Fregean theories of fictional objects

REFERENCES

�9 Bencivenga E., "Free Semantics for Indefinite Descriptions", Journal of Philosophical Logic 7, 1978, 389-405. "Free Semantics", Boston Studies in the Philosophy of Science 47, 1980, 37-48.

�9 Birkhoff, G., Lattice Theory (Jd edition), American Mathematical Society Colloquium Publications v.xxv, 1967.

�9 Church, A., Introduction to Mathematical Logic, Volume 1, Princeton University Press, 1956.

�9 Cohn, P., Universal Algebra, Harper and Row, 1965.

�9 Fine, K., "Vagueness, Truth and Logic", Synthese 30, 1975, 265-300.

�9 Herzberger, H.G., "Canonical Superlanguages" Journal of Philosophical Logic 4, 1975, 45-65.

�9 Kamp, H., "Two Theories About Adjectives", in E. Keenan, editor, Formal Semantics of Natural Language, Cambridge University Press, 1975, 123-155.

�9 Ore, O., "Galois Connexions", Transactions of the American Mathematical Society 55, 1944, 493-513.

�9 Thomason, R.H., "Indeterminist Time and Truth- Value Gaps", Theoria 36, 1970, 264-281. "A Semantic Theory of Sortal Incorrectness", Jour- nal of Philosophical Logic 1, 1972, 209-258.

�9 van Fraassen, B.C., "Presupposition, Implication, and self-Reference", Journal of Philosophy 65, 1968, 136-152. "Presuppositions, Supervaluations, and Free Logic", in K. Lambert, editor, The Logical Way of Doing Things, Yale University Press, 1969, 67-71. Formal Semantics and Logic, Macmillan, 1971.

FREGEAN THEORIES OF FICTIONAL OBJECTS*

by Terence Parsons

University of California, Irvine

Introduction

For some time now I've been working on the topic of nonexistent objects. My main approach has been to try to develop a theory of the least popular kind, a quasi- Meinongian theory according to which there really are nonexistent objects.., lots of them.., and they have properties, just as you and I do. Sherlock Holmes, for example, is an object that is a detective, solves crimes,..., and doesn't exist. His nonexistence doesn't prevent him from having (in the actual world) quite or- dinary properties, such as being a detective. As I've worked on developing such a theory, certain critics have occasionally said to me: "Look, you ought to compare your theory with the Fregean theory, and say how it is that your theory is better". (This is what they say; sometimes I have the suspicion that they think the Fregean theory is better, and that if I tried to compare the two theories, I'd find this out). My response to this suggestion has always been the same; I would say: "What Fregean theory?" You see, Frege himself had very little to say about nonexistent objects, and what my critics had in mind was some kind of theory that could, perhaps, be developed using the resources of Frege's theory of sense and reference. Bt~t in fact no such theory has been developed; to date, it is a

* This paper was written to be delivered orally, which explains its style. Drafts were read at Rice University and at the Alberta Univer- sities Philosophy Conference; 1 am indebted to participants at both places for helpful discussion.

paradigm example of a nonexistent object. What I want to db in this paper is to discuss some of the ways in which such a theory might be developed, to discuss certain problems that arise in the development, and see what options there are for the solution of those problems. My ultimate goal is to compare the Fregean and Meinongian approaches, but I'm not in a position to do that yet because I don't yet understand the Fregean approach well enough. This paper is an effort in that direction. The problem of nonexistence can be approached in a completely abstract and a priori manner. But I've found it more profitable to focus on a certain kind of (purported) nonexistent object - - fictional objects -- because this is a special case in which we have some relatively concrete data to work with. In particular, we all have a number of specific beliefs about fictional objects, and these beliefs can be utilized to test the theories that we develop. Many of these beliefs appear to commit us to there being (nonexistent) fictional objects. I want to look at how a Fregean theory would account for these beliefs, and whether it would or would not support this appearance of commitment to nonexistent objects. I'll begin by discussing what Frege himself said I.

Frege's views

It's clear, first off, that Frege did not believe' that there are any nonexistent objects, and that this constrains his

Topoi 1 (1982) 81-87. Copyright �9 1980 by Terence Pqrsons.

options. Given that constraint as background, here is what he said about simple sentences containing fictional names. The sentence he discussed in most detail is: '

(1) Odysseus was set ashore at Ithaca while sound asleep.

The name -Odysseus,, is a fictional name, and it will help in understanding Frege's treatment of it if we begin instead with a similar sentence which contains a ,,nor- mab, name. So let's look for a moment at the sentence:

(2) Socrates was set ashore at Ithaca while sound asleep,

which, I assume, is a false sentence. The sentence is meaningful; in Fregean terms it expresses a Thought or proposition, which is a special kind of sense. The parts are meaningful too, i.e., they also express senses, though senses of a different kind. The predicate expresses a sense of a kind appropriate for predicates of individuals to express, which I'll call a property (Frege himself had no special term for it). The name also expresses a sense of the sort appropriate to names, and for which Frege also had no special term; I'll follow Carnap in calling these sorts of senses in~" dividual concepts. According to the theory, the parts: have to have senses, since the whole sentence does, and the sense of the whole is a function of the senses of the parts. If one of the parts lacked a sense - say, if the predicate were just gibberish - then the whole sentence would not express a complete thought. In sentence (2) each meaningful part of the sentence also refers to something. The name refers to the man, Socrates. The predicate also refers to something (so the theory says); it refers to a function which maps anything that was set ashore at Ithaca while sound asleep to the truth-value Truth, and maps everything else to the truth-value Falsehood. And the whole sentence refers to a truth-value; it refers to whichever truth-value the reference of the predicate maps the reference of the subject to (in this case, presumably, to Falsehood). The reference of the whole is a function of the references of the parts, just as the sense of the whole is a function of the senses of the parts. The theory also says that there is a certain relationship between the senses expressed and the things referred to. Namely, each sense presents a unique thing (if it presents anything at all, see below), and if a word expresses a sense, then the word has to refer to whatever is presented by the sense it expresses. In the case just above, the sense of -Socrates,, is an individual concept that presents the man, Socrates; the sense of the predicate, namely, the property of being a thing that was set ashore at Ithaca while sound asleep, presents the function defined above; and the sense of the whole sentence, the proposition that Socrates was set ashore at Ithaca while sound asleep, presents the truth-value, Falsehood (because it is a false proposition). The pic- ture we have is:

the proposition that Socrates was set ashore at Ithaca while sound asleep

the property of being set ashore at Ithaca while sound asleep

jF/s/\ the function which maps things set ashore at Ithaca while sound asleep to Truth, and all other things to Falsehood

the individual concept, Socrates

I

Falsehood

Here ,F,, stands for the predicate, -was set ashore at Ithaca while sound asleep,, and ,s,, stands for -Socrates,,. The arrows pointing up represent the ex- pressing relation and the unlabelled arrows pointing down represent the referring relation; the presentation relation is also diagrammed. Now Frege's view is that the original sentence about Odysseus is to be analysed in exactly the same manner as this one, except that there are two parts missing in the analysis. First, since Odysseus doesn't exist, there is no such man as Odysseus, and so the name ,,Odysseus,, refers to nothing at all. And this means that the whole sentence must also lack a reference. For the sentence refers to whatever the reference of the subject gets mapped to by the function referred to by the predicate; since there is no reference of the subject in this case, that function yields no value. The sentence, then, lacks a truth-value; it is neither true nor false. And this is supposed to be one of the virtues of Frege's theory. It is supposed to be part of the data that the sentence does indeed lack a truth-value, and that there is no such person as Odysseus; the theory automatically predicts the former from the latter. There is one more complication in Frege's theory that is relevant to the discussion that follows; this has to do with his notion of indirect reference. Frege held that in certain contexts, called indirect contexts, words change their mode of reference, and come to refer to the sense that they ordinarily express. An example of such a context would be the context ,Agatha Christie wrote that...,,; words that are inserted for the dots refer to what is customarily their sense. One consequence of this view is that it saves the theory from a problem about failure of reference that would otherwise arise. Consider the sentence:

(3) Agatha Christie wrote that Odysseus was set ashore at Ithaca while sound asleep.

If the words in the subordinate clause behaved in their normal manner, that clause would lack reference, and

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then the whole sentence would have to lack reference too. (For on Frege's theory, the reference of a whole is always a function of the references of the parts, even in complex cases). However, in this context the name ,,Odysseus,, does not lack reference; here it refers to the individual concept that it normally expresses. And likewise the sentence ,,Odysseus was set ashore at Ithaca while sound asleep,, refers to the proposition that Odysseus was set ashore at Ithaca while sound asleep. As regards the question of fictional objects, then, I've now stated pretty much all of what Frege had to say about the topic. Names which appear to name fictional objects normally are meaningful - they express individual concepts - but these concepts fail to present anything, and so the names fail altogether to refer. This means that sentences containing such names are normally neither true nor false, the only exception being cases in which the names appear in indirect contexts, where they denote the individual concepts that they normally express.

A minor problem

There is a minor problem with this account, easily solved. It's this. Often we treat a sentence such as ,,Odysseus was set ashore at Ithaca while sound asleep,, as true, and distinguish it from false sentences like ,,Sherlock Holmes was set ashore at Ithaca while sound asleep,,. In some sense the former sentence is correct, while the latter is incorrect. Yet according to the theory, they are both on a par - they both lack truth- value altogether. A plausible response here is to say that when we treat the one as correct and the other as incorrect, we are actually focussing on certain other propositions, propositions that could be more literally expressed by ,,It says in the relevant body of literature that Odysseus was set ashore at Ithaca while sound asleep,, and ,,It says in the relevant body of literature that Sherlock Holmes was set ashore at Ithaca while sound asleep,, 3. But these sentences have truth-values (according to the theory); although they do contain names that ordinarily fail to refer, the names here appear in an indirect context: ,,It says in the relevant body of literature that ..... , and so the names do refer (to their customary senses). It seems to me that an enormous number of apparent counterexamples to Frege's theory can be handled by this simple expedient, and that if there were no other problems, then we would possess a reasonably well worked-out theory of the apparent phenomena of fictional objects. But there are more problems.

Some complications

Consider the following sentences: (4) Sherlock Holmes is a fictional detective who is more

famous thaia any real detective, living or dead. (5)A certain fictional detective is more famous than

any real detective. (6)Some fictional characters who are based on real

people are less lifelike than others who are entirely products of their authors' imaginations.

(7)Things would be better off if certain politicians, who (unfortunately) exist only in fiction, were runn-

�9 ing this country, instead of the ones we now have. These sentences seem to be true, not truth-valueless, and they seem to commit us to there being fictional objects. They are problematic because they cannot be analysed as containing an implicit prefix, 'According to the relevant body of literature.. 2. It's not true that according to the relevant body of literature Sherlock Holmes is a fictional detective. How are these sentences to be accounted for? The most popular view is that such sentences stand in need of paraphrase into some logically perspicuous notation; the paraphrase itself would clearly not be committed to fictional objects. Popular as this view is, no one knows what the paraphrases are, and so I won't have anything to say about this approach. A second option is simply to ignore such sentences. There's a lot we can't account for, and it might be a waste of time to worry about these cases. Maybe, but I think that more can be said. A third option, one that I have worked on, is to take the sentences at face value, as committing us to nonexistent fictional objects. The results of that work are now in a book 4. But that view rankles a lot of people, and here is where some have urged me to explore the Fregean alternative. The problem is, what would it be? Frege himself didn't address examples like these, and the simple expedient mentioned in the last section won't work here. The proposal that I have heard most is that the sentences in question contain nonextensional or indirect contexts. I'm not sure that this is quite what people have in mind (see below), but it is what they say; they say that the phrases ,,more famous,, and ,,less life like,, create nonextensional or indirect contexts, and that the fact can be exploited in explaining away the apparent commitment to nonexistent things. I don't think this is right. First, I don't think that the sentences contain the relevant indirect (or nonextensional) contexts, and even if they did, that wouldn't help. Why wouldn't it help? Well, it might help with sentence (4); if we could say that in sentence (4) the name ,,Sherlock Holmes,, refers to its customary sense, then we would not be referring to a nonexistent individual. But even if this device worked here, it wouldn't help in the case of sentence (5). For (5) has the form of a quantified sentence; when symbolized, the quantificational phrase ,,A certain fictional detective,, would come outside the scope of ,,is more famous than,,; the sentence would read ,,At least one thing is a fictional detective and ..... Whether there is indirect reference inside the dots doesn't help avoid the claim that there are fictional detectives'. The sentences in question don't contain the purported indirect contexts anyway, or at least the evidence is against it. The main evidence that a context is indirect is that it is nonextensional, i.e., that the law of substitutivity of identity does not hold within it. But that law holds for contexts like ,,is more famous than,,.

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For example, it is true that (8) Jimmy Carter is more famous than Walter Mon- dale. and it is true that (9) Jimmy Carter is the present President of the U.S. These two sentences do entail that (10) The present President of the U.S. is more famous than Walter Mondale. That is, substitutivity of identity does apply here 6. There is, however, a more promising use of Fregean resources here. Even without nonextensional or indirect contexts we still might be referring to individual concepts when we appear to be discussing fictional objects (and this may be the view that some people have had in mind when urging the Fregean alternative). This is not an unusual phenomenon; in discussing Frege's theory we refer to individual concepts even though we are not employing indirect speech. For example, if I say ,,some individual concepts present individuals and some don't,,, or ,,the individual concept expressed by the name 'Odysseus' does not present any individual,,, then I am quantifying over or referring directly to individual concepts, but there is no indirect reference involved. Perhaps something like that is what is going on in sentences ( 4 ) - (7). Perhaps in sentence (4) the name, ,,Sherlock Holmes,,, does refer to the individual concept, Sherlock Holmes, not because it is in an indirect context, but because that's what happens when we discuss fictional characters; and in sentence (5) we quantify over individual concepts. We would then be saying that there really are fictional objects, but we avoid the heresy normally associated with that claim by saying that fictional objects just are certain individual concepts. And when we say that these particular individual concepts don't exist, we aren't saying that there aren't any such individual concepts, we are saying rather that they don't present anything. There is such a thing as the fictional object, Sherlock Holmes, it's an individual concept, and it ,,doesn't exist,,, i.e., it fails to present an individual 7. But now we have another complication. There seem to be two quite different kinds of predicate in the sentences we are dealing with. One kind, epitomized by ,,is fictional,, and ,,exists,,, is a kind of predicate that applies meaningfully to individual concepts (according to the view being examined), whereas another kind, epitomized by ,,is a detective,,, is appropt~iate to individuals. We've decided to say (with some awkward- ness) that individual concepts are fictional, and that they don't exist, but we can't say literally of an individual concept that it is a detective. Individual concepts are abstract entities, and detectives aren't. So we are going to have to do some paraphrasing. Let me say that certain individual concepts include the property of being a detective. Then we represent

(11) There are nonexistent fictional detectives, a s :

(12) (3o~) ( -or exists & o~ is fictional & o~ includes the property of being a detective)

in which o~ ranges over individual concepts (and ,,a exists,, is defined as ,,(3x)(o~ presents x),,)L The general proposal can be roughly summed up as follows: for factual claims about fictional objects (that do not otherwise contain indirect contexts) we symbolize the claims in the normal manner, except that:

(a) Names of fictional characters name the individual concepts that they ,,normally,, express, i.e., they name the concepts that they express when used in telling the story they are taken from, (b) We quantify over individual concepts instead of individuals,

and

(c) We replace any predicate ,,F,, that is appropriate to an individual by ,,includes Fness,, 9.

Now you're going to wonder about the meaning of ,,includes,,, and I confess that I'm not going to be able to explain it very well. As far as I can see, the Fregean approach will require the use of such a notion, and there are problems in explaining it. If we were ignoring nonexistent objects, there would be no difficulty at all; we could just say;

(13) o~ includes Fness =dj (3x) (a presents x & Fx) '~

But when we deal with nonexistent objects, we need to have individual concepts that fail to present things, yet still include certain properties appropriate to individuals. What we want is something more like:

(14) a includes Fness = ~j if o~ were to present something, it would present something that is F.

There are problems with this too, but it's not bad, I think, as an informal guide to how ,,includes,, is supposed to work.

Objections

I'll now present three different and independent objections to the theory that has been formulated. I don't think any one of these is conclusive, but, taken together, I think they clearly show that we are not yet in possession of a plausible Fregean account. Objection number one: Many mystery stories have a plot that goes like this: Early on in the story we en- counter what appear to be two different characters, say ,,Dr. Heckle,, and ,,Mr. Chide,,. Later we discover that these are one and the same man; that the names ,,Alex- ius von Heckle,, and ,,Gilbert Chide,, are aliases used by the murderer to promote his evil purposes. Now the first objection to the theory is that when applied to such stories the theory is simply false. Suppose, for sake of simplicity, that at the point of discovery the narrative reads ,,Alexius von Heckle is Gilbert Chide,>. Certainly the sentence makes an informative contribu- tion to the plot. Paralleling Frege's discussion of the morning star/evening star case, it is clear that the names ,,Alexius von Heckle,, and ~,Gilbert Chide,,

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when used in the course of the story, express different senses. Now suppose we are having a factual discussion about the novel and its characters, and we refer to Dr. Heckle and to Mr. Chide. According to the theory, the characters we are now referring to are the senses that those names express in the telling of the story. So Dr. Heckle and Mr. Chide are (according to the theory) different characters. But this is false; Dr. Heckle is Mr.Chide. They are one and the same character; a character who, in the novel, leads a double life. The only way to get around this that I can see is for the theory to deny the supposed data that Heckle is Chide. The story says that Heckle is Chide, but in fact they are different characters. Unfortunately, this reply is both implausible and unclear. It is implausible because it says incorrectly that the story has two villains, when in fact it has only one villain, who uses two different aliases. And it is unclear because it leaves us in the dark concerning what the difference is between the two purported characters; both presumably include the same properties, so if they differ, the difference must show up elsewhere. But where? Objection number two: The first objection said that we know enough about which individual concepts fictional characters are to see that the theory is false. The second objection says that in other respects we really don't know what individual concepts we're talking about. The idea is this: Everything we know about what is included in Holmes we find out from the story. By the ,,story,, I don't mean just the words we read, but rather an expanded account that you get by filling in details based on your understanding of what is supposed to be happening. For example, it says literally in the written story that Watson and Holmes lived together, but it does not literally say that no one else lived with them; yet this latter fact is just as much a part of the account of what went on as the former. Hereafter when I refer to the ,,story,,, I intend to be referring to the expanded account of the literal story. With this in mind, I think it is plausible to maintain that the story is the source of all of our data concerning what properties are included in a given fictional character. Holmes is a detective (i.e., includes detectivehood) because the story says so; he lived with only one person because the story, properly expanded, says so. He neither has nor lacks a mole on his back because the story doesn't say either. (I.e., he neither includes having a mole on his back, nor does he include not having a mole on his back; this paraphrase in terms of inclusion lets us avoid the apparent contradiction in saying that he neither has nor lacks one). Now here is the objection: even though we know a great deal about what properties the individual concept, Sherlock Holmes, is to include, this doesn't deter- mine which individual concept he is. For individual concepts are supposed to be individuating, i.e., in any possible state of affairs they are supposed to present a unique individual (or present none at all). But stories typically have a type of generality which prevents them from grounding any individuating process. This is not

obvious in the case of Sherlock Holmes, because the Conan Doyle novels are so detailed with respect to times and places, but other stories will clearly raise problems. Consider the character, Piggy, in Lord of the Flies, and consider a state of affairs in which the story comes true. The individual concept expressed in the story by the name ,,Piggy,, should present a unique individual, presumably the one who did the things that Piggy did in the story' ~. But what about states of affairs in which the events described in the story took place twice, on two different islands, with two different sets of people involved? Which individual will the individual concept then pick out? It cannot pick out both, for individual concepts must present at most one individual. The only solution I can think of here is to suppose that in such a possible state of affairs the individual concept picks out nothing at all. But then there will be problems in the case of other stories. Suppose that the novel ended with the sentence: ,,Events just like these have happened before, and may happen again,,. That story can't come true unless there are two or more enactments of the events described. Should its characters, unlike the characters of many other stories, be necessarily nonexistent? None of these remarks suggest that the theory says anything incorrect; they rather suggest that a story underdetermines which individual concepts are supposed to be its characters according to the Fregean theory. And they only suggest this, they don't prove it. But what is clear, I think, is that we do not yet have a theory which addresses this issue. The theory tells us that Sherlock Holmes is an individual concept, but it does not tell us which individual concept he is, nor does it tell us bow to find out. Objection number three: Our theory of fictional characters says that if a story attributes certain properties to a character, then the individual concept which is that character includes those properties and fails to include any others. And this presupposes a principle about the ,,availability,, of individual concepts; let me call this, in its most general form, the General Availability Principle:

GAP: For any set of properties appropriate to individuals, there is at least one individual concept which includes every property in the set and no others.

There is some reason to believe that this principle is false, no matter how we understand the problematic notion of inclusion. For whatever ,,includes,, means, the GAP entails that there are more individual concepts than there are properties appropriate to individuals. (Because it entails that the cardinality of the set of individual concepts is at least as great as the cardinality of the power set of the set of properties appropriate to individuals)'2. This is not automatically objectionable, as far as I can see. But GAP is inconsistent with another principle that seems equally natural, a principle about the Retention of Diversity of senses. Fictional objects come in groups, one group per story. Holmes and Watson are members of the same group; Holmes and Robinson Crusoe are not. This fact will

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have various effects on any theory about such objects. Here is one effect on the present theory. The character, Sherlock Holmes, includes the property of having lived with Watson. This is a relational property, which may be formed by combining the sense of the relational predicate, ,,lived with,,, with the individual concept, Watson (i.e., with the sense expressed by the name ,,Watson,, as used in the story). Frege is quite explicit about there being such properties, and I see no reason for disallowing them. If 0 is the sense of a relational word R, and if o~ is an individual concept expressed by the name a, then let me symbolize the sense of the relational predicate ,,bears R to a,, as ,,[0oe],,. Then the principle of the Retention of Diversity of senses is:

RD: If o~ and t~ are distinct individual concepts and if 0 is the sense of a relation word, then [0o~] and [0i~] are distinct properties.

This is a generalization from examples like: if the names ,,Quine,, and ,,Carnap,, express different senses, then so do the predicates ,,sees Quine,, and ,,sees Car- nap,,; or, if ,,Cicero,, and ,,Tully,, express different senses, then so do ,,murdered Cicero,, and ,,murdered Tully>,. The GAP is inconsistent with the RD principle because the latter principle requires that there be at least as many properties as individual concepts. So we have to give up one of the principles. But which? Well, GAP has all the earmarks of a ,,hasty generalization,,. Our theory presupposes that for any set of properties defined by a story, there is an individual concept that includes exactly the properties in that set. If we just limit GAP to such sets, then the cardinality result vanishes, or at least our ability to prove it vanishes. Well, this preserves consistency, but it raises doubts about plausibility. For we would then be saying that a principle that is known not to hold in general holds for the cases we are interested in. But how do we know that? The other option is to reject RD, but here too we need at least a restricted version of it; it should hold when o~ and f~ are fictional characters and when 0 is the sense of a relational word occurring in their story. For otherwise we would have a case like the following one: although Watson and Moriarty are different characters, the predicates ,,lived with Watson,, and ~,lived with Moriarty,, have the same sense. So when we learn that Holmes lived with Watson, we are simultaneously told that he lived with Moriarty. But that's just wrong. Again we need the principle as restricted to fictional characters, and we undercut the plausibility of our case by denying it in general, without some explanation. Now this third objection is a pretty abstract one; probably if you inquire into the metaphysical presuppositions of any comparable theory, you're bound to find such unresolved questions. My motive in pointing them out here is really to undermine a certain attitude toward another theory - the quasi-Meinongian one that I've worked on elsewhere. The attitude is: ,~Let's not go running off hogwild into crazy metaphysical excesses;

better to stick to approaches that are familiar and safe,,. Frege's theory is thought to be a familiar and safe theory, at least in comparison to its Meinongian alternatives. Well, perhaps it is a safe theory when applied to old and familiar problems, but if it's to deal with the same data that inspires Meinongian alternatives, then it may have to be applied in an unsafe and unfamiliar way. It is the application of the theory to fictional objects that raises new issues, such as the GAP - in the sense that it now becomes important to face them - and now the safety of the original theory has been left behind. Other Problems: There are a host of other problems as well. Any theory will have to cope somehow with stories that contain subsidiary stories, and characters from these subsidiary stories; with characters from original novels that reappear in new stories by different authors; with characters that carry on dialogues with their authors; with characters that do things that are logically impossible; etc. But it is likely that these will be problems for just about any theory of fictional characters, and so I haven't belabored them here. I have also skipped over recent criticisms of the Fregean view that names have senses '3. If these criticisms are correct, then names.do not have Fregean senses, and any theory that is at all like the one I have discussed is hopeless from the outset. ! don't find the criticisms conclusive, but many people do, and they must somehow be faced in constructing a Fregean theory of fictional objects. In conclusion, I should emphasize that I have not shown here that there could not be a good theory of fictional objects within the Fregean tradition. I've only tried to show that no such account presently exists, and that the viability of this approach is mainly an article of faith. Perhaps some of the problems that I've discussed will help to provide a framework for the development of a better Fregean account.

Notes

(') The Fregean theory outlined below can mostly be found in Frege's essays ,,Function and Concept,,, ,,On Concept and Object,, and ,,On Sense and Reference,, in P. Geach and M. Black (eds.) Translations From the Philosophical Writings of Gottlob Frege. London, Blackwell, 1960.

(2) In ,,On Sense and Reference,, op. cit. pp. 62-63. (~) Ideas such as this have been discussed by many writers, from

very early on. Cf. G. Ryle, ,,Symposium: Imaginary Objects,,, Pro- ceedings of the Aristotelian Society, Supp. Vol. XI1, 1933.

(') Nonexistent Objects, Yale University Press, 1980. (~) The proposal is problematic in another way, in that it ap-

parently requires us to ,,quantify into- an indirect context, and this does not make sense within Frege's semantics; cf. A. Church, ,,Outline of a Revised Formulation of the Logic of Sense and Denotation (Part. II),, Nous VIII, 1974. There is a popular view to the effect that a ,,Fregean, treatment of ,,quantifying into indirect contexts,, can be given by quantifying over individual concepts instead of over individuals. Closer scrutiny reveals that such bound variables actually appear within direct contexts that are designed to mimic indirect contexts in certain ways. Cf. D. Kaplan, ,,Quantify- ing In-, in L. Linsky (ed.) Reference and Modality, Oxford Univer- sity Press, 1971. (Kaplan is clear about this point). This is still a ,,Fregean,, approach, but it is an approach that follows

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Frege's view about how language should work, as opposed to his views about how (natural) language does work. It is similar to the view I explore below.

(~) This is discussed in Nonexistent Objects, op. cir. Section 2 of Chapter 2, and in T. Parsons, ,,The Methodology of Nonexistence,,, Journal of Philosophy, LXXV1 11, November 1979.

(~) The proposal to analyse nonexistence statements in terms of reference to individual concepts that fail to present anything is discussed favorably in A. Church, op. tit.

(8) Notice that this proposal presumes that there is something like an indirect context in certain parts of the sentence, but the altered reference is of ,,detective,, not of ,,Holmes,,. And this seems right, for the ,,data,, indicates that the word ,,detective,, is in a nonextensional context in the original sentence (unlike everything else). If all and only (real) detectives were bakers, then it would not follow from (5) that Sherlock Holmes is a fictional baker! But if all and only .fictional things are nonexistent things, it does follow that he is a nonexistent thing.

U) Notice that if clauses (b) and (c) were omitted, and if we were to ignore all quantificational sentences, then this proposal would be indistinguishable from the proposal that in such discourse fictional

names always have indirect reference; this may be why the ter- minology ,,indirect reference,, is often used when something more like the present proposal is envisaged. I think that the distinction here of predicates appropriate to individuals from' those appropriate to individual concepts is roughly the same as the Meinongian distinction of nuclear from extranuclear predicates; see Nonexistent Objects, op. cir. for discussion of this latter ter- minology.

(~0) D. Kaplan uses a notion like this for other purposes in Kaplan, op. cit.

(' ') Notice that in the counterfactual situation described, the individual who is presented by the individual concept, Piggy, would not thereby be the fictional character, Piggy (for the character would still be an individual concept, and the person would not). This appears to be a virtue of the analysis.

(,2) The proof of this result utilizes the axiom of choice. This means that the potential difficulties discussed below could be avoided by denying this axiom. However, this would probably jeopar- dize the plausibility of the theory.

('~) Cf. S. Kripke, ,,Naming and Necessity,,, in D. Davidson and G. Harman (eds.), Semantics of Natural Language (Reidel, 1972).

A LOGICAL INTERPRETATION OF MEINONG'S PRINCIPLE OF INDEPENDENCE

By Karel Lambert

University of California, Irvine

I. Objects and the Principle o f Independence

Meinong said that: ,, . . .the totali ty of what exists, in- cluding wha t has existed and will exist, is infinitely small in compar i son with the totality of the objects of knowledge. This fact easily goes unnoticed, p robably because the lively interest in reality which is par t of our nature tends to favor that exaggerat ion which finds the non-real a mere nothing - or, more precisely, which finds the non-real to be something for which science has no application or at least no application of any worth,, '.

Indeed, he believed the att i tude expressed in the final sentence of this passage quite unjustified. Take the case of mathemat ica l objects - the number 2 or the set of as t ronauts , for example. N o one denies, he said, that they are objects of considerable scientific interest even though they do not exist. Reflecting the Humel ike in- fluence of his early philosophical training under Bren- tano, Meinong held that exis tent objects are objects having location in space-time; objects that are not spat io- temporal ly locateable but nevertheless have being he called (merely) subsistent objects. And among the latter are all sorts of interesting entities; not only the vast array of mathemat ica l objects, but also for in- stance ,,ideal,, relations such as similarity, and many of the proposi t ionl ike entities he called objectives. The difference between (merely) subsistent objects and exist- ent objects corresponds very roughly to the currently

popular distinction between abstract and concrete objects 2.

Wha t really sets Meinong apar t f rom the majori ty of philosophers, however , is not the distinction between the two kinds of being an object might possess - existence or mere subsistence 3, a kind of view, after all, advocated by many philosophers f rom Aristotle on - rather, it is his belief in nonsubsistent objects, objects that have neither existence nor subsistence nor any other kind of being, that is truly distinctive. Meinong did toy in a tentative way f rom time to t ime with the idea of a pervasive kind of being possessed by all objects, and especially in unpublished lectures toward the end of his careeH. But most Meinong scholars agree that Meinong 's most widely promulga ted (and interesting!) view is that there are objects having no being in some appropr ia te sense of ,,there are,, '. Certainly this is the position in Meinong ' s essay, ,{)ber Gegenstands- theorie,,, the most explicit s tatement of his considered thought . Those having a taste for paradoxical ways of speaking, he said, would appreciate another s tatement of the position: There are objects such that there are no such objects 6.

The domain of nonbeings Meinong called Aussersein, literally the domain of objects outside of being 7. Among the denizens of Aussersein are possible objects such as Pegasus and the golden mounta in and impossible objects such as the round square of Mill and the

Topoi 1 (1982) 87-96. 0167-7411/82/0011 0087501.50. Copyright �9 1982 by D. Reidel Publishing Co., Dordrecht, Holland and Boston, U.S.A.

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Fregean theories of fictional objects