Abstract
In this paper, we examine the issue of the empirical or non-empirical status of philosophical metatheories. In particular, we ask whether a specific type of metatheoretical product, formal reconstructions of scientific theories, can be empirically tested. To answer this, we take Metatheoretical Structuralism as a metatheory and Classical Mechanics as our case studies. We show how classical mechanics can be reconstructed from structuralism. We then present a computer program, called Reconstructor, and show how it can be used to test the adequacy of the reconstruction. Finally, we discuss some philosophical points regarding these tests, namely, the issues of holism, circularity and metatheoretical predictions.
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Notes
In this regard, our project can be considered part of this naturalistic or “(meta-)empirical” tradition in the philosophy of science (we thank an anonymous reviewer for this suggestion), from Whewell and Mach, through Carnap and Neurath, to Van Fraassen or Giere. This tradition, though, is complex and the different positions within it involve subtle differences in which we cannot enter here. What matters to our present concerns, is that it suggests that metascience (or at least some of its parts) could in principle be tested in an analogous manner to science itself. Our following testing proposal elaborates this suggestion in one of its possible directions, for there may be other “meta-testing” proposals that test other parts of meta-science (for instance, Estany, 1990, tests Kuhn’s, Lakatos’ and Laudan’s different meta-scientific models of scientific change against different historical episodes).
One might object that the project of empirically testing metatheories would make sense if the task of metatheories were descriptive, which is at least controversial; for instance, Moulines (1991) has defended that the task of metatheories is better characterized as interpretation than as description (we thank an anonymous reviewer for this comment). First, it is not clear that interpretations cannot be tested, they seem to be testable, to the extent that they generate (metatheoretical) predictions—see below. Second, and relatedly, even if metatheories are interpretations they may have a descriptive component (Moulines himself acknowledges this in a later work, see Díez and Moulines 1997). For example, all theories that are not non-directly self-confirmed (the usual case in science) are tested with data that are measured/gathered independently of the theoretical assumptions/laws used to make the relevant predictions, which is why those predictions can, and sometimes do, fail. Different metatheories may reconstruct this fact in partially different ways, and some ways may be more fruitful than others, but all metatheories (that have a minimal adequacy) should be suitable for our kind of meta-testing in this regard.
Note that this distinction between “primitive” and “derived” laws has nothing to do with the distinction in MS we introduce below between general guiding principles and their special laws, which, as we will clarify, are not “derived” from the guiding principles at all, but introduce new content by specifying some parameters left open in the guiding principles. In the sense of “primitive” used here, (some) specializations are primitive (and of course, some others are derived from the former).
Since forces (symbolized by f) are 3-dimensional vectors, the right-hand side of the following equalities must also be vectors. In 3 this is already so, given the vectorial difference of positions. In 2 and 4, where the gravitational constant g intervenes, we take g to be a vector (of magnitude 9,81 m/s2 in the MKS system, and a downward direction, perpendicular to Earth’s surface—or towards the Earth’s center from the particle’s position, to be more precise). For the electrostatic case (axiom 5), we multiply by the unitary vector (s(p1, t) − s(p2, t)) / |(s(p1, t) − s(p2, t))| in the direction from one particle to the other. For a technically more elegant formulation, cf, Balzer et al. ch 4.
Notice that there is an additional function here (the electrical charge function q), as well as several constants, that we did not introduce above as part of the basic language / potential models of the theory. This was for simplicity’s sake. In the computer program below, we load everything at once.
Since a T-non-theoretical concept may be T*-theoretical relative to different theory T*, T-data may be “theory-laden”, but laden by a theory that is not the one being tested against this data. This is why there are no (local) self-confirmations and T-tests are fallible. Important as these issues are, we are not going to deal with them here any further, since nothing in what follows, and in the examples below, depends on it.
MS also introduces two other sets representing two other kinds of theoretical restrictions on T-models: Constraints (C) and intertheoretical links (L), but since nothing in our case depends on these complexities we will skip them here.
To avoid confusion later on, remember that this empirical claim describes how the object theory (in this case, CM) is to be tested, not the metatheory (structuralism).
Note the automatic coloring of parenthesis to make it easier to keep track of them, as well as the fact that the program ignores whitespaces.
Note that, in the following examples, the intended applications are accounted for by combining theoretical laws that belong to different specialization branches of the theory-net (e.g., free fall and Hooke laws), which makes them technically “conjoin subspecializations”. Whether these conjoin subspecializations may be represented in the theory-net as new “terminal” specializations, or it is better to consider their combination simply as a case of a practical joint application, is an interesting intra-structuralist issue we cannot enter here (just briefly: it is one thing to use different specializations to account for one intended application, it is another quite different thing to further specialize two different theory elements by conjoining their laws and adding some new ones, as it happens in a complete reconstruction of CM—as it is done e.g. in Balzer, Moulines & Sneed, 1987, ch. 4). Nothing, though, hinges on that for our present concerns.
If, later on, we ask Reconstructor to evaluate sentences in this model that make use of those constants, they will likely get the indeterminate value as an output. In fact, Reconstructor uses a 3-valued paracomplete logic to evaluate sentences in models. The semantics are such that for classical inputs, the program always returns classical values (true and false), but we might get the indeterminate value if some denotation is empty or incomplete. See Roffé (2019, 2020) for a complete specification of the semantics that the program uses.
In Reconstructor, we multiply the previous version of Coulomb’s law by a factor of (s(p1, t) − s(p2, t)) / | s(p1, t) − s(p2, t) |. This is just to give the corresponding force a direction.
As a side note, the second point is worth mentioning since the use of computer programs in science is ubiquitous, and computational tools are not the kind of thing that is usually thought of as being a part of what is being tested in discussions of holism. Also, to reassure the reader, both Reconstructor and the programming language it is written in (Python) have been extensively tested (which is not to say that some corner cases may originate bugs).
This is debatable and assumes Díez’s account of explanation (see Díez, 2013). There is also a debate as to whether all or some of the new concepts in the explanans have to be T-theoretical, see the papers mentioned in footnote 8.
This is not to say that fundamental laws are never revised, but only that when they are, then, in Kuhnian terms, a scientific revolution is taking place (i.e. the researchers are not working with the same theory anymore).
We thank an anonymous reviewer for bringing this to our attention.
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Acknowledgements
Ariel Jonathan Roffé acknowledges the support of the following research projects: PUNQ 1401/15 (Universidad Nacional de Quilmes, Argentina), UNTREF 32/19 80120190100217TF (Universidad Nacional Tres de Febrero, Argentina), UBACyT 20020190200360BA (Universidad de Buenos Aires, Argentina), PICT-2018-3454 and PICT-2020-SERIEA-01653 (ANPCyT, Argentina), José Díez acknowledges the support of the following Catalan and Spanish research grants: 2021-SGR-00276, FFI2016-76799-P, PID2020-115114GB-I00, and CEX2021-001169-M funded by MCIN/AEI/https://doi.org/10.13039/501100011033.
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Roffé, A.J., Díez, J. Is it Possible to Empirically Test a Metatheory?. Found Sci (2024). https://doi.org/10.1007/s10699-024-09938-z
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DOI: https://doi.org/10.1007/s10699-024-09938-z