Abstract
The major argument against Ramsey-style epistemic structural realism is the model-theoretic refinement of Newman’s objection against Russell, presented in Ketland (Brit J Philos Sci 55(2): 409–424, 2004), where a technical result is interpreted as showing that the Ramsey-sentence approach collapses into instrumentalism. This paper addresses some questions raised by the application of model theory to the scientific realism debate. Firstly, I will suggest three different formal semantics for the positions in the debate. Then, some technicalities of Ketland’s result will be scrutinized in light of comments by Zahar and Demopoulos. Finally, I will formalize Ketland’s argument by means of an intensional operator and focus on one problematic premise. The conclusion is that, with some adjustments, the Ramsey-sentence approach can represent an intermediate position between realism and instrumentalism, but the term “structuralism” does not suit it well.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Notes
The abbreviation “TC” refers to the distinction between “theoretical postulates” (in which no observational term appears) and “correspondence postulates” (in which both kinds of terms appear, linking the two vocabulary levels). I use “TC” referring sometimes to an arbitrary theory, finitely axiomatized, and sometimes to the matrix obtained by substituting its theoretical terms with variables; the context will make clear which is intended.
Worrall (1989) is the seminal paper in which structural realism is presented as a solution to the main arguments put forward in the debate: the pessimistic induction against scientific realism and the no-miracle argument against instrumentalism. Worrall’s line of thought is referred to as epistemic structural realism. Another version of scientific structuralism, known as ontic structural realism, pertains metaphysics. Frigg and Votsis (2011) and Bokulich and Bokulich (2011) are comprehensive surveys of both forms of structural realism. In this paper, I exclusively focus on epistemic structural realism, omitting the word “epistemic”.
Mathematical entities are usually considered as theoretical entities. Carnap even claimed that the theoretical entities assumed by mature sciences are reducible to mathematical entities (I thank an anonymous referee for stressing this point). Personally, I would prefer to posit an independent subdomain of mathematical entities beside a subdomain of genuine, non-mathematical theoretical entities, but in the following I will not address this difficult issue, which would make the model-theoretic formalism still more cumbersome.
See Azzouni (2000: Part III), where arguments by Quine, Field and Putnam are considered.
See Putnam (1978: 123–140).
See Psillos (1999: 278): “I am personally sceptical about the prospects of formalizing the notion of truth-likeness. There is an irreducibly qualitative element in the notion of approximation, i.e. the respects in and degrees to which one description may be said to approximate another. But I do not think that the intuitive notion of truth-likeness already operating in science is unclear. Here the comparison with the formal Tarskian understanding of truth is not helpful”.
The use of free logic is recommended in Lewis (1970). Actually, free logic deals with the reference failure of individual constants, while theoretical terms in science are usually predicates. The possibility of transforming predicate symbols into individual constants that denote predicate extensions will be discussed in Sect. 3 below.
Completions are similar to extensions (structures with an enlarged domain), but they involve the interpretation of constants that are not interpreted in the basic structure (for this reason, completions should be distinguished from extensions).
“Part of the structure” is a comfortable but imprecise expression. The right technical expression would be “the reduct of the substructure of the full model”: the domain Do of Mo is a subset (therefore the term “substructure”) and the interpretation function io is restricted to the O-vocabulary (therefore the term “reduct”).
Ketland (2004) uses two sorts of individual variables, one ranging over the observational subdomain, the other ranging over the theoretical subdomain. Ketland (2009: 41–42) considers a one-sorted formalization. This technical subtlety in the formalism involves some changes in the definitions for the two systems.
It seems to me that Demopoulos’s appeal to arbitrary extensions conflates the Ramsey-sentence approach into instrumentalism, in light of the general model-theoretic result that Van Benthem formulates as follows: “For first-order theories T, each model M of TLO has an LO-elementary extension to a model for T in its full language, i.e. a model of M+ with possibly new objects where all tuples of M-objects still satisfies the same first-order formulas as in M″ (Van Benthem 2012: 779).This amounts to saying that the Ramsey-sentence formulated with is true iff the theory is weakly empirically adequate.
As highlighted by an anonymous reviewer, the ether hypothesis was shown to be empirically incorrect by Michelson and Morley. Therefore, the empirical adequacy of Fresnel’s theory should be relativized to a specific set of optical phenomena. Even when loosely applied to the history of science, empirical adequacy is slippery and definitely far from being a trivial property of scientific theories.
In this example, I adopt the less immediate understanding of a concept as a provisional criterion of theoreticity.
The stronger notion of O-adequacy defined in Ketland (2009) implies T-cardinality correctness. If Ketland’s theorem is formulated with the notion of O-adequacy, it loses some argumentative strength, because the link between O-adequacy and the intuitive notion of empirical adequacy is blurred.
Ketland’s truth conditions for the Ramsey-sentence refers to the privileged interpretation domain “(DO, DT)” which is equivalent to our W. Ketland (2004) identifies structural realism with the position that asserts the truth of the theory’s Ramsey-sentence (instead of the truth of the full theory) under the interpretation in “(DO, DT)”; this identification is problematic (see Sect. 2.3 above).
I skip the issues of mixed predicates (relations that connect observational with theoretical entities) and of the two sorts of individual variables. Furthermore, I substitute with identity the isomorphism relation between the observational parts of different models.
More precisely: if the second-order semantics considers Henkin structures (so-called general semantics), the variables do not range over the entire power set of Wn, but over the subsets which are definable from formulas of the theory’s language and parameters. However, this technical detail is not relevant for my argument.
I admit that this quick explanation of the distinction is highly problematic: an instrumentalist would plausibly abstain from the metaphysically loaded expression “structure of reality”.
Chakravartty and van Fraassen (2018) discuss how the doxastic attitude of belief enters in the definition of scientific realism. My proposal of an intensional operator for metatheoretic claims is probably coherent with van Fraassen’s idea that the realism vs. instrumentalism debate turns on the norms of rationality for belief at the meta-level of analysis and interpretation of science.
Cruse (2005) similarly introduces the expression “Ramsey-sentence realism”.
An accurate translation of Sneed’s structuralist approach into a more standard logical format can be found in Andreas (2020, Chapters 5–6). I thank an anonymous referee for pointing out this reference.
Sneed (1979: Chapter IV) explains cases of reciprocal constraints among different limited applications of a ramsified theory. Sneed considers constraints on function values, but our problem of completion cardinalities is similar.
References
Ainsworth, P. (2009). Newman’s objection. British Journal for the Philosophy of Science, 60(1), 135–171.
Andreas, H. (2020). Dynamic tractable reasoning: A modular approach to belief revision. Cham: Springer.
Azzouni, J. (2000). Knowledge and reference in empirical science. London: Routledge.
Bencivenga, E. (1986). Free logics. Alternatives to classical logic. In D. Gabbay & F. Guenther (Eds.), Handbook of philosophical logic (Vol. III, pp. 373–426). Dordrecht: Reidel.
Bokulich, P., & Bokulich, A. (Eds.). (2011). Scientific structuralism. Boston studies in the philosophy of science (Vol. 28). Dordrecht: Springer.
Chakravartty, A., & van Fraassen, B. (2018). What is scientific realism? Spontaneous Generations: A Journal for the History and Philosophy of Science, 9(1), 12–25.
Cruse, P. (2005). Ramsey sentences, structural realism and trivial realization. Studies in the History and Philosophy of Science, 35, 557–576.
Demopoulos, W. (2011). Three views of theoretical knowledge. British Journal for the Philosophy of Science, 62(1), 177–205.
Demopoulos, W., & Friedman, M. (1985). Critical notice: Bertrand Russel’s The Analysis of matter: Its historical context and contemporary interest. Philosophy of Science, 52, 621–639.
Frigg, R., & Votsis, I. (2011). Everything you always wanted to know about structural realism but were afraid to ask. European Journal for Philosophy of Science, 1(2), 227–276.
Ketland, J. (2004). Empirical adequacy and ramsification. British Journal for the Philosophy of Science, 55(2), 409–424.
Ketland, J. (2009). Empirical adequacy and ramsification, II. In A. Hieke & H. Leitgeb (Eds.), Reduction, abstraction, analysis (pp. 29–45). Frankfurt a. M.: Ontos Verlag.
Lewis, D. (1970). How to define theoretical terms. Journal of Philosophy, 67, 427–446.
Psillos, S. (1999). Scientific realism: How science tracks truth. London: Routledge.
Putnam, H. (1978). Realism and reason. In H. Putnam (Ed.), Meaning and the moral sciences (pp. 123–138). London: Routledge.
Sneed, J. D. (1979). The logical structure of mathematical physics. Dordrecht: Reidel.
van Benthem, J. (2012). The logic of empirical theories revisited. Synthese, 186, 775–792.
Worrall, J. (1989). Structural realism: The best of both worlds? Dialectica, 43, 99–124.
Zahar, E. (2007). Why science needs metaphysics: A plea for structural realism. Chicago: Open Court.
Acknowledgements
I am deeply indebted to two anonymous reviewers whose suggestions led to considerable improvement of a previous version of the paper. My special thanks go to them and to Prof. Pierdaniele Giaretta for valuable discussions and encouragement.
Funding
Not applicable.
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest
The corresponding author states that there is no conflict of interest.
Rights and permissions
About this article
Cite this article
Del Din, G. Some Model-Theoretic Remarks on the Ramsey Sentence, with a Closer Look at Ketland’s Argument. Found Sci 26, 881–900 (2021). https://doi.org/10.1007/s10699-021-09778-1
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10699-021-09778-1