Reply to Bourget and Mendelovici

ABSTRACT

We detect three main critical ideas in Bourget and Mendelovici's (2022; henceforth BM) discussion of Narrow Content (Yli-Vakkuri and Hawthorne 2018). We will discuss each in this reply.

KEYWORDS:

• Narrow mental content
• semantic externalism
• semantic internalism

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

1 Our formalizations are in the language of higher-order logic with the following non-logical constants, where a numerical superscript indicates the adicity of a predicate. (1) $\mathsf{A}:o\to o\left(\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{f}\mathrm{u}\mathrm{n}\mathrm{c}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n}\mathrm{t}\mathrm{h}\mathrm{a}\mathrm{t}\mathrm{m}\mathrm{a}\mathrm{p}\mathrm{s}\mathrm{a}\mathrm{t}\mathrm{h}\mathrm{o}\mathrm{u}\mathrm{g}\mathrm{h}\mathrm{t}\mathrm{t}\mathrm{o}\mathrm{i}\mathrm{t}\mathrm{s}\mathrm{a}\mathrm{g}\mathrm{e}\mathrm{n}\mathrm{t}\right)$(1) (2) ${\mathsf{T}\mathsf{h}\mathsf{o}\mathsf{u}\mathsf{g}\mathsf{h}\mathsf{t}}^3:o\to o\to t\to t$(2) (3) $\mathsf{I}\mathsf{n}\mathsf{t}\mathsf{r}\mathsf{i}\mathsf{n}\mathsf{s}\mathsf{i}\mathsf{c}:(o\to o\to t)\to t$(3) (4) $\mathsf{Q}\mathsf{u}\mathsf{a}\mathsf{l}\mathsf{i}\mathsf{t}\mathsf{a}\mathsf{t}\mathsf{i}\mathsf{v}\mathsf{e}:(o\to o\to t)\to t$(4) o here is the type of objects, which we take to include both agents and events. We only assume that o is some simple type or other. On Russell–Carnap proposal considered below, o is $e\to t$. We adopt the following further definitions. (5) ${\mathrm{T}\mathrm{h}\mathrm{o}\mathrm{u}\mathrm{g}\mathrm{h}\mathrm{t}}^1:=\lambda t.\mathrm{\exists }ap.\mathrm{T}\mathrm{h}\mathrm{o}\mathrm{u}\mathrm{g}\mathrm{h}\mathrm{t}tap$(5) (6) ${\mathrm{T}\mathrm{h}\mathrm{i}\mathrm{n}\mathrm{k}\mathrm{s}}^2:=\lambda ap.\mathrm{\exists }t.\mathrm{T}\mathrm{h}\mathrm{o}\mathrm{u}\mathrm{g}\mathrm{h}\mathrm{t}tap$(6) We should have made it more explicit in Narrow Content that our key primitive is the three-place thought predicate, the one we use when we say things like ‘t is a thought of agent a that p’. A more natural use of this notion is found in sentences like ‘I have a thought that p, and that thought has a different etiology than your thought that p’. The property of being a thought (${\mathsf{T}\mathsf{h}\mathsf{o}\mathsf{u}\mathsf{g}\mathsf{h}\mathsf{t}}^1$) and the dyadic relation of thinking (${\mathsf{T}\mathsf{h}\mathsf{i}\mathsf{n}\mathsf{k}\mathsf{s}}^2$) are defined as existential generalizations of that primitive, as above. The notion of a content assignment ($\mathsf{C}\mathsf{A}$) is defined as follows. $\mathrm{C}\mathrm{A}:=\lambda R.\text{□}.(\mathrm{F}\mathrm{u}\mathrm{n}\mathrm{c}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n}\mathrm{a}\mathrm{l}R\wedge \mathrm{\forall }x.((\mathrm{\exists }p.Rxp)\leftrightarrow {\mathrm{T}\mathrm{h}\mathrm{o}\mathrm{u}\mathrm{g}\mathrm{h}\mathrm{t}}^{1}x\left)\right)$That is, a content assignment is a relation that is necessarily functional (where $\mathsf{F}\mathsf{u}\mathsf{n}\mathsf{c}\mathsf{t}\mathsf{i}\mathsf{o}\mathsf{n}\mathsf{a}\mathsf{l}:=\lambda R.\mathrm{\forall }xyz.\left(\right(Rxy\wedge Rxz)\to y=z)$) and necessarily relates all and only thoughts to anything. In Narrow Content we called content assignments ‘functions’, which is unfortunate because it suggests that content assignments assign whatever they assign to a thought necessarily (our notation also suggested this). ‘Functional relation’ would have been a better term. We also presupposed some system of higher-order logic but never said what it was. One of us (Yli-Vakkuri) thinks that the book would have been better, albeit perhaps less approachable, if we had included some definite formal system in an appendix. We now think that the right system to use, had we had such an appendix, would have been $\mathsf{L}\mathsf{F}$ from Goodsell and Yli-Vakkuri (n.d.).

2 In Chapter 3 of Yli-Vakkuri and Hawthorne (2018). See also Yli-Vakkuri (2018).

3 We are using three-place rather than two-place relations here because that makes it easier to encode the mereological structure of the agent in the $\mathsf{A}\mathsf{P}$. Thanks to Zachary Goodsell for suggesting this approach.

4 See Russell (1927): Ch. XXIII and 246–247, and Carnap (1958): 161.

5 One of us (Hawthorne) is somewhat inclined to do so, while one of us (Yli-Vakkuri) fully embraces the advice and adopts Carnap's Language Form IIIα (Carnap 1958: 161) in the section on physics in Goodsell and Yli-Vakkuri (n.d.)

6 Namely, as: (12) $\le :=\lambda X^o{Y}^o.(\mathrm{\exists }X\wedge (X\subseteq Y\left)\right).$(12)

7 See Arntzenius (2012): Chs. 4–5.

8 Those who adopt the aforementioned Russell–Carnap proposal can define the relevant notion of environment in pourely logical terms: $\mathsf{E}\mathsf{n}\mathsf{v}\mathsf{i}\mathsf{r}\mathsf{o}\mathsf{n}\mathsf{m}\mathsf{e}\mathsf{n}\mathsf{t}:=\lambda X^{e\to t}.V_e\setminus X,$i.e. as the universe (spacetime) without the region at which the agent is located.

9 Note that this is not the much more contentious Kripkean doctrine that Juhani's existence at a time necessitates the fertilization of a particular human egg at an earlier time – just necessitating the fertilization of something shaped approximately like a human egg at an earlier time is enough to put qualitative constraints on the environment. Indeed, necessitating the fertilization of anything smaller than the universe at some earlier time would be enough, as would necessitating the unfolding of some process roughly qualitatively like the fertilization of an egg of some animal species or other.

10 Of course, given Plenitude, there are plausibly parts of Juhani that are not necessarily parts of Juhani and whose existence puts no qualitative constraints on his environment. One could try out a version of BM's idea according to which the things that ‘have’ content are such modal roamers. We leave it to others to pursue this.

11 We may want something a little stronger than this. In principle there could be a pair of Juhani's parts whose individual existence puts no qualitative conditions on his environment beyond those imposed by his existence but whose joint existence does. One way to control for this is to use classes of parts of the agent rather than parts in the definition: let's say that a class of parts is internal to the agent iff the joint existence of the members of the class puts no qualitative constraints on the agent's environment beyond those imposed by the agent's existence. We then might look to use the maximal class of parts of the agent that is internal to the agent in this sense in the definition of agential profile. Notice, though, that there is no logical guarantee of the existence of a unique maximal class of this sort per agent.

12 See Goodsell and Yli-Vakkuri (n.d.) for a book-length treatment of reasons for such pessimism.