Here, we deal with the question of under which circumstances can scientists achieve a legitimate understanding of defective theories qua defective. We claim that scientists understand a theory if they can recognize the theory’s underlying inference pattern(s) and if they can reconstruct and explain what is going on in specific cases of defective theories as well as consider what the theory would do if non-defective—even before finding ways of fixing it. Furthermore, we discuss the implications of this approach to understanding the meta-metaphysics of Quantum Mechanics, specifically with regard to Quasi-set theory. We illustrate this by employing Quasi-set theory to structure a defective scientific theory and make possible the understanding of the theory.
- Scientific understanding
- Quasi-set theory
- Non-individuality in quantum mechanics
María del Rosario Martínez-Ordaz’s research was supported by the Programa Nacional de Pós-Doutorado PNPD/CAPES (Brazil).
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We are presupposing some form of scientific realism is true as part of their working assumptions.
It is important to notice that it’s no requirement of ours that this type of epistemic modality should be metaphysically primitive.
For a similar characterization of the components of understanding, see Bengson (2018: 19–20).
What happens in cases where agents might think they understanding, but they are wrong about that will be discussed in Sect. 6.3.
We are aware of the fact that there is an ongoing philosophical debate about the status of the different characterizations of scientific theories (see Halvorson (2016) for a comprehensive revision of the different views on scientific theories); however, we think this will suffice for the purposes of the paper.
In the literature we can find examples of metaphysicians defending that possibility that reality itself is indeterminate, inconsistent, disjoint and so on (Cf. Cartwright, 1999; Priest, 1985; Torza, 2021). However, on the methodologically conservative picture reality is consistent or coherent; fully determinate and unified or integrated into a whole.
For a comprehensive critical analysis of the epistemic robustness of quantum mechanics see Hoefer (2020).
Russell gives a metaphysical defense of the principle in his An Inquiry Into Meaning and Truth (1959). On the interpretation of Principia Mathematica’s metaphysical logic see Landini (1998), Linsky (1999), and Klement (2018). It is interesting, in this connection, to consider that philosophers such as Russell and Frege felt that there had to be a philosophical elucidation of the systems of higher-order logic they were working on in spite of them being systems of logic and not applied mathematics. We think this bolsters our view about the generality of understanding as an epistemic activity.
Such as the left-hand and the right-hand.
It is important to notice that for the non-factivist, the non-true propositions that can be included into the content of understanding are exclusively those that lead to (empirical) success when being used. These propositions have been called felicitous falsehoods and are falsehoods that facilitate understanding by virtue of being the falsehoods they are and whose “divergence from truth or representational accuracy fosters their epistemic functioning” (Elgin, 2017: 1) .
We do not take a stance on the nature of possible worlds in this paper, we use the concept as shorthand for possibilities. For a contemporary sympathetic and systematic approach to possible world realism, however, see Bricker (2020).
Relatedly, the notion of “structure” plays an important role in debates about scientific realism, structural realism, and so on (Russell, 1927; Frigg and Votsis, 2011; French, 2014). We assume that the notion of a mathematical structure e.g., the natural number structure, the real number structure, is robust enough that there is no methodological need to dive further here given our aims.
The notion of modal understanding has been used by Le Bihan (2017) to address the way in which we understand theories and models that misrepresent the actual world by not being true. Here, we extend its scope in two directions: we cover other cases of defects, besides falsehood, and we explain its structuralist grounds.
This point is discussed in more detail in Sect. 6.5.2.
For a detailed discussion on this topic, see Macías-Bustos (2022a).
For the sake of argument suppose you take all axioms of a plurality of fundamental theories as the axioms of the one fundamental metaphysical theory, as in the Best System Accounts of Laws according to which the laws of nature are the axioms of our best theory that best balance simplicity and strength.
Quasi-set theory is also not a classical theory at the level of its logical consequence relation, which is paraconsistent i.e., it is inconsistency tolerant.
Infinite dimensional when we consider the position, even for a single particle as there will be an infinite number of mutually orthogonal eigenvectors associated with the position operator.
For a more comprehensive discussion on this issue, see Macías-Bustos (2022b).
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The first author wants to thank Phil Bricker and Kevin Klement for valuable discussions on metaphysics and the philosophy of logic relevant to portions of this work. We thank the reviewer for the suggestions and critical comments. Also, thanks to Jonas Arenhart and Raoni Arroyo for their assistance during the process of getting the paper ready: they kindly dealt with our delays and other difficulties still inherent to editorial processes.
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Macías-Bustos, M., Martínez-Ordaz, M.d.R. (2023). Understanding Defective Theories. In: Arenhart, J.R.B., Arroyo, R.W. (eds) Non-Reflexive Logics, Non-Individuals, and the Philosophy of Quantum Mechanics. Synthese Library, vol 476. Springer, Cham. https://doi.org/10.1007/978-3-031-31840-5_6
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