Abstract
In this article, I will offer a ground-theoretic proposal to explore the so-called ‘constitution question of scientific representation’: in virtue of what does a scientific model represent a part of the world? In particular, I will provide a schematic, unifying account, according to which scientific representation is grounded in both structural similarities and agent’s intentional actions. This new framework not only characterizes the nature of the dependence of scientific representation on these two sorts of factors, but also determines the geometry of the dependence. Furthermore, it underlies certain intuitions which the hybrid approach to scientific representation, while acknowledging such a form of dependence but leaving its nature untouched, relies on.
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Notes
The views included in these three families, perhaps except Suárez’s one which should be treated with some caution (see Sect. 3), are all substantialist in that they take scientific representation as a relation which is based on some substantive or constitutive concepts explaining why a scientific representation obtains. Another side of the story unfolds by full-blown deflationary views which submit there is no more substantial notion undergirding scientific representation. According to the fully inferentialist-expressivist account as a purely deflationary view, for instance, saying ‘M scientifically represents T’ is nothing more than expressing that some surrogative inferences from M to T are justified (Khalifa et al., 2022). Granted the distinction, this paper engages directly with the substantialist views.
Boesch (2019) has recently put forward a similar, schematic proposal for agent-based accounts. His Means-End account “does not offer an account of the nature of scientific representation... It begins with the assumption that some pragmatic account or group of accounts has already provided a good analysis of the nature and use of representation in scientific practice. Following on this assumption, it offers an analysis of a component which has been heretofore unexamined: the nature of the actions that undergird and ground representation for these accounts” (Boesch, 2019, p. 2316). In a similar vein, the ground-theoretic, unifying scheme developed here tries to analyze the nature of the dependence involved in hybrid accounts.
Although there is no consensus on how long the question of ground can be traced back, there is an agreement that the discussion about the nature of ground has been sparked by the three papers of Fine (2001), Schaffer (2009) and Rosen (2010). For different analyzes of this conception, its history, related notions and applications, see Raven (2020).
Of course, ‘ground-theoretically’ has no single meaning, since the philosophers of ground have analyzed this notion differently. Despite this diversity, I focus on just those aspects of grounding on which there is some sort of agreement. Whether or not the different notions of grounding lead to different conceptions of scientific representation is left as an open question for further exploration.
Due to using the limiting condition to obtain \( K(r)=0 \), and applying other idealizations, there is no total isomorphism between \( \mathcal {S} \) and \( \mathcal {T} \). The advocates of the structuralist account (Bueno & French, 2011; French, 2017) argue that partial mappings, e.g. partial isomorphism, can accommodate the notion of idealization in scientific representation. \( \mathcal {A} = <A,R_i>_{i \in I} \) is a partial structure where A is a non-empty set and each \( R_i \) is an n-tuple partial relation over A. Each partial relation \( R_j \) is characterized by an ordered triple \( <R_{j1}, R_{j2}, R_{j3}> \) where \( R_{j1} \), \( R_{j2} \) and \( R_{j3} \) are mutually disjoint sets with \( R_{j1} \cup R_{j2} \cup R_{j3} = A^n \). \( R_{j1} \) is the set of n-tuples that belong to \( R_j \), \( R_{j2} \) is the set of n-tuples that do not belong to \( R_j \) and \( R_{j3} \) is the set of n-tuples for which it is not determined whether they belong to \( R_j \) or not. Now let \( \mathcal {A} = <A,R_i>_{i \in I} \) and \( \mathcal {B} = <B,R'_i>_{i \in I} \) be two partial structures. They are partially isomorphic if there exists a bijective function \( f:A \rightarrow B \) such that for all \( (x_1, x_2,...,x_n) \in A^n \), \( R_{j1}(x_1, x_2,...,x_n) \leftrightarrow R'_{j1}(f(x_1), f(x_2),...,f(x_n)) \) and for all \( (y_1, y_2,...,y_n) \in A^n \), \( R_{j2}(y_1, y_2,...,y_n) \leftrightarrow R'_{j2}(f(y_1), f(y_2),...,f(y_n)) \). Pincock (2005) and Frigg and Nguyen (2020, Chap. 4) have argued that partial structuralism cannot explicate the notion of idealization in scientific representation. In the following, we shall ignore this sort of partiality and treat structures and isomorphisms as total set-theoretic constructions.
For more details about the set-theoretic characterization of models of classical electrodynamics, see Muller (2007).
‘Purely’ might be construed as pointing to two different features of DEKI. Indicating that scientific representation is not based on more fundamental relations between model and target, the first feature distinguishes DEKI from similarity views. The second one suggests that scientific representation is not accounted for by picking out inferential model-target relations, enabling DEKI to be in contrast with inferentialist views.
The emphasis has been added.
The second emphasis has been added.
“However, although there are no full mappings between the empirical world and the mathematical structures [in cases involving idealizations], there are partial mappings between these empirical and mathematical structures.. A formal framework that represents these mappings very naturally is provided by the partial structures approach... The idea is that if there’s no complete information about a certain domain of investigation, we can represent formally the partiality of that information and structural relations between the various components involved in terms of the notions of partial structure and partial relation... In terms of partial structures, it’s possible to define various forms of partial mappings between these structures, such as partial isomorphism and partial homomorphism” (Bueno and Colyvan, 2011, p. 358).
The advocate of DEKI might be tempted to claim that ‘CE does not represent the magnetic field since the former does not denote the latter at all’. Such a response requires a criterion for denotation, though Frigg and Nguyen (2020, p. 180) have claimed that their account seems to be convenient to embed any theory of denotation. Millson and Risjord (2022b) have recently argued that the proponent of DEKI account, adopting either theory of denotation, causal-historical or descriptivist, is faced with a dilemma: either denotation is an entirely free action of user and then DEKI cannot distinguish justified from unjustified surrogative inferences, or DEKI can differentiate them and then denotation rides on other components of DEKI. For more on this, see Frigg and Nguyen (2022) and Millson and Risjord (2022a).
Any adequate theory of scientific representation, the proponents of DEKI account hold, needs to answer two, among others, certain questions, i.e. the semantic question (in virtue of what does a scientific model represent: a part of the world?) and the accuracy question (in virtue of what does a scientific model represent a part of the world accurately? (see e.g. Nguyen and Frigg, 2022).
“Whether a given representation serves certain purposes or not is a question that stands outside an account of representation.. The liquid drop model of the nucleus is useful to calculate fission energies; it leads us astray when we want to understand the inner structure of a nucleus. Representations represent what they do, and an account of representation has to tell us how they do so. Such an account doesn’t have to also issue warnings about what we can and cannot do with certain representations, or warn us about when these representations are misleading. When and to what extent a representation can be trusted is an important question, but it is not one that we should expect to be answered by an account of representation” (Frigg and Nguyen, 2020, p. 183). Thus understood, while DEKI examines the question ‘why is (not) a scientific representation accurate?’, ignores the question ‘why is (not) a key function found such that the target possesses (does not possess) the imputed features?’.
For an exposition, see Klausen (2020, Chap. 6).
Khalifa et al. argue that “there is a sense in which our account is explanatory” (Khalifa et al., 2022, p. 287) because, in their view, “(talk of) representation” is explained “by appeal to surrogative inference” (Khalifa et al., 2022, p. 288). However, the crucial point is that this kind of explanation is not substantial or constitutive, since the explanans does not constitute the explanandum. In other words, while substantialist accounts aim to explain the constitution question constitutively, deflationary ones do so by using deflationary explanation. For this reason, Khalifa et al. define a deflationary view by a thesis called ‘Deflationary Explanation’, which states: “The account does not explain the use of the concept scientific representation in terms of substantive relations” (Khalifa et al., 2022, p. 288). The alignment of the deflationary explanation concerning scientific representation with a specific non-constitutive notion of metaphysical explanation, perhaps one articulated by the non-cognitivist account of metaphysical explanation (Miller & Norton, 2023), raises an intriguing question that is beyond the scope of the present article.
For a quick survey, see Tahko and Lowe (2020).
This ‘tie’ may have several meanings. For instance, some grounding theorists (e.g. Audi, 2012; Schaffer, 2012) argue that ground is the backing relation for constitutive explanation, just as causal relation is the backing relation for causal explanation. Others (e.g. Fine, 2012; Raven, 2012) argue that ground is some sort of metaphysical explanation.
One may think of other sorts of explanation, e.g causal (the apple falls down towards the earth because the earth gravitationally attracts the apple) or mathematical (most of the sticks which are thrown upwards fall down horizontally because the number of degrees of freedom of horizontal movement is greater than of vertical movement (Lipton, 2009)). In both cases, the explanans does not constitute the explanandum. There are other sorts of metaphysical explanation which are not linked to ground. For instance, the explanation induced by supervenience is intensional, while the explanation of ground is hyperintensional (Raven, 2015).
For such a take on how ontological dependence is best regimented by the notion of grounding, see, for instance, Rosen (2010).
The emphasis has been added.
In their presentation of Suárez’s view, “A represents B if and only if (i) the representational force of A points toward B, (ii) A allows competent and informed agents to draw specific inferences regarding B, and (iii) x” (Khalifa et al., 2022, p. 289).
“While we have provided necessary and sufficient conditions for ‘M represents T’ we must not be misled by superficial matters of form.., not all formulations that use necessary and sufficient conditions are substantive analyses” (Khalifa et al., 2022, p. 287).
Here I intentionally use the term ‘thing’ to refer to the relata of grounding, refraining from adopting a certain position on the ontology of relata. I will return to this issue later in the Concluding Remarks.
Here I do not discuss whether partial ground is to be defined in terms of full ground or vice versa. For a discussion, see Trogdon and Witmer (2021).
Treisman and Gelade (1980) call feature types and their values, respectively, ‘dimensions’ and ‘features’.
For details of these problems and further ones challenging the application of Treisman’s model to multisensory perception, see Spence and Frings (2020).
The emphasis has been added.
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Acknowledgements
I would like to extend my sincere appreciation to the anonymous reviewers for this journal for their constructive engagement, invaluable comments and constructive feedback, which significantly contributed to the enhancement of this paper. Funding for this research was provided by Shahid Beheshti University (grant number sad/600/1316).
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Yaghmaie, A. Grounding scientific representation. Synthese 202, 197 (2023). https://doi.org/10.1007/s11229-023-04423-9
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DOI: https://doi.org/10.1007/s11229-023-04423-9