Challenging Kirchhoff on the Semantics of Models and Theories
Zoe Drayson
The bold claim at the heart of Kirchhoff’s (2025) The Idealized Mind is that some scientific theories are neither true nor false. This makes Kirchhoff one of the very few philosophers since the logical empiricists to deny semantic realism: the view that all scientific theories, including those which posit unobservables, have truth conditions. Most contemporary scientific realists and anti-realists remain committed to semantic realism and disagree instead on the epistemic aspect of scientific realism: whether we have knowledge of all the unobservable entities posited by our best-supported mature theories (standard scientific realism), only a subset of those unobservable entities (selective realism), or only the observable posits (anti-realism). What makes Kirchhoff’s denial of semantic realism particularly interesting is that it is part of an attempt to defend scientific realism.
Kirchhoff’s worry is that scientific realism is incompatible with our reliance on scientific idealizations (such as frictionless planes, infinite populations, and ideally rational agents) which seem to deliberately distort features of the actual world by misrepresenting it. He argues that (i) if idealization involves misrepresentation, then it involves falsehood; and that (ii) falsehood is in tension with scientific realism. To retain scientific realism, Kirchhoff proposes that (iii) scientific discourse based on idealizations is neither true nor false, because idealizations neither represent nor misrepresent. He argues that (iv) scientific realism is easier to reconcile with discourse lacking truth conditions than false discourse. In what follows, I’ll challenge each of these four points in turn, before suggesting an alternative way for Kirchhoff to avoid classifying idealization as misrepresentation.
- “if idealization involves misrepresentation, then it involves falsehood”
If scientific idealization is, as many suppose, a form of misrepresentation, this does not entitle Kirchhoff to conclude that “because idealization is a form of misrepresentation, it is a falsehood” (40). Kirchhoff’s focus is on idealization in scientific models, which misrepresent by being inaccurate or non-veridical rather than false. Scientific theories, understood as “families of models” (70), misrepresent by being false. The truth of a theory cannot require the veridicality of all its models, at risk of collapsing the distinction between representing and accurately representing. If we accept that the truth of a theory requires only that there be one model and one interpretation for which the model is an accurate representation of the target (Ruyant 2021), then a theory can be true even if most of its models misrepresent.
- “falsehood is in tension with scientific realism”
Even on the assumption that idealized theories result in false scientific discourse, this isn’t obviously in tension with scientific realism. Scientific realism is the view that our theories give us epistemic access to the mind-independent world; idealizations are generally thought to contribute toward such epistemic achievements, and even lead to the discovery of truths. A tension only arises if we, like Kirchhoff, characterize scientific realism as “the view that science aims at discovering the true nature of reality” (33, my emphasis). Many philosophers of science caution against characterizing scientific realism in this way, considering it an eccentric view which should be avoided (Rowbottom 2014, 2019).
- “scientific discourse based on idealizations is neither true nor false because idealizations neither represent nor misrepresent”
Kirchhoff proposes that idealizations neither represent nor misrepresent, on the grounds that “the function of idealization is not to represent aspects of target systems” (47). He claims that idealized models have alternative functions: their role is to downplay or isolate the role of certain causal mechanisms in the target system, for example. But how could we use the model to reason about the roles played by aspects of the target system unless the model also performed some sort of representational function with respect to the target system? Kirchhoff also claims that idealized models do not function as representations because they fail to denote (56). But only a model which purports to denote can fail to denote, and purported denotation is sufficient for a model to function as a representation; only accurate representation requires successful denotation (Nguyen and Frigg 2022).
- “scientific realism is easier to reconcile with scientific discourse which lacks truth conditions than it is with false scientific discourse”
Kirchhoff thinks that only some aspects of idealized models fail to play a representational function, and that the remaining representational aspects are therefore conducive to scientific realism. I struggle to see how this is preferable to the position he is rejecting, on which some aspects of idealized models misrepresent while other aspects accurately represent. Kirchhoff worries that if we understand idealization as misrepresentation, we end up “having to justify how obvious falsehoods can have epistemic value” (60). But on the assumption that we are working with a truth-conditional theory of meaning (to which Kirchhoff offers no alternatives), rejecting semantic realism results in idealization-discourse avoiding obvious falsehood by being simply meaningless: we are unable to understand this discourse if it lacks truth conditions for us to grasp. How can such meaningless discourse benefit our scientific reasoning, as Kirchhoff claims? Consider Kirchhoff’s example of scientific discourse about neural representations, which he takes to lack truth-conditions because it involves non-representational idealization. He thinks that this discourse is epistemically valuable “as a means of acknowledging that we should not, and could not, mean what we are saying when making use of these theoretical terms” (107). This would require the discourse to have truth-conditions, however: it is only by understanding it as literally false that we are directed toward its supposed non-literal meaning. And such an approach, which is taken by fictionalists about scientific discourse, falls squarely on the antirealist side of the scientific realism debate.
Kirchhoff’s proposal, that idealized models play no representational function, seems to be neither necessary nor sufficient for a defense of scientific realism. If Kirchhoff is determined to avoid the claim that idealized models misrepresent, then an alternative strategy is available: he could understand idealized models as accurate representations of their target systems (Nguyen 2020). Idealized models are only taken to misrepresent on the ‘literalist’ assumption “that models have to be interpreted as sharing features with their targets in order to be accurate representations of those features” (Frigg and Nguyen 2021a, 2435). Kirchhoff thinks that Frigg and Nguyen’s ‘non-literalist’ approach “lends support” (62) to his own treatment of idealization, but their approach rejects neither semantic realism nor the representational role played by idealized models. Kirchhoff also claims that their approach is incompatible with scientific realism, on the grounds that it is ‘fictionalist’. But this is to conflate two distinct questions in the scientific modeling literature: Frigg and Nguyen (2021b) are clear while they favor a view of models as fictions over a view of models as set-theoretic entities, this view of the ontology of scientific models is entirely independent from their non-literalist approach to scientific representation. (It is worth emphasizing that questions about the relation of scientific representation are orthogonal to questions about the ontological status of scientific models, because Kirchhoff seems to confuse the two questions at several points, suggesting that his approach supports scientific realism on the grounds that it supports “realism about scientific models”.)
References
Frigg, Roman & Nguyen, James (2021a). Mirrors without warnings. Synthese 198 (3):2427-2447. https://doi.org/10.1017/9781009003575
Frigg, R., Nguyen, J. (2021b). Seven Myths About the Fiction View of Models. In Cassini, A. & Redmond, J. (eds.) Models and Idealizations in Science (pp. 133-157). Springer. https://doi.org/10.1007/978-3-030-65802-1_6
Kirchhoff, M. (2025) The Idealized Mind: From Model-Based Science to Cognitive Science. MIT Press. https://doi.org/10.7551/mitpress/15860.001.0001
Nguyen, James (2020). It’s Not a Game: Accurate Representation with Toy Models. British Journal for the Philosophy of Science 71 (3):1013-1041. https://doi.org/10.1093/bjps/axz010
Nguyen, J. & Frigg, R. (2022) Scientific Representation (Cambridge Elements). CUP. https://doi.org/10.1017/9781009003575
Rowbottom, D. (2014) Aimless science. Synthese 191 (6):1211-1221. https://doi.org/10.1007/s11229-013-0319-8
Rowbottom, D. (2019) Scientific realism: what it is, the contemporary debate, and new directions. Synthese 196 (2):451-484. https://doi.org/10.1007/s11229-017-1484-y
Ruyant, Q. (2021) Semantic realism in the semantic conception of theories. Synthese 198, 7965–7983. https://doi.org/10.1007/s11229-020-02557-8
The debate between Kirchhoff and his Zoe Drayson over whether idealized scientific theories possess truth conditions reflects a deeper categorical confusion about the nature of semantic realism itself. Both parties treat semantic realism as a dimension-independent property that theories either possess or lack absolutely. Drawing on dimensional epistemology, I argue that this debate can be dissolved by recognizing that semantic realism is valid at certain epistemic levels while necessarily collapsing into relativism at others. This approach preserves the intuitions of both sides while avoiding their respective difficulties.
1. The Dialectical Impasse
Kirchhoff’s central claim is that scientific discourse based on idealizations (frictionless planes, infinite populations, ideally rational agents) is neither true nor false because such idealizations neither represent nor misrepresent. His motivation is to defend scientific realism by avoiding the conclusion that our best theories are systematically false.
The critic responds that discourse lacking truth conditions is meaningless, and meaningless discourse cannot provide epistemic value. If idealized models have no representational function, they cannot guide our reasoning about target systems. The critic suggests that Kirchhoff should instead adopt a non-literalist view on which idealized models accurately represent their targets despite not sharing their features.
Both positions face difficulties. Kirchhoff struggles to explain how non-representational discourse can be epistemically valuable. The critic must explain how models that deliberately distort reality can count as accurate representations. I contend that this impasse results from treating semantic realism as an all-or-nothing affair rather than recognizing its epistemic stratification.
2. Dimensional Epistemology: A Brief Framework
Dimensional epistemology posits that cognitive access to the world operates through four qualitatively distinct epistemic dimensions:
D₁ (Reactive): Immediate, affective, instinctive responses (millisecond timescale)
D₂ (Systematic): Rule-governed, analytical, symbol-processing operations (seconds to minutes)
D₃ (Reflexive): Metacognitive operations, methodological reflection (minutes to hours)
D₄ (Contextual): Cultural, social, linguistic embedding of knowledge (hours to years)
A complete epistemic state P is represented as a four-tuple P = (p₁, p₂, p₃, p₄), where each component represents the activation of that dimension. Scientific claims are not simply true or false, but possess dimensional truth profiles T(A) = (t₁, t₂, t₃, t₄) indicating their validity structure across epistemic dimensions.
Crucially, what counts as “real” or as possessing “truth conditions” differs systematically across these dimensions. This is not relativism in the pejorative sense, but recognition that epistemic structures have different architectures at different levels of abstraction.
3. The Dimensional Structure of Scientific Idealization
Consider the idealized claim: “A body falls in a vacuum with constant acceleration g.”
On D₂ (systematic dimension), this statement has clear truth conditions. It functions within a rule-governed system of classical mechanics, generates successful predictions, and guides experimental design. The claim is pragmatically true within its theoretical framework. Semantic realism is justified here because the systematic operations of science produce stable, intersubjectively accessible truth conditions.
On D₃ (reflexive dimension), we recognize that “vacuum” and “constant g” are methodological constructs, not descriptions of actual physical situations. We see that the idealization serves specific epistemic functions: isolating causal factors, enabling mathematical tractability, revealing structural relationships. At this level, we understand that D₂-truth is constructed rather than discovered.
On D₄ (contextual dimension), we recognize that the validity of this idealization depends on historical developments (the emergence of classical mechanics), cultural factors (the Western emphasis on mathematical precision), and paradigmatic commitments (the Newtonian worldview). Here, semantic realism collapses into relativism, as we see that what counts as “truth conditions” is itself culturally and historically constituted.
4. Dissolving Kirchhoff’s Dilemma
Kirchhoff’s error is projecting D₃/D₄ insights back onto D₂. He correctly recognizes (at D₃) that idealizations are constructive simplifications rather than literal descriptions. He then concludes (incorrectly) that they therefore lack truth conditions at D₂. This is a category mistake: the recognition that truth conditions are epistemically constructed does not entail that they don’t exist at the level where they function.
The dimensional framework shows that idealizations simultaneously:
• Possess truth conditions and epistemic value (D₂)
• Are recognized as methodological constructs (D₃)
• Depend on paradigmatic and cultural contexts (D₄)
There is no contradiction here because these are claims about different epistemic levels. Kirchhoff is right that idealizations don’t represent mind-independent reality in any transcendent sense (D₄-level insight), but wrong to conclude they therefore lack representational function altogether (confusing this with D₂ operation).
5. Responding to the Critic
The critic objects that discourse without truth conditions is meaningless. This objection assumes that truth conditions must be understood in a dimension-independent way. But on the dimensional view, a statement can possess robust truth conditions at D₂ while being recognized as constructed at D₃ and paradigm-relative at D₄.
The critic’s suggestion that we adopt non-literalism (idealizations accurately represent despite not sharing features with targets) actually supports the dimensional view. Non-literalism is essentially the recognition that D₂-level representational accuracy doesn’t require the naive correspondence assumed by literalism. But this is compatible with dimensional epistemology: D₂ truth conditions exist and function effectively even though D₃/D₄ reflection reveals they are not simple mirrors of a mind-independent reality.
The critic also worries that Kirchhoff’s position collapses into fictionalism and therefore antirealism. The dimensional view avoids this: we can be realists at D₂ (science gives us reliable epistemic access to stable structures) while recognizing at D₄ that this “reality” is epistemically constituted rather than transcendent. This is a sophisticated realism, not antirealism.
6. The Category Error in Standard Debates
Most debates between scientific realists and antirealists commit the same category error as Kirchhoff and his critic: they assume semantic realism is dimension-independent.
Traditional semantic realists argue from D₂ and project universally: because scientific theories have stable truth conditions in systematic practice, there must exist mind-independent truth-makers. They fail to recognize that D₂ truth conditions are themselves epistemically constructed.
Antirealists and constructivists argue from D₃/D₄: because reflection reveals the constructed nature of scientific concepts, theories don’t really have objective truth conditions. They fail to recognize that construction at D₃/D₄ doesn’t negate functional reality at D₂.
Both positions are partially correct within their operative dimension but err in universalizing beyond it.
7. Implications for Scientific Practice
The dimensional framework has practical implications. It suggests that:
Methodological pluralism is rationally required: Different epistemic dimensions may call for different methodological approaches. D₂-level work requires rigor in systematic theory construction; D₃-level work requires reflexive awareness of methodological limitations; D₄-level work requires attention to cultural and historical context.
Paradoxes often signal dimension confusion: When scientists or philosophers encounter apparent contradictions (wave-particle duality, the measurement problem), this often indicates that phenomena are being described from incompatible epistemic dimensions without recognizing the shift.
Idealization is not a problem to be solved but a feature of dimension-stratified cognition: The “problem” of idealization arises only when we demand dimension-independent truth conditions. Once we recognize that D₂ truth is constructed yet functionally robust, idealization becomes explicable as an essential feature of systematic knowledge.
8. Conclusion
The debate over whether idealized theories have truth conditions cannot be resolved within the flat ontology assumed by both Kirchhoff and his critics. Dimensional epistemology dissolves the debate by showing that semantic realism is dimension-relative: justified at D₂, where systematic science operates; transforming into constructivism at D₃, where we reflect on methods; collapsing into relativism at D₄, where we recognize cultural-historical constitution.
This is neither a capitulation to relativism nor a naive realism. It is a recognition that epistemic structures have different architectures at different levels of abstraction. Scientific idealizations possess truth conditions, representational function, and epistemic value at the systematic level (D₂), even while being recognized as constructed at reflexive (D₃) and contextual (D₄) levels.
The solution to Kirchhoff’s worry is not to deny that idealizations have truth conditions, but to recognize that truth conditions themselves are dimension-stratified. Reality is not “out there” waiting to be discovered, nor is it arbitrary construction. It is stable structural relations within the epistemic field, and these relations manifest differently at different dimensions of cognitive access.
Both Kirchhoff and his critic are partly right and partly wrong because they operate within an impoverished one-dimensional epistemology. A properly dimensional approach preserves scientific realism where it matters (at the operative level of systematic science) while acknowledging the constructive and contextual nature of knowledge (at reflexive and cultural levels) without contradiction.