Abstract
In the early days of natural language semantics, Donald Davidson issued a challenge to those, like Richard Montague, who would do semantics in a model-theoretic framework that gives a central role to a model-relative notion of truth. Davidson argued that no theory of this kind can claim to be an account of real truth conditions unless it first makes clear how the relativized notion relates to our ordinary non-relativized notion of truth. In the 1990s, Davidson’s challenge was developed by Etchemendy into an argument against the model-theoretic account of logical consequence, one that also threatens the attempt to capture natural language entailment relations in modeltheoretic terms—one of the central desiderata of semantics. Nevertheless, the modeltheoretic framework has flourished within natural language semantics. But it has flourished without any consensus among semanticists as to how to answer Davidson’s challenge. The aim of this essay is to develop an answer. I argue that model-theoretic semantics is best understood as model-based science: a semantics for a natural language is a scientific model of truth conditions. This makes good sense of the way model-theoretic tools are used in natural language semantics. And it allows us to answer Davidson’s challenge by showing how a theory that employs a relativized notion of truth manages to tell us about ordinary truth conditions. Moreover, I argue that it helps us see how semantics can provide genuine explanations for natural language entailment and other truth-conditional phenomena.
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Notes
See e.g. Chierchia and McConnell-Ginet (2000), Jacobson (2014), and Kamp and Reyle (2013), as well as Partee (2008) and Dowty et al. (1981). Heim and Kratzer (1998) do not use a model-theoretic approach. But they make heavy use of Montague-style semantic types, and some of the ideas developed below about the theoretical significance of types can be applied to their approach as well. Larson and Segal (1995) is another influential textbook that eschews model theory; they share Davidson’s conviction that we need to move away from the model-theoretic framework if we are to capture ordinary truth conditions. To the extent that this essay is successful in clearing away the obstacle presented by Davidson and Etchemendy, it might help make the model-theoretic approach more broadly appealing.
Model-theoretic accounts typically treat truth as relative to further parameters as well, such as an assignment of values to variables. We’ll leave this aside here to simplify the discussion.
This is analogous to the question of how to distinguish logical consequence; just as a good account of structural entailment will not treat the ‘bachelor’/‘male’ entailment as structural, a good account of logical consequence presumably will not either. But though analogous, the questions are different. For one thing, characterizing logical consequence requires us to say something about how to distinguish the logical constants from other lexical items; but structural entailment patterns do not in general depend on the logical constants.
In fact, Etchemendy thinks that Tarski himself clearly had the interpretational construal in mind, and that it is just a mistake to construe his account of logical consequence representationally.
Strictly speaking, on the representational construal there is a class of structures that correctly represent reality; ordinary truth is taken to be truth relative to any of the structures in that class.
Sher (2020, (1996) gives a response to Etchemendy’s attack on the Tarskian account of logical consequence that is a version of the representational construal, insofar as it regards structures as representing all and only the possible ways the world could have been (in a very broad sense of possibility). Sher distinguishes logical consequence from necessitation by treating the former as a special case of the latter, one in which the logical constants play a certain role. Sher’s response to Etchemendy won’t help us to distinguish structural from lexical entailment in natural language, however. The paradigm instances of both structural and lexical entailment we have been working with here don’t even contain any logical constants.
See Balcerak Jackson (2006).
See Etchemendy (1999, Chapter 6).
Glanzberg (2009) also argues that we should not confuse semantic values with meanings.
Yalcin (2018) agrees that we should not think of assignments like (9) as specifying meanings in the ordinary, pre-theoretic sense. But he does think they provide more precise, theoretically well-informed successors to pre-theoretic meanings. I of course agree that semantic values have a job to do in the theory of meaning. But as we will see in Sect. 6, I do not think we need to view lexical semantic values as meanings in any sense in order to understand how they do that job.
See, for example, Elliott (2008).
We bracket the role of extra-linguistic context here for simplicity.
To think of the target system solely in terms of truth conditions is too simple; semantics is concerned with a broader range of phenomena that also includes at least presupposition and implicature. It is an interesting question how the model-theoretic account of truth conditions, and model-theoretic tools more generally, can be brought to bear to help us understand this broader range of phenomena.
Yalcin (2018, pp. 348-350) argues that lexical entries like (12) do not belong in a suitably scientific semantics, because science does not employ ordinary non-theoretical notions like smoking. But this concern is out of place when we approach semantics as model-based science. It is analogous to criticizing the MONIAC model on the grounds that a suitably scientific theory of the British macroeconomy should not employ ordinary plastic tubes and bathtub silicon.
Thanks to an anonymous referee for raising this question.
The expectation of compositionality might be justified in several different ways. One might regard compositionality as a conceptual or metaphysical truth about the target system. Or it might be motivated by views about the relationship between linguistic meaning and our ability to understand language. Or it might be justified on more methodological grounds internal to semantic theorizing. See Szabó (2017) for discussion.
Simchen (2017, (2019) recommends a related kind of explanatory structure fit, one that aims to capture the explanatory priority of the semantic properties of singular terms, predicates, and so on in settling sentential truth values. Some so-called interpretationists, such as Lewis (1975), take the opposing view that there are not enough determinate compositional facts to let us choose one semantics among many truth-conditionally equivalent competitors. From the present perspective, this is a disagreement about the nature of the target system modeled by semantics, and consequently about what there is for semantics to model.
See Balcerak Jackson (2017).
Whether the focus is on the actual truth conditions of sentences, or more on the way they are determined (or both) depends on what sort of fit we expect from our model.
The model was in fact independently developed by its two namesakes to model these two target systems.
I would like to thank Otávio Bueno, Michael De, Paul Dekker, Peter Godfrey-Smith, Paul Pietroski, and Ede Zimmermann for helpful discussion of the ideas in this paper, as well as audiences at the Logic Colloquium at the University of Konstanz, and the Semantics and Philosophy in Europe 11 conference at the University of Warsaw. I am also grateful to Magdalena Balcerak Jackson for her always thoughtful and unerringly helpful feedback.
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Magdalena Balcerak Jackson, Otávio Bueno, Michael De, Paul Dekker, Peter Godfrey-Smith, Paul Pietroski, Thomas Ede Zimmermann.
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Jackson, B.B. Model-theoretic semantics as model-based science. Synthese 199, 3061–3081 (2021). https://doi.org/10.1007/s11229-020-02924-5
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DOI: https://doi.org/10.1007/s11229-020-02924-5