Abstract
This paper criticizes Soames’s main argument against a variant of two-dimensionalism that he calls strong two-dimensionalism. The idea of Soames’s argument is to show that the strong two-dimensionalist’s semantics for belief ascriptions delivers wrong semantic verdicts about certain complex modal sentences that contain both such ascriptions and claims about the truth of the ascribed beliefs. A closer look at the formal semantics underlying strong two-dimensionalism reveals that there are two feasible ways of specifying the truth conditions for claims of the latter sort. Only one of the two yields the problematic semantic verdicts, so strong two-dimensionalists can avoid Soames’s argument by settling for the other way.
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Notes
I agree with Dever concerning this point. See Dever (2007, pp. 9–10).
Soames finds Jackson to be ‘[…] less than fully explicit […]’ (Soames 2005b, p. 172) about the semantics of attitude ascriptions, but argues that he should be understood as implicitly endorsing the strong two-dimensionalist proposal (See Soames (2005b, pp. 173–175)). Concerning Chalmers, Soames admits that ‘[…] he has very little explicitly to say about the semantics of propositional attitude ascriptions in The Conscious Mind.’ (Soames 2005b, p. 235).
A different perspective on Argument 1 has recently been offered in Dever (2007). I largely agree with Dever’s diagnosis of his more abstract reconstruction of Argument 1, but I also think that Soames’s original formulation of the argument raises important issues concerning the two-dimensionalist treatment of belief ascriptions that are lost in Dever’s reconstruction.
Some authors call them 1- and 2-Intensions or A- and B-Intensions, respectively.
See Chalmers (2006) for a comprehensive discussion of different interpretations of the primary intension and of Chalmers’s favoured epistemic interpretation of two-dimensional semantics.
Formulas that occur in prose sentences are sometimes mentioned, sometimes used. I will take the liberty of omitting the usual quotes.
The syntax and the semantics could easily be modified to account for the beliefs of multiple individuals by adding a set of indexed belief-operators to the language, by adding a set of individuals I to the model and by replacing b by \({b' \in \lbrace F: I \times C \times W \mapsto \fancyscript{P}(C) \rbrace. }\) Worlds considered as actual could then be identified with tupels of a world and an individual \(\langle w, i \rangle\) (centered worlds).
Note that models as defined above lack the accessibility-relation one comes to expect in a modal semantics. This simplification is unproblematic in the context of this paper, since such a relation plays no role in Soames’s argument.
The idea underlying the semantics for the ‘actually’-operator @ is that ‘actually’ shifts the semantic focus to the current world considered as actual. A formally similar semantics for ‘actually’ is discussed in Cresswell (1990), chapter 3. The major alternative for a two-dimensionalist is a semantics that lets @ shift the world under consideration to a fixed world that is specified as a part of the model. This approach requires a different model theory, the classical exposition of which can be found in Davies and Humberstone (1980). The approach pursued in the current paper is briefly mentioned on p. 4–5 and in notes 4 and 5 on p. 26 of Davies and Humberstone (1980). My main argument can be made given either kind of model theory.
Compare the definition of content on p. 546 and the definition of character on p. 548 of Kaplan (1989).
T5a and T5b are introduced on pp. 268–269 of Soames (2005b). The semantics for □ and B captures the contents of the two definitions, so I will not quote them here.
The formalization treats sentences of the form ‘The actual F is the actual G’ and ‘Actually, the F is the G’, where F and G are definite descriptions, as having the same meaning. This is unproblematic in the context of this paper.
More precisely: Assume that logical truth is defined in the following way: ϕ is a logical truth iff for every \({{\mathfrak{M}}, {\text{for}}\,c \in C \in {{\mathfrak{M},{\text{for}}\,w \in {W} \in {\mathfrak{M}}},{\mathfrak{M}},c,w\,\vDash\,\phi.}}\) Given this definition, \(( B(\phi) \leftrightarrow B(@ \phi) )\) is a logical truth of strong two-dimensionalism, since per definition \({\left[\left[\phi\right]\right]_{1}^{\mathfrak{M}} = \left[\left[ @ \phi \right]\right]_{1}^{\mathfrak{M}}.}\)
A more compelling example can be given in a model that contains more than one individual: Johann’s actually false belief that Johann does not exist could rightly be said to be true with respect to a world considered as actual that contains a subject other than Johann, in which Johann does not exist and in which he consequently entertains no beliefs.
The two proposals notably differ in their treatment of instances of @ in sentences of the form Tr (@ ϕ). Given PT2, @ is vacuous if it occurs embedded under Tr, so the equivalence \(Tr (\phi) \leftrightarrow Tr ( @ \phi)\) holds. This equivalence does not generally hold given ST.
I am not convinced that we have reliable theory-independent intuitions about the truth values of complex modal sentences of the kind in question, but I accept Soames’s claim for the sake of the argument.
See footnote 12.
Note that the truth value of p is not sensitive to the world considered as actual since it contains no indexical element.
From here on, strong two-dimensionalism will be taken to include ST, unless explicitly stated otherwise.
Chalmers (2011) presents a two-dimensionalist theory of attitude ascriptions which employs complex propositions of a similar kind.
Such a valuation function v′ could be defined in the following way: \({v' \in \lbrace F: \mathsf{P} \mapsto \langle \fancyscript{P}(C), \langle \langle c_1, \fancyscript{P}(W) \rangle, \ldots , \langle c_n, \fancyscript{P}(W) \rangle \rangle \rangle \rbrace. }\) The first element in the sequence represents the primary proposition, the elements in the embedded sequence represent secondary propositions relative to the members of C. This gives us the following semantics:
$$ \begin{aligned} {\mathfrak{M}},c,w \,&\vDash\, p\quad\hbox{iff}\;w \in \left[\left[\phi\right]\right]^{{\mathfrak{M}}}_{2} \in \langle c,\left[\left[\phi\right]\right]^{{\mathfrak{M}}}_{2} \rangle \in v'(p)\\ {\mathfrak{M}},c,w \,&\vDash\, \neg \phi\quad\hbox{iff}\;{\mathfrak{M}},c,w \,\nvDash\, \phi\\ {\mathfrak{M}},c,w \,&\vDash\, (\phi\land\psi)\quad\hbox{iff}\;{\mathfrak{M}},c,w\,\vDash\,\phi \,\hbox{and}\, {\mathfrak{M}},c,w\,\vDash\,\psi\\ {\mathfrak{M}},c,w \,&\vDash\, \square \phi \quad\hbox{iff\;for\;all}\; w': {\mathfrak{M}},c,w'\,\vDash\,\phi\\ {\mathfrak{M}},c,w \,&\vDash\, @ \phi \quad\hbox{iff}\; {\mathfrak{M}},c,c\,\vDash\,\phi\\ {\mathfrak{M}},c,w \,&\vDash\, B(\phi) \quad\hbox{iff}\; b( \langle c,w \rangle ) \subseteq \left[\left[\phi\right]\right]_{1}^{{\mathfrak{M}}} \in v'(\phi)\\ {\mathfrak{M}},c,w \,&\,\vDash\, Tr (\phi) \quad\hbox{iff}\; {\mathfrak{M}},c,w\,\vDash\,\phi \;\hbox{and}\; \exists\;c',\;w' \,\hbox{so\;that}\; {\mathfrak{M}},c',\;w'\,\vDash\, B (\phi) \end{aligned} $$See Soames (2005b), pp. 313ff for the original definition.
Note that the second strategy could rightly be called ad hoc, if it turned out that the only motivation for the proposed reformulation was its utility for the sketched response to the argument against ST.
Lewis could be read as advocating a view like this. See Lewis (1986), chapter 1.2, pp. 40–41.
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Acknowledgements
Versions of this paper have been presented at a research colloquium at the University of Konstanz, at GAP.7 in Bremen, at the reading group of the Emmy Noether-Research Group Understanding and the A Priori in Cologne and at the Meaning, Modality and Apriority symposium in Cologne. Thanks to all who provided feedback on these occasions. I am especially grateful to an anonymous reviewer, Brendan Balcerak Jackson, Fabrice Correia, Natalja Deng, Maryia Ramanava, Wolfgang Schwarz, Scott Soames, Wolfgang Spohn, and most of all Peter Fritz for valuable suggestions, comments and discussions. The research leading to these results has received funding from the European Community’s Seventh Framework Programme FP7/2007–2013 under grant agreement no. FP7-238128.
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Michels, R. Soames’s argument 1 against strong two-dimensionalism. Philos Stud 161, 403–420 (2012). https://doi.org/10.1007/s11098-011-9746-x
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DOI: https://doi.org/10.1007/s11098-011-9746-x