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Abstract
‘Ahab is a whaler’ and ‘Holmes is a whaler’ express different propositions, even though neither ‘Ahab’ nor ‘Holmes’ has a referent. This seems to constitute a theoretical puzzle for the Russellian view of propositions. In this paper, I develop a variant of the Russellian view, Plenitudinous Russellianism. I claim that ‘Ahab is a whaler’ and ‘Holmes is a whaler’ express distinct gappy propositions. I discuss key metaphysical and semantic differences between Plenitudinous Russellianism and Traditional Russellianism and respond to objections that stem from those differences.
Acknowledgments
Earlier versions of this paper were presented at the Dobrovnik Philosophy Conference in 2013 and at The Inland Northwest Philosophy Conference in 2014. Thanks to those audiences for their helpful comments. I also thank David Braun, Ben Caplan, Shieva Kleinschmidt, Lewis Powell, David Sanson, Chris Tillman, and two anonymous referees for this journal.
Notes
1. This is an instance of a more general problem of non-referring names. Just as (S1) and (S2) express different propositions, so too it seems that ‘Vulcan is a planet’ and ‘Zeus is a planet’ express different propositions. The response that I defend in this paper can be generalized to solve the more general problem.
2. Some people may take this theoretical puzzle as a reason to favor Frege’s (Citation1892/1980) view over Russell’s. I am interested, however, in defending Russellianism. So, I will set Frege’s view of propositions aside.
3. Some alternative theories of propositions will face a similar theoretical problem. Consider, for example, the theory according to which each proposition is identical to the set of possible worlds at which it is true (Lewis Citation1986). On this view, the proposition expressed by (S1) is the set of possible worlds at which Ahab is a whaler and the proposition expressed by (S2) is the set of possible worlds at which Holmes is a whaler. But Kripke (Citation1980, Citation2013) has persuasively argued that there is no possible world at which Ahab exists and there is no possible world at which Holmes exists. It seems to straightforwardly follow, then, that there is no possible world at which Ahab is a whaler and there’s no possible world at which Holmes is a whaler. Hence, if the possible worlds theory is true, then both (S1) and (S2) express the same proposition; they both express the proposition that is identical to the null set. Whether Lewis’s own view is subject to the theoretical puzzle is a bit unclear. Lewis seems to hold a view on which a fictional name, at least when it appears within the scope of a fictional operator, is a non-rigid designator that does pick out various individuals at various worlds (Citation1978). On this view, the sets of worlds picked out by (S1) and (S2) may be non-empty. Thanks to an anonymous referee for noting the peculiarities of Lewis’s view.
4. Gappy propositions were first introduced by Kaplan (Citation1989) and have been extensively defended by Braun (Citation1993), Adams and Stecker (Citation1994), Adams, Fuller, and Stecker (Citation1992, Citation1997), Salmon (Citation1998), and Taylor (Citation2000). I have defended Plenitudinous Russellianism from a different angle (Citation2014). Everett (Citation2003) and Mousavian (Citation2011) are both critical of gappy propositions.
5. Since we can safely ignore context sensitivity in our discussion, I will drop the ‘in a context’ modification for the remainder of the paper.
6. Here and throughout I will make simplifying assumptions about roles in both sentences and propositions. I assume that sentences have subject roles and predicate roles while propositions have corresponding subject-like roles and predicate-like roles. A more sophisticated linguistic theory would spell out more detailed roles in sentences and, on the Russellian view I advocate, a sophisticated theory of propositions would entail correspondingly sophisticated roles in those propositions.
7. For more detailed examples of these other methods of representation see Braun (Citation1993, Citation2005).
8. Braun Citation(1993, Citation2005), Brock (Citation2004), and Salmon (Citation1998) all seem to believe that (S1) and (S2) express the same gappy proposition if ‘Holmes’ and ‘Ahab’ really are non-referring terms. Similarly, in another context, Markosian (Citation2004) considers a view on which declarative sentences that contain names that once but no longer refer express gappy propositions. He rejects that view on the grounds that if ‘Socrates’ no longer refers and ‘Beethoven’ no longer refers, then the sentences ‘Socrates was a philosopher’ and ‘Beethoven was a philosopher’ express the same gappy proposition. Everett (Citation2003) argues against the gappy propositions approach under the assumption that if gappy propositions were the semantic content of sentences with non-referring names, then sentences like (S1) and (S2) would express the same gappy proposition.
9. Braun (Citation2005) seems to accept a view according to which (S1) and (S2) would express the same gappy proposition if ‘Ahab’ and ‘Holmes’ really were non-referring terms, but sentences like (S1) and (S2) would seem to express different propositions because they would bring to mind different ways of believing the same proposition. Adams and Stecker (Citation1994) accept that if ‘Ahab’ and ‘Holmes’ are non-referring, then (S1) and (S2) express the same propositions. But they defend a view on which (S1) and (S2) seem to express different contents because (S1) and (S2) pragmatically convey different information. More generally, a standard Russellian might simply treat the seeming difference in content between (S1) and (S2) the same as the seeming difference in content between ‘Hesperus is hot’ and ‘Phosphorus is hot’.
10. Kripke in (Citation2011, 2013) may be advocating such a position. Salmon (Citation1998) suggests that Kripke believes fictional names like ‘Holmes’ and ‘Ahab’ are ambiguous. Fictional names are used by the authors of the various fictions in a non-referring way; authors pretend to express propositions with declarative sentences that contain those names, but they don’t really express any propositions at all. Fictional names are used by critics, on the other hand, to refer to fictional characters; critics really do express propositions when they use fictional names in that way. Salmon points out that Kripke’s view doesn’t seem to accommodate cross-fictional comparisons like ‘Holmes is saner than Ahab’ and cross reality comparisons like ‘Holmes is smarter than any actual detectives’.
11. This view has been defended by Currie (Citation1990), Korman (Citation2006), and Ludlow (Citation2003).
12. Braun (Citation2005); Kripke (Citation2011, Citation2013); Salmon (Citation1998); Thomasson (Citation1999); and van Inwagen (Citation1979, 1983, 2000, 2001) all hold views on which there are fictional characters. These authors may not all agree, though, that fictional characters are the semantic contents of fictional names or that declarative sentences in which those fictional names appear express propositions that contain those fictional characters as constituents. For a nice overview of the case for fictional characters see Friend (Citation2007).
13. It would take a bit of work to extend this definition to all structured propositions. But, for our purposes, we can just restrict our discussion to simple subject-predicate propositions and employ the definition as given.
14. Here is a formalization of the argument. Let ‘[p]F’ be a term that refers to the fact that p. Let ‘Spq’ abbreviate ‘p is structurally identical to q’. Let ‘O[p]F’ abbreviate ‘[p]F obtains’. ‘[p]F grounds [q]F’ abbreviates (roughly) ‘the fact that p grounds the fact that q’. The box, ‘□’ is of course metaphysical necessity and the other logical constants have their standard interpretation. Now, we can represent the argument for line (2) as follows:
(1.0) □∀p∀q(Spq → [Spq]F grounds [p = q]F) [Assumption].
(1.1) □∀p∀q(if [p]F grounds [q]F → (O[p]F & O[q]F)) [Premise].
(1.2) □∀p∀q(Spq → (O[Spq]F & O[p = q]F)) [(1.0), (1.1)].
(1.3) □∀p(O[p]F → p) [Premise].
(1.4) □∀p∀q(Spq → (Spq & p = q)) [(1.2), (1.3)].
(1.5) □∀p∀q(Spq → p = q) [(1.4)].
(2.0) □∀p∀q(Spq → [Spq]F grounds [p = q]F) →[(1.0)-(1.5), Conditional Proof].
□∀p∀q(Spq → p = q)
15. Moreover, the proposition expressed by ‘Ahab is a whaler’ and the proposition expressed by ‘Holmes is a whaler’ are both necessarily false. But given the course-gained identity grounding conditions above, it follows that the proposition expressed by ‘Ahab is a whaler’ is identical to the proposition expressed by ‘Holmes is a whaler’. That, though, is exactly the result that I want to avoid by endorsing Plenitudinous Russellianism.
16. Lewis (Citation1986) endorses an argument for the conclusion that there’s at least one proposition toward which no possible being can have any attitude. This argument can easily be extended to show that there are several such propositions. Lewis, of course, assumes that propositions are merely sets of worlds. But the argument goes through, given Russellianism, under the plausible assumption that for any set of worlds, there is a proposition that is true at all and only the members of that set.
17. Salmon (Citation1987) has a similar argument for the slightly narrower conclusion that, necessarily, for any x and y, if x is identical to y, then there are no qualitative facts that ground that x is identical to y.
18. I am, of course, taking tense seriously here. If you do not take tense seriously, then add the words ‘at a particular time’ to the end of premise (4).
19. The proof is straightforward and involves the following four assumptions:
(a) For any x, y and z, if x is a part of y and y is a part of z, then x is a part of z.
(b) For any x and y, if x is not a part of y, then some part of x does not share any parts with y.
(c) For any x and y, x is a part of y and y is a part of x iff x = y.
(d) For any xs and any y, the xs compose y iff anything that shares a part with y shares a part with one of those xs.
I leave the proof as an exercise to the reader.
20. Lewis (Citation1991) seems to have been a mereological monist. But he had a radically different view of propositions. See Tillman and Fowler (Citation2012) for an extensive discussion of mereological monism in combination with the view that constituency is a kind of parthood.
21. Thanks to Lewis Powell for this example.
22. Thanks to an anonymous referee for pressing me to address this kind of worry.
23. If we were to accept the claim that structurally identical propositions are inexpressible, then we would undermine the primary motivation for accepting Plenitudinous Russellianism. That motivation is that there are pairs of declarative sentences which, if they express anything at all, express structurally identical propositions. Moreover, we have reason to believe that each sentence in that pair does express a proposition.
24. Epistemicism is defended by Sorensen (Citation1988, Citation2001), and Williamson (Citation1994) (among others). Sorensen clearly holds that the boundaries of vague predicates are unknowable, at least for human beings.
25. Williamson (Citation1994) disagrees. Williamson seems to think that there will always be some facts about the world that help to ground that one property is the content of a vague predicate rather than another. I find this claim rather incredible.
26. This presupposes that if what’s expressed by vague predicates were grounded, then those grounds would themselves knowable. I have no argument to back up that claim. But it does seem plausible to me.
27. This view has been defended by Breckenridge and Magidor (Citation2012).
28. A view in the metaphysics of propositions that seems to be gaining popularity is the view that propositions are mental events or actions. This view is advocated by Soames (Citation2012) and Hanks (Citation2014, Citation2015). If propositions were events or actions, then they (or their potential to be tokened) might have causes.
29. In some cases, nothing is successfully dubbed with a name because a dubbing attempt fails to pick anything out. In other cases, nothing is successfully dubbed with a name because no attempt to dub was made. Presumably, Melville’s authorial activities are an instance of the latter cases. This might not be what Donnellan had in mind when he introduced the notion of a block. But I think it is a fair extension of the concept.
30. Admittedly, whether or not this is true depends on how we individuate names. Thanks to an anonymous referee for pointing this out to me.