Gappy Propositions?

Introduction

After introducing Millianism and touching on two problems raised by genuinely empty names for Millianism (section I), I provide a brief exposition of the Gappy Proposition View (GPV) and of how different versions of this view can reply to the problems in question (section II). In the following sections I develop my reasons against the GPV. First, I will try to argue that apparently promising arguments for the claim that gappy propositions are propositions are not successful (section III). Then, I will develop two arguments against GPs via demonstrating two odd consequences of the GPV: (a) that there can be an atomic proposition which contains other propositions that are not the semantic contents of any part of the sentence expressing that atomic proposition, and (b) that propositional structures are propositions (section IV). And finally, I will attempt to show that if any of these views can provide a successful defense of Millianism, it can do so without GPs, given some slight changes (section V). I will conclude that GPs should be avoided (section VI).

I Millianism and Empty Names

By 'Millianism' I mean the following thesis:

(M) The semantic content of a name² is the individual (or object) to which the name semantically refers.

By 'a genuinely empty name' I mean a name that does not refer to any individual. According to Millianism such names do not have semantic content. This raises several problems with regard to these names and sentences containing them. For example, assume that 'Vulcan'³ is a genuinely empty name. So, by definition, 'Vulcan' does not refer to any thing.⁴ Therefore, by (M), 'Vulcan' does not have semantic content. Then, consider utterances of the following sentences:

1. 1. Vulcan is existent.

2. 2. Vulcan is nonexistent.

If 'Vulcan' does not have semantic content, by a version of the Principle of Compositionality,⁵ it follows that (1) and (2) do not have semantic content. Given that the semantic content of a sentence⁶ is the proposition semantically expressed by that sentence, then (1) and (2) do not semantically express any proposition. This, however, raises at least two important problems: first, the problem of (apparent) meaningfulness: (1) and (2) seem to be meaningful. But if (1) and (2) do not semantically express any proposition, they are not meaningful. Second, the problem of (apparent) truth value: (1) seems to be false and (2) seems to be true. If 'Vulcan' does not refer to any thing, it might be said, we have strong evidence to consider (1) as false and (2) as true. But if (1) and (2) do not semantically express any proposition, they do not have any truth value at all (given that propositions are truth value bearers).⁷

II The Gappy Proposition View

The Structured Proposition View contends that propositions are structured entities, not functions from possible worlds to truth values.⁸ Some proponents of the Structured Proposition View take the constituents of propositions to be objects, properties, and relations; others do not.⁹ It is standard to call the propositions of the former kind 'Russellian propositions' (RP).¹⁰ Russellian propositions containing an individual or a particular object are called 'singular Russellian propositions' (SRP).¹¹ A gappy proposition (GP), also called 'incomplete (structured) proposition,' 'unfilled (structured) proposition,' and 'structurally challenged proposition,' is what is left from a singular Russellian proposition after taking the constituent individual or particular object from it. Any view committed to GPs is a version of the Gappy Proposition View (GPV), as I use the term here. According to the GPV the semantic content of a sentence containing a genuinely empty name is a GP. Put differently, the proposition semantically expressed by a sentence containing a genuinely empty name is a GP.

An example may help to clarify the distinction between a singular Russellian proposition (SRP) and a gappy proposition (GP). Assume 'a' is an ordinary referring proper name and 'is F' is an ordinary predicate whose semantic content is the property of being-F. Consider:

1. 3. a is F

(3) semantically expresses a SRP. This proposition can be represented by the following ordered pair:

1. 3p. <a...