Russellians should have a no proposition view of empty names

ABSTRACT

Empty names are a problem for Russellians. I describe three ways to approach solving the problem. These are positing gappy propositions as contents, nonsingular propositions as contents, or denying that sentences containing empty names have contents. I discuss methods for deciding between solutions. I then argue for some methods over others and defend one solution using those methods. I reject the arguments that either intuitions about truth value, truth, content, or meaningfulness can decide between the solutions. I give an alternative argument which does decide between the three solutions. The alternative is based on the idea that a sentence and its internal negation are contrary: they cannot both be true, but they might both be false. I argue from Russellian premises to the conclusion that such sentences cannot be assigned truth values when they contain empty names. The argument shows that no Russellian should assign a truth value to a sentence containing an empty name, and therefore that no Russellian should assign a proposition as the content of such a sentence. This shows that Russellians should conclude that sentences containing empty names do not have contents, i.e. the no proposition view.

KEYWORDS:

• Content
• empty names
• reference
• Russellianism
• truth

Disclosure statement

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

Notes

1 This view might be called ‘Millianism’, following, e.g. Braun (2005) and referring to John Stuart Mill's view of names. And, given Russell's actual view, perhaps the view should be called ‘neo-Russellian’, ‘Russellianism–Millianism’, or even ‘neo-Russellianism–Millianism’. All of these options seem unnecessarily complicated to me, and ‘Russellianism’ suggests that the focus is on the nature of propositions, which is where I want it to be.

2 See Gaskin (2008), King (2007), Collins (2011), King, Soames, and Speaks (2014), Hanks (2015), and Soames (2015) for discussion of the problem of the unity of the proposition.

3 Braun (1993) uses the term ‘unfilled proposition’; Braun (2005) switches to ‘gappy proposition’. Salmon (1998) uses the term ‘structurally challenged proposition’. Braun (1993, 468, endnote 23) mentions an unpublished manuscript by Kaplan. Almog (1991, 618, endnote 15) refers to a manuscript by Kaplan as ‘a 1973 unpublished lecture at the Connecticut conference on translation’ in response to a lecture by Kripke, which may well be the same manuscript. I believe that the conference is the one that is the subject of Synthese (Volume 27, Issue 3–4, July/August 1974, https://link.springer.com/journal/11229/27/3/), and that Kripke's lecture is the one eventually published as Kripke (2011).

4 Crane attributes this view to Moore (1953, 289).

5 One might want to deny that there should be special cases. The no proposition view does not entail that there are, whereas the gappy proposition view and nonsingular proposition view do. Braun's treatment of negation in negative existentials is presumably motivated by recognising that the gappy proposition view must treat negative existentials as a special case which preclude internal negation.

6 I will talk as if sentences have at most one content. There are views committed to denying this (Bach 1999; Neale 1999). I will also ignore context sensitivity.

7 Braun (1993, 450) describes a Russellian view without propositions as ‘fundamentalism’ and, page 466, endnote 5, attributes it to Wettstein (1988) and Almog (1991). The difference between Almog and Wettstein, and Donnellan is that the former reject propositions entirely while the latter proposes a no proposition view about sentences containing empty names; all three endorse the claim that some sentences have truth values without having propositional contents.

8 The quote marks in Sentence truth and other claims I will formulate in the course of making this argument should be read as quasi-quotes (Cappelen, Lepore, and McKeever 2019, section 6.2).

9 I have chosen to represent the difference between negating a whole sentence and negating a predication using different scopes of a negation operator on the right-hand side. This is not a suggestion about the syntax of English. Another option would be to define the complement of a predicate, F, with extension A, as a predicate $\overline{\mathrm{F}}$ with the extension $\{x:x\notin \mathrm{A}\}$.

10 It is clear that (1) and (8) cannot both be true, given Sentence truth and Sentence truth for internal negation. If (8) is true, then $\mathrm{\exists }x({\mathrm{R}}_{\text{'Neptune'}}!x\wedge \mathrm{\neg }\mathrm{P}\mathrm{l}\mathrm{a}\mathrm{n}\mathrm{e}\mathrm{t}(x\left)\right)$, by Sentence truth for internal negation. And, if (1) is true, then $\mathrm{\exists }x({\mathrm{R}}_{\text{'Neptune'}}!x\wedge \mathrm{P}\mathrm{l}\mathrm{a}\mathrm{n}\mathrm{e}\mathrm{t}(x\left)\right)$, by Sentence truth.

11 Braun (2005, 604–605) is responding to, among others Salmon (1998, 381). Salmon's point is that many things are not true and are thereby not false. Braun's reply is that those things are not propositions. I take it that Braun is assuming bivalence for propositions, i.e. that there are no further truth values than true and false. Braun also discusses an argument by Adams and Stecker (1994) for the conclusion that gappy propositions lack truth value and attributes the view to Reimer (2001a, 2001b).

12 In recent debates about what propositions are, propositions are sometimes said to be representational and sometimes not. Merricks (2015) takes representation to be essential, and argues on that basis against Russellian views. King has a view compatible with Russellianism (King 2007; King, Soames, and Speaks 2014, chapter 4). King says that propositions represent, but takes this to be equivalent to their having truth conditions (King, Soames, and Speaks 2014, 47). Soames and Hanks have different theories of the nature of propositions, but they both say that a major goal of a theory of propositions is to explain how it is that propositions represent (King, Soames, and Speaks 2014, chapter 6; Soames 2015; Hanks 2015). Speaks says that propositions do not represent, but do have truth values (King, Soames, and Speaks 2014, chapter 5). Richard (2013) and Grzankowski and Buchanan (2019) also take this view.

13 On similar lines, Mousavian (2011, 131–132) argues against gappy propositions on the basis that they do not represent, and therefore that they are not propositions. One might say that there is a sense that properties represent, and that a gappy proposition represents in this sense. But, properties are not true or false, so any sense in which they represent is not the sense that is at issue here.

Additional information

Funding

This work was supported by Irish Research Council [grant number GOIPD/2015/66].