Intro to Language: Singular Terms

by Luke Muehlhauser on November 26, 2010 in Intro to Language

Part 3 of my Intro to Language series.


It seems natural that sentences have meaning in virtue of the things to which their words refer. But last time, we explored why reference alone cannot account for meaning in language.1

Still, one might think the Referential Theory of Meaning would hold at least for ‘singular terms’ (as opposed to ‘general terms’). Singular terms supposedly denote individual things like “Charlie Chaplin,” “Saudi Arabia,” “3:20 pm,” “the cat on the mat,” “she,” “this,” and “that.” General terms can apply to more than one thing, like “dog” or “brown” or “intoxicated.”

But there are four problems that seem to prohibit us from saying that the Referential Theory of Meaning holds even for singular terms.

The Problem of Apparent Reference to Nonexistents


(1) The present king of France is bald.

But now, consider the following set of statements, all of which seem to be true:

J1: Sentence (1) is meaningful.

J2: Sentence (1) is a subject-predicate sentence.

J3: A meaningful subject-predicate sentence is meaningful only in virtue of its picking out some individual thing and ascribing some property to that thing.

J4: Sentence (1)’s subject term fails to pick out or denote anything that exists.

J5: If (1) is meaningful only in virtue of picking out a thing and ascribing a property to that thing [J1, J2, J3], and if (1)’s subject term fails to pick out anything that exists [J4], then either (1) is not meaningful after all [contrary to J1] or (1) picks out a thing that does not exist. But:

J6: There is no such thing as a “nonexistent thing.”

The problem is that it’s logically impossible that J1-J6 is each true, and yet they all seem to be true.

The Problem of Negative Existentials


(2) The present king of France does not exist.

Sentence (2) seems to be true about the present king of France.

But wait a minute. If (2) is true, it can’t be true about the present king of France, for there exists no such entity for (2) to be true about. But if (2) is about the present king of France, then (2) is false, for the present king of France would have to then exist.

Some have said that the present king of France has being of a sort other than existence, but he lacks the property of existing. The present king of France likes donuts but he fails to exist. It happens.

But it is hard to see what it means to say that something has being without existing.

Frege’s Puzzle About Identity

An identifying statement like

(3) The present Pope is Joseph Ratzinger.

has two singular terms (“the present Pope” and “Joseph Ratzinger”), both of which denote the same person or thing (assuming the sentence is true). But then the meaning of (3) is that this person is identical with this person, which is trivial; (3) basically says “the present Pope is the present Pope.” And yet (3) does not seem to be trivial: it is contingent because it might have been otherwise, and it is informative because it might tell you something you didn’t already know.

So it seems like one of the terms in (3) must contribute some meaning beyond that to which it refers.

The Problem of Substitutivity

If singular terms get their meaning solely from referring to things, then we would expect that we could take two singular terms that refer to the exact same thing and use them interchangeably within sentences without changing those sentences’ meaning, or at least their truth value. But consider:

(4) Albert believes the author of Euclid and His Modern Rivals was a noble thinker.

and suppose that (4) is true. But Alfred is unaware that the author of Euclid and His Modern Rivals, Charles Dodgson, is the same Lewis Carroll (author of Alice’s Adventures in Wonderland) whom Alfred knows was probably a pedophile, and not somebody Alfred believes to be a “noble thinker.” But then we cannot substitute “the author of Euclid and His Modern Rivals” with “Lewis Carroll” without making (4) false, even though “the author of Euclid and His Modern Rivals” and “Lewis Carroll” refer to the same man!

Bertrand Russell offered an ingenius solution to these four puzzles, and we shall examine his solution next time.

  1. In the first several posts of this series, I am following along with William Lycan’s superb Philosophy of Language: A Contemporary Introduction. []

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{ 7 comments… read them below or add one }

EvanT November 26, 2010 at 4:46 am

This is series certainly seems promising! BTW, if your linguistic ventures ever bring to ancient Greek (and/or biblical greek), drop me a line. I’d be happy to lend you a hand.


Luke Muehlhauser November 26, 2010 at 8:10 am


Will do, thanks.


Paul November 26, 2010 at 11:26 am

Regarding J6″

Why can’t we say that nonexistent things don’t exist in one sense yet do exist in another sense? The other sense in which they do exist is the sense of the imagination. Non-existent things are so labelled because they don’t exist apart from our imaginations, yet they do exist as part of our imaginations.


Mike Young November 26, 2010 at 1:25 pm

Paul, that Idea has already been knocked out See Russel. Luke, if you go any further without reading this article by Peter Stawson called “on Referring” then son I am disappoint:
You should also read “on denoting” by Bertrand Russell and the Chapter called “descriptions” from his book “Introduction to Mathematical Philosophy.”
If you have not read these yet, then you must do so before you go any further or you will end up doing very bad philosophy.


Paul November 26, 2010 at 3:34 pm

Mike, could you summarize the argument against my idea briefly?


Silas November 27, 2010 at 11:20 am

Man I can’t wait to hear Bertrand’s solution! Great post, Luke.


Mike Young November 30, 2010 at 1:53 pm

Russel Gets owned by Strawson. Think indexicals.
Second solution turns out to be that It is false that Unicorns exist in our imaginations. It is rather that the concept of a unicorn exists. To think that the unicorn exists in our imagination is to think there is some object in my imagination that is (is of identity) a unicorn. False. I have a concept OF a unicron. And thats a big difference.


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