class of appropriate linguistic production that is constructed by their makers. They are mostly used (...) to generate fictitious instances of this class, although these fictions can be performative when appropriated by humans. The main implication of this analysis is that conversing with a LLM chatbot amounts to engaging in a fiction, where our own imagination plays a central role. I examine some ethical consequences of this conclusion regarding how LLMs are currently deployed in numerous places to serve as “AI assistants”. (shrink)

Big data is opening new angles on old questions about scientific progress. Is scientific knowledge cumulative? If yes, how does it make progress? In the life sciences, what we call the Consensus Principle has dominated the design of data discovery and integration tools: the design of a formal classificatory system for expressing a body of data should be grounded in consensus. Based on current approaches in biomedicine and systematic biology, we formulate and compare three types of the Consensus Principle: realist, (...) contextual-best, and coordinative. Contrasted with the realist program of the Open Biomedical Ontologies Foundry, we argue that historical practices in systematic biology provide an important and overlooked alternative based on coordinative consensus. Systematists have developed a robust system for referring to taxonomic entities that can deliver high quality data discovery and integration without invoking consensus about reality or “settled” science. (shrink)

Feynman diagrams are used to calculate scattering amplitudes in quantum field theory, where they simplify the derivation of individual terms in the corresponding perturbation series. Considered mathematical tools with an approximative character, the received view in the philosophy of physics denies that individual diagrams can represent physical processes. A different story, however, can be observed in physics practice. From education to high-profile research publications, Feynman diagrams are used in connection with particle phenomena without any reference to perturbative calculations. In the (...) first part of the paper, I argue that this illuminates an additional use of Feynman diagrams that is not calculatory but representational. It is not a possible translation into mathematical terms that prompts this practice but rather the epistemic insights into the target phenomenon that the diagrams provide. Based on this practical use, I intend to push back against the received view. In the second part of the paper, I conceptualize the representative use of Feynman diagrams as models that provide modal understanding of their associated target phenomena. The set of Feynman diagrams corresponding to an interaction is taken as a possibility space whose dependency relations can be analysed, allowing an agent to grasp possible target behaviour, leading to understanding. In clearly separating the diagrams from perturbative calculations for their use as a model, the concerns that hinder a representative reading can be resolved. (shrink)

The central theorem of this paper is a selection jump. For a decidable source-independent stagewise verifier $\Cert(n,c)$, let \[ S_{\Cert} = \{e:\forall n\,\exists t\,(\KleeneT(e,n,t)\wedge \Cert(n,\KleeneU(t)))\}. \] If $S_{\Cert}\neq\varnothing$, then $S_{\Cert}$ is $\Pi^0_2$-complete. Thus a single successful seed already forces maximal stagewise complexity. We prove a companion one-shot calibration theorem: for every decidable $D(c)$, the class \[ O_D=\{e:\exists t\,(\KleeneT(e,0,t)\wedge D(\KleeneU(t)))\} \] is either empty or $\Sigma^0_1$-complete. Together these results yield a witness-shape universality principle for exact local verification: one-shot local exactness yields (...) $\Sigma^0_1$-universality, while stagewise local exactness yields $\Pi^0_2$-universality. We place this principle inside a broader barrier hierarchy. At the lower level, finite stagewise prefixes are uniformly insufficient, and undecidable co-c.e.\ witness architectures admit neither decidable one-shot positive certifiers nor exact-domain witness compilers. At the higher level, same-theory adequacy along a universal $\Pi_1$ embedding yields full $\Pi_1$ reflection, while arithmetic exact terminality on a truth-faithful image exists exactly when the corresponding fragment truth set is arithmetical, yielding Tarski and diagonal barriers. For fixed propositions with exact two-sided decidable witness packages, these results assemble into a two-sided bridge trichotomy: isolated extensional bridges are vacuous; the effective bridge layer splits into a positive stagewise fibre that is empty or $\Pi^0_2$-complete and a negative one-shot fibre that is empty or $\Sigma^0_1$-complete; and assertion-enriched resolver layers are truth-universal.} . (shrink)

Mechanistic explanation is typically understood as a model-based activity, yet the role of structure in mechanistic modeling remains insufficiently clarified. This paper argues that mechanistic modeling requires two irreducible types of structure, dynamical and hierarchical, and analyzes structure as a constraint on model construction within Frigg's framework of scientific representation. Dynamical structure captures the temporal organization of mechanisms, whereas hierarchical structure captures their compositional organization, together imposing complementary constraints on the construction of mechanistic models. A case study of the action (...) potential shows that adequate mechanistic explanation requires the coordinated integration of both forms of structure. The paper thereby provides a unified framework integrating mechanistic modeling, mechanistic explanation, and scientific representation through structured model construction. (shrink)

Strip the empirical claim to what has actually been measured, and the inventory is short. Stars orbit something dark and very massive at the center of our galaxy; we have tracked S2's twenty-year ellipse around Sagittarius A* and can fit its motion to general relativity, within a few percentage points. X-ray binaries throughout the disk emit spectra consistent with accretion onto compact, gravitationally deep objects whose mass functions exceed any neutron-star upper limit. Gravitational-wave detectors record the chirps of two such (...) compact objects spiraling together, and the resulting waveforms agree with numerical-relativity templates built from a vacuum solution of Einstein's equations called the Kerr metric. The Event Horizon Telescope, a planet-scale interferometer operating at 230 gigahertz, has imaged the immediate vicinity of M87* and Sagittarius A* and produced rings of emission whose diameters are consistent with what the Kerr exterior predicts. That is the entire empirical content. Compact dark masses with near-Kerr exterior geometry, observed across four independent channels, in approximate agreement with the same family of solutions. Everything else, every claim about event horizons as one-way membranes you can cross but never return from, every assertion about singularities of infinite density at the center, every paragraph in every popular science book about Hawking radiation and the information paradox, every theoretical edifice of complementarity and firewalls and ER=EPR and replica wormholes and the Page curve, sits past the empirical anchor. None of it has astrophysical observational contact. None of it is implied by what we have measured. All of it depends on extrapolating the same vacuum solution into regimes where the equations themselves break down and then treating the breakdown as the content of the breakdown rather than as the signal of the model's reach being exceeded. (shrink)

This paper develops Representational Sealing Theory (ReST), a theory of the limits encountered by any inquiry that turns to ask after its own preconditions. Its premise is a claim in the philosophy of representation: theoretical representation of a domain is conducted within a structured system of admissible distinction and inference, and that structure constitutes, rather than merely accompanies, what such representation can represent. From this premise the paper derives a ‘representational seal’: a domain dependent upon a prior generative condition cannot (...) theoretically represent the intrinsic nature of that condition, since its only means of representation is a structure the condition does not share. What such a domain may establish is thin and exact: that it has a generative condition, and that the condition was adequate to it. The paper’s principal positive consequence concerns time. A generated domain must represent its own states as non-self-grounding, as referring beyond themselves to a condition it cannot represent. These features are identified as the materials of temporal order: not a single succession, and not the arrow of time, but the dependence-character through which generatedness appears from within. The account is distinguished from relational theories of time, in particular Rovelli’s. Its bounds are stated explicitly: the seal supplies the materials of temporal order, but not their assembly into a single succession, nor the orientation of such a succession. The account contributes nothing to the content of physics; it is a constraint on how a domain may theorise its own preconditions. (shrink)

This paper presents the first system of Kasei-Theory as a non-modal readability maintainability architecture. -/- The paper does not propose a theory of implementation, operational use, or functional deployment. Instead, it fixes non-applicability, configurational non-transferability, application drift, non-operational configuration, structural resonance, peripheral contact, and constrained transfer pressure as distributed structural positions within constrained local readability maintainability. -/- Configuration does not become application. -/- Readability does not establish usability. -/- Applicability does not emerge from readability. -/- Configuration does not transfer between (...) domains. -/- Non-applicability is not failure. -/- Non-applicability is not uselessness. -/- Application drift remains fixed only as recurrent pressure toward operational transfer. -/- The first system remains non-total and non-final without operational grounding, executable closure, universal transferability, or final philosophical closure. -/- No subject is presupposed. -/- No operational applicability is secured. -/- This paper is part of Kasei-Theory. (shrink)

In recent years, discussions on the epistemology of model organism-based research have emerged in the philosophy of science. A key topic of discussion is how the epistemic insights gained from model organisms differ from those gained through other experimental organisms used in laboratory and field research. Here, we argue that model organisms are epistemically special due to their nature as ontogenetically changeable, standardized, and evolved material model carriers. These characteristics afford six important kinds of modeling versatility that biologists marshal in (...) their investigations: (i) synchronic target versatility; (ii) synchronic scope versatility; (iii) diachronic target versatility; (iv) diachronic scope versatility; (v) manipulation versatility; and (vi) discovery versatility. In presenting these dimensions of modeling versatility, we also clarify key notions such as ‘representational target,’ ‘representational scope,’ and ‘representational power’ as these apply to modeling practices that involve model organisms. (shrink)

Epistemics understands epistemic practice as model management under finite conditions (Rapp 2026a). This determination remains incomplete, however, as long as it remains unclear how fields of experience become model-capable, that is, available for model formation, in the first place. Models do not arise directly from experience; rather, they presuppose that experience has already been ordered, differentiated, and epistemically stabilized. The present paper examines this prior level of stabilization and determines models as explicitly identifiable, workable, and revisable stabilizations of epistemically ordered (...) fields of experience. The central thesis is this: epistemic stabilization does not simply reduce uncertainty; it often first makes it localizable. As long as a field of experience remains diffuse, it also remains unclear what precisely its uncertainty consists in. Only when an epistemic system posits a provisional order, such as a heuristic, a schema, a case hypothesis, or a model, does it become apparent which relations hold, which information is missing, which assumptions are too strong, and where fault lines arise. This provisional stabilization is therefore not merely a preliminary stage of secured knowledge, but an epistemic act of testing. From this perspective, central concepts of Epistemics are made more precise. Validity designates the carrying capacity of a stabilization under finite conditions. Friction is the point at which its boundary becomes visible. Revision is the restructuring of a stabilization when this boundary becomes epistemically relevant. At the same time, the paper shows that degrees of stabilization, from heuristic through schema and model to formalization, do not form a ladder of progress. Stronger stabilization is not automatically better inquiry; what is decisive is the adequacy of the stabilization in relation to the state of information, purpose, domain of validity, costs, and revisability. The paper supplements Epistemics by systematically opening up the area before the explicit model. Model management does not begin only with completed models, but wherever an epistemic system stabilizes a field of experience in such a way that it can become visible what holds, what is missing, and what does not fit. (shrink)

If (or when) mathematics is dispensable for solving empirical problems, why can the detour through mathematics be so useful? Typical discussions of applicability only approach this problem indirectly, saying just enough about it to argue that whatever gain mathematics offers (e.g., a gain in inferential power) can be enjoyed without ontological costs. In this paper, I first clarify this problem and distinguish it from other, related ones; in particular, I make it clear that the problem has nothing specifically to do (...) with the application of mathematics to empirical sciences, and arises in the same way for many so-called applications of mathematics to mathematics (which I argue are best defined as deployments of new mathematical resources to make progress on a mathematical problem). I then survey possible solutions, including a particularly promising one, inspired by Ken Manders and in line with recent work on reformulations: mathematics offers tools for systematic expressive restriction, allowing for attentional management in problem solving. (shrink)

For various reasons, it has become common wisdom in science that there exists a principled epistemic distinction between direct and indirect observation. In this paper, I present a twofold argument. First, I argue against such a principled epistemic distinction. Second, I highlight a pervasive incongruence between the methodological and epistemological distinctions between direct and indirect observations. My arguments revolve around the idea that it is one thing to make a methodological distinction between observations and another to ascribe epistemic significance to (...) them. I begin by unfolding the historical and philosophical foundations of the distinction, identifying three tenets that have served to sustain the distinction to the present day. I then provide a detailed analysis of two recent philosophical efforts to preserve the epistemic distinction in astrophysics and specific areas of astrophysics, ultimately suggesting that these approaches face significant challenges. (shrink)

It is plausible that the models of scientific theories correspond to possibilities. But how do we know which models of which scientific theories so correspond? This paper provides a novel proposal for guiding belief about possibilities via scientific theories. The proposal draws on the notion of an effective theory: a theory that applies very well to a particular, restricted domain. We argue that it is the models of effective theories that we should believe correspond, at least in part, to possibilities. (...) It is thus effective theories that should guide modal reasoning in science. (shrink)

Contemporary action theory is generally concerned with giving theories of action ontology. In this paper, we make the novel proposal that the standard view in action theory—the Causal Theory of Action—should be recast as a “model”, akin to the models constructed and investigated by scientists. Such models often consist in fictional, hypothetical, or idealized structures, which are used to represent a target system indirectly via some resemblance relation. We argue that recasting the Causal Theory as a model can not only (...) accomplish the goals of causal theorists, but also give the theory greater flexibility in responding to common objections. (shrink)

The New Mechanism has traditionally focused on identifying constitutively relevant components in mechanistic explanation but has largely overlooked how temporal organization encompassing order, duration, and rate should be formally represented. This paper develops a structuralist approach to mechanistic explanation by integrating insights from scientific representation and category theory. Drawing on Hughes’ DDI (Denotation, Demonstration, Interpretation) account, it establishes a representational framework for modeling temporal constraints as explanatory targets. Category–theoretic tools including index categories, functorial mappings, and Petri nets are employed to (...) formally encode dynamical and sequential structures. Using protein synthesis as a case study, the paper demonstrates that mechanistic explanation must account not only for token–level causal dependencies but also for type–level structural constraints. By bridging the theory of scientific representation with mechanistic explanation, it clarifies how temporal organization underlies and enables explanatory models in biology. (shrink)

Craver's diagram, comprising symbols such as X (entity), S (mechanism), Φ (activity), and Ψ (phenomenon), is widely used to represent biological mechanisms in the New Mechanism. However, this paper demonstrates that Craver’s framework lacks the formal capacity to adequately capture the organizational structures and functional dynamics essential for mechanistic explanations, particularly the temporal interplay among entities and activities or the relational nature of enzymatic state transitions. To address these limitations, this paper proposes a supplementary framework based on category theory, enabling (...) the abstraction of mechanisms as temporally organized structures of state transitions. By integrating key features such as order, frequency, and duration, categorical diagrams provide a cohesive representation of type mechanisms, supporting the deficiencies of token-centric approaches. Using protein synthesis as a case study, the paper illustrates how categorical abstractions enhance the formal representation of biological mechanisms while emphasizing the philosophical importance of organizational dimensions. (shrink)

Modeling cuts across sundry scientific practices, contributing to theorizing, experimentation, prediction, measurement, scientific instrumentation, and science education. Beyond the sciences, modeling plays a crucial role in citizen engagement with science and public policy decision-making. It plays a major role in the efforts to address the huge challenges of the 21st century, including but not limited to climate change, shortage of natural resources, loss of biodiversity, and economic forecasting in increasingly unforeseeable situations. The diversity of scientific models is astounding; side-by-side mathematical (...) and scale models, technological advances such as rapidly expanding big data, computational and synthetic approaches, and generative AI are pushing modeling toward new frontiers, redefining the epistemic agency between humans and scientific instruments. A discussion of what we can achieve through modeling, and how we should manage model-based practices, is critical for ensuring a good and responsible use of this epistemic resource. The chapters of The Routledge Handbook of Philosophy of Scientific Modeling, written by experts in various areas of the philosophy of science, seek to provide enduring philosophical insights and useful analyses for understanding modeling in its multiplicity. -/- . (shrink)

Models are used to explore possibilities across all scientific fields. Climate models simulate the potential future climatic conditions under various emissions scenarios, macroeconomic models investigate the implications of various fiscal and monetary policy initiatives, and infectious diseases models study the spread of viral diseases under a range of conditions. Such modeling approaches have not gone ignored by philosophers of science, but they have only recently started to explicitly address modeling the possible. So far, the discussion has been spread across a (...) variety of more or less isolated pockets of debate in the philosophy of science. Modeling the Possible: Perspectives from Philosophy of Science draws together these studies, focusing specifically on how various modeling practices probe possibilities and justify claims concerning them. -/- The volume is divided into three sections, plus an introductory chapter. The introductory chapter provides a state-of-the-art survey of the discussions of modeling possibilities within the philosophy of science, as well as an introduction to the book’s main themes and individual papers. The three sections focus on different kinds of possibility concepts, possibility spaces, and how-possibly modeling in practical situations. The chapters contained in this volume address conceptual and theoretical issues while also presenting case studies from various scientific domains: physics, evolutionary and synthetic biology, network science, climate science, economics, and epidemiology. -/- Essential reading for philosophers of science, epistemologists, and modelers in various scientific disciplines, Modeling the Possible is also suitable for anyone interested in model-based scientific inferences, their validity, and the policy conclusions derived from them. (shrink)

Was macht wissenschaftliches Verstehen aus? Und inwiefern können visuelle Repräsentationen, wie sie vielfach in der (Ergebnis-)Präsentation (Publikationen, Vorträgen etc.) in unterschiedlichen wissenschaftlichen Disziplinen Verwendung finden, zum Verstehen untersuchter Fragestellungen beitragen? Diesen Themen soll im folgenden Beitrag genauer nachgegangen werden. Den Ausgangspunkt bildet dabei Henk W. de Regts Studie (2017) zum wissenschaftlichen Verstehen. De Regt plädiert dafür, Kriterien des wissenschaftlichen Verstehens aus der aktuellen wissenschaftlichen Praxis zur Anwendung zu bringen – was auch bedeutet, ihre historische Variabilität ernst zu nehmen. Ein Punkt (...) seiner Untersuchung betrifft den Zusammenhang zwischen Visualisierbarkeit und wissenschaftlichem Verstehen. Erörtert wird von ihm die Frage, inwiefern Anschaulichkeit eine notwendige Bedingung für das Verstehen von Theorien und Phänomenen ist. De Regt bezieht dabei letztlich eine kritische Position, indem er sich gegen den Status einer solchen notwendigen Bedingung ausspricht, da sich in der Wissenschaftshistorie zeigen lasse, dass Anschaulichkeit nicht durchgängig als wesentliches Kriterium angesehen wurde. Dieses Votum contra eine notwendig bedeutungsvolle Rolle von Visualisierungen im Verstehensprozess scheint allerdings de Regts eigener Argumentation für eine Kontextabhängigkeit des Verstehens zuwiderzulaufen. Im vorliegenden Text soll diese Spannung aufgezeigt und zu Gunsten der Rolle von Visualisierungen im Prozess wissenschaftlichen Verstehens gewendet werden. Am Beispiel der maritimen Raumplanung (MRP) wird veranschaulicht, inwiefern die Redeweise von der Einsehbarkeit von Gründen mehr als eine bloße Metapher im Kontext des wissenschaftlichen Verstehens darstellen kann. (shrink)

In this article, we mobilize and refine the DEKI account of scientific representation to contend that model organisms are not models tout court but model ‘carriers,’ only abstracted and selected ‘parts’ of which are included in biological models. These parts correspond to phenomena of interest that are interpreted as mechanisms or other kinds of causal processes within certain theoretical domains. The models can then be used to represent similar target phenomena in other organisms. Our proposal paves the way to reconcile (...) opposing positions apropos the representational status of model organisms and build a more robust epistemology of model organism-based research. (shrink)

Scientific realists with traditional semantic inclinations are often pressed to explain away the distinguished series of referential failures that seem to plague our best past science. As recent debates make it particularly vivid, a central challenge is to find a reliable and principled way to assess referential success at the time a theory is still a live concern. In this paper, I argue that this is best done in the case of physics by examining whether the putative referent of a (...) term is specifiable within the limited domain delineated by the range of parameters over which the theory at stake is empirically accurate. I first implement this selective principle into a general account of reference, building on Stathis Psillos’s works. Then, I show that this account offers a remarkably reliable basis to assess referential success before theory change in the case of effective theories. Finally, I briefly show that this account still works well with other physical examples and explain how it helps us to handle problematic cases in the history of physical sciences. (shrink)

Among much else, Peirce was concerned with understanding the nature of experimentation. And while Peirce scholarship frequently appeals to the role of experimentation in his philosophy, no one has yet provided the account appealed to. This is not because Peirce's understanding of experimentation is too obvious to deserve discussion, nor is it because Peirce was quiet on the subject. Indeed, Peirce attempted to articulate what he meant by an experiment in many ways over the course of decades. But these articulations (...) have received limited attention and have not been brought together with the aim of understanding Peircean experimentation. Notably, two of the key sources—Peirce's writings on Petrus Peregrinus de Maricourt and his many drafts of "What Pragmatism Is"—have received little critical engagement. This essay has two aims. The first is to lay out and bring together Peirce's various discussions on the nature of experimentation, providing a sketch of the whole picture. The second is to draw attention to three aspects of this sketch—(1) that experimental inquiry is interest-based, (2) that abduction occurs at key stages throughout, not merely in the production of hypotheses, and (3) that experimental inquiry clarifies and distinguishes two roles for doubt: as a skeptical attitude held towards a hypothesis, and as an uncomfortable state caused by surprise, with only the first sense being crucial. (shrink)

Accounts of scientific representation typically assume that there is a single sense of “represent”, and they attempt to develop a theory that can account for all its features. The aim of this article is to draw the consequences of a distinction between two senses of “represent” that has been proposed recently. Taking inspiration from the distinction between speaker-meaning and expression-meaning in philosophy of language, a first sense is analysed in terms of the mental states of the user of a vehicle (...) in context, and a second sense in terms of communal norms constraining contextual uses. I argue that making this distinction, and thus understanding the representation relation as essentially indexical and normative, can help us move beyond the controversies between various accounts of scientific representation, notably what have been dubbed informational and functional accounts, as well as debates regarding the ontology of scientific models. (shrink)

In this paper, I first argue that similarity accounts of scientific pictures fail with more realistic cases of scientific pictures. My primary case study is the picture of a black hole, to which I apply an interpretation-based account of picture representation analogous to how models represent: a picture represents a designated target system iff, once interpreted, it exemplifies properties that are imputed to the target via a de-idealising function. Then, I argue that the justification of the inferences from mechanically produced (...) pictures depends on their causal mechanisms of production, in contrast with the standard justificatory strategies employed for model inferences. (shrink)

Several philosophers of science have drawn attention to a number of modeling practices where scientific models primarily contribute modal information. Examples now abound, and, recently, there have also been some preliminary attempts to address questions of under what conditions, and by virtue of what, models can perform this modal epistemic function. This paper sets out to constructively review those attempts through a prism of the more general literature on the epistemology of modality. One aim of this exercise is to expose (...) the underlying justificatory strategies of the modal modeling accounts – which are strikingly convergent with those already identified by modal epistemologists. Another aim is to highlight some challenges familiar to modal epistemology and discuss the form they take in the context of modal modeling as well as the resources that modal modeling accounts have for dealing with them. This is all done with an eye to pointing out ways forward in further developing the work on the epistemology of modal modeling. (shrink)

The notion of shape space was introduced in the second half of the 20th Century as a useful analytical tool for tackling problems related to the intrinsic spatial configuration of material systems. In recent years, the geometrical properties of shape spaces have been investigated and exploited to construct a totally relational description of physics (classical, relativistic, and quantum). The main aim of this relational framework—originally championed by Julian Barbour and Bruno Bertotti—is to cast the dynamical description of material systems in (...) dimensionless and scale-invariant terms only. As such, the Barbour-Bertotti approach to dynamics represents the technical implementation of the famous Leibnizian arguments against the reality of space and time as genuine substances. The question then arises about the status of shape space itself in this picture: Is it an actual physical space in which the fundamental relational dynamics unfolds, or is it just a useful mathematical construction? The present paper argues for the latter answer and, in doing so, explores the possibility that shape space is a peculiar case of a conceptual space. (shrink)

The philosophical literatures on models and thought experiments have been developing exponentially, and independently, for decades. This independence is surprising, given how similar models and thought experiments are. They each have “lives of their own,” they sit between theory and experience, they are important for both pedagogy and cutting-edge science, they galvanize conceptual changes and paradigm shifts, and they involve entertaining imaginary scenarios and working out what happens. Recently, philosophers have begun to highlight these similarities. This entry aims at taking (...) the idea further, by trying to systematically identify places where insights from one literature can be taken up in the other. Along the way, important differences will also be highlighted. (shrink)

Conceptions about the nature of scientific models held by science students frequently involve distorted views, with a tendency to consider them as mere copies of reality. Besides encompassing an untenable view about the nature of science itself, this misconstruction can effectively be a pedagogical impediment to learning. Objectives: We evaluate whether Mario Bunge’s epistemology might contribute to tackling issues related to the nature of models in science education contexts. De-sign: After identifying Bunge’s main model categories, we employ them to examine (...) aspects of the historical development of atomic models and contrast the resulting framework with issues about model conceptions in science education, as pointed out in the literature. Setting and participants: Due to this research’s theoretical nature, this study did not include human participants other than authors from the literature and the theoretical framework. Data collection and analysis: We per-formed a constant comparative analysis to identify patterns of meanings shared between the historical case and the theoretical framework. Results: Features of models pointed out by Bunge were identified in the development of atomic models and could provide consistent and explanatory viewpoints about key issues related to model conceptions in science education. Conclusions: Bunge’s framework might help to clarify aspects of the nature of models relevant to science education contexts. -/- . (shrink)