12.1.1 Meinong's Characterization Principle and Russell's theory of descriptions
What does it mean to be something? It is natural to countenance certain inferences that involve the English word ‘something’. For example, you might infer that something is four-legged from the claim that most dogs are four-legged. Similarly, you might infer that Tom has something on his shoulder from the claim that Tom has a bird on his shoulder. But you wouldn't infer that Tom has something on his shoulder from the claim that Tom has a chip on his shoulder. We can then ask the general question: when are these sorts of something-inferences valid? That is, for what elements of a language T is the following inference logically valid?
(1) T M's.
(2) Therefore, something M's.
Many logicians and philosophers have suggested that this inference from (1) to (2) is valid whenever T is a referring expression or term. In general, proper names seem to be referring expressions. Thus, the following inference is valid.
(3) Houston grows rapidly.
(4) Something grows rapidly.
There are other expressions, however, that mimic the grammatical function of referring expressions without actually referring to any particular thing. Logicians call these expressions quantifiers. Among the quantifiers are ‘nothing’, ‘no man’, ‘something’, ‘some city’, and ‘everything’. The fact that the expression ‘nothing’ (or ‘no man’) is both grammatically similar to and logically different from a proper name was noticed by the Greek poet Homer in a famous passage from the Odyssey. Odysseus and his men are captured by the monstrous Cyclops Polyphemus. When captured, Odysseus tells Polyphemus that his name is ‘No Man’. Later, when Odysseus escapes from his bonds, he attacks Polyphemus, gouging out his single eye with a sharp stick. Polyphemus cries out to his fellow Cylcopses with the words, “No Man is attacking me.” Naturally, they ignore him, and Odysseus escapes. Homer's story illustrates the logical invalidity of the inference from (5) to (6):
(5) No man is attacking me.
(6) Something is attacking me.
Another illustration of this distinction comes from Lewis Carroll's Alice in Wonderland. Alice explains to the Mad Hatter that she sees no one on the road, and the Mad Hatter replies that she must have sharper eyes than he does, treating the expression ‘no one’ as if it named a peculiar kind of entity, which Alice could see and the Hatter could not.
In many natural languages, including English, there are expressions that grammarians call definite descriptions. These are formed in English by placing the definite article ‘the’ in front of a noun phrase, as in ‘the queen of England’, ‘the highest peak in the Rocky Mountains’, ‘the shortest spy’, and so on. These definite descriptions seem in many cases to function exactly the way proper names function. When successful, they pick out exactly one thing, to which some attribute is then predicated. Consider, for example:
(7) The shortest spy works for the NSA.
(8) Samuel H. Ortcutt works for the NSA.
If (7) is true, this is because the person picked out by the phrase ‘the shortest spy’ works for the NSA. Similarly, (8) is true if and only if the person picked out by the name ‘Samuel H. Ortcutt’ works for the NSA.
What, then, are we to do with definite descriptions that do not refer to anything? Consider such expressions as ‘the present reigning king of France’ or ‘the round square spot on my desk’. There is in fact no present reigning king of France, and there is not and could not be a spot on my desk that is both round and square.
Meinong argued that we should take all definite expressions as referring to something. The difference between ‘the present queen of England’ and ‘the present king of France’ is that the first expression refers to something that exists, while the second refers to something that doesn't exist. Similarly, ‘the round square spot on my desk’ refers to something that does not and could not exist. In fact, Meinong proposed what has been called the ‘Characterization Principle’ as an axiom of logic:
Characterization Principle. The F is an F (where ‘F’ can be any meaningful noun phrase).
From the Characterization Principle, we can infer, with obvious correctness, that the present queen of England is a queen of England, and that the highest peak in the Rockies is a highest peak in the Rockies. Consequently, it follows logically that the highest peak in the Rockies is a peak and is in the Rockies. So far, so good.
What about the present king of France? The Characterization Principle entails that the present king of France is a present king of France, and so is a king. According to Meinong, this poses no problem so long as we remember that the present king of France is a non-existent king. Consequently, we should not be surprised when we don't see him on a throne in Paris or Versailles.
However, the Characterization Principle brings serious logical problems in its wake, especially when we consider logically contradictory descriptions. Consider again the round square spot on my desk. According to the Characterization Principle, this spot is both round and square. However, the laws of geometry dictate that whatever is round cannot be square. Hence, the spot is both square and not square, a logical contradiction. In fact, we can reach a contradiction even more quickly by considering the thing that is both square and not square.
Meinong's answer was to propose that the laws of logic apply only to things that are capable of existence. Things whose existence is impossible fall out of the range of logic. Hence, from the fact that the square and not square thing is square and not square, nothing follows. This object violates the Law of Non-Contradiction, but that is permissible since it is necessarily non-existent.
However, this solution seems to lead to further difficulties. Consider the possibly existing round square. According to the Characterization Principle, the possibly existing round square possibly exists, and so it should be subject to the laws of geometry and logic. However, it clearly is not.
In response to these difficulties, some Meinongians proposed a distinction between nuclear and extra-nuclear properties (see Parsons 1980 and Zalta 1983, 1988). Nuclear properties are ordinary properties, like being round or being a king. Extra-nuclear properties include special properties like existing or being possible. Meinongians restrict the Characterization Principle to expressions that attribute nuclear properties to the designated object.
There is, however, a much simpler solution of all of these difficulties that is available to the Meinongians (as pointed out by Priest 2005): simply deny the Characterization Principle. Denying the Characterization Principle does not, by itself, entail that everything exists. In place of the Characterization Principle, we could use one or the other of these weaker principles:
Modal Characterization Principle. The F, if it existed, would be an F (or if it had existed, would have been an F).
Representation Characterization Principle. The F is normally represented as an F.
These principles do not generate contradictions, even if they are applied to logically contradictory descriptions. It is true that the round square, if it were to exist, would be round and square. Since it is impossible for it to exist, such a conditional is either trivially true or it could be taken to refer to some logically impossible situation. We are not forced to say that the round square is both square and not square, but only that it would be square and not square, which is not in violation of the Law of Non-Contradiction. Similarly, there is no contradiction in supposing that the round square is represented as both square and not square.
The round square (that RCK is thinking of) does not exist, but it is neither round nor square. It is thought of by me as being round and square, but that does not make it really round or square. Ponce de León's Fountain of Youth was not a fountain, nor did it have any magical, youth-restoring powers. It was, however, believed by de León to be a fountain with such powers. Similarly, Sherlock Holmes was not a detective. He is a fictional detective, but fictional detectives are no more detectives than imaginary mountains are mountains. A list of the world
's detectives would include Eliot Ness but not Sherlock Holmes. Conversely, a list of the world's fictional detectives would include Holmes but not Ness. Similarly, golden mountains are neither golden nor mountainous; they are things that, were they to exist, would be golden and mountainous, and that are represented as golden and mountainous. Reformed Meinongians (like Graham Priest) hold that non-existent things have only intentional properties (like being thought to be so-and-so) and modal properties (like being possible or impossible).
RUSSELL'S THEORY OF DESCRIPTIONS Bertrand Russell proposed in his paper “On Denoting” (Russell 1905) a radically different approach to the understanding of definite descriptions. According to Russell, definite descriptions are quantifiers (like ‘something’ or ‘nothing’) and not referring expressions at all. Their semantic function is not to pick out a single entity. According to Russell's theory, the use of a definite description, such as ‘the round square’ or ‘the man who lives on the North Pole and delivers gifts every Christmas’, need not commit the user to the existence of anything. Everything depends on the context. For example, we can interpret the simple sentence:
‘The F is a G.’
as expressing the following:
‘There is one and only one F, and every F is G.’
This paraphrase is important, since one can then deny that the F is a G without being committed to the existence of a something called ‘the F’. If one negates the sentence ‘The F is a G’, either one of two sentences may result, depending on the scope of the negation:
(9) There is one and only one F, and not every F is G. (Narrow scope negation)
(10) It is not the case that: there is one and only one F, and every F is G. (Wide scope negation)
(10) is logically equivalent to: there are no F's or there are more than one F or some F is not G. Consequently, (10) is true whenever there is no unique F, while (9) would be false in that case.
This means that we can say that the round square does not exist without attributing a property (that of non-existence) to a thing (the round square). Instead, Russell argues that we can interpret that statement as saying, simply, that the expression ‘the round square’ does not signify anything at all. Russell thereby provides an account of definite descriptions that is consistent with Actualism.
Russellians have applied the same analysis to empty proper names like ‘Santa Claus’ and ‘Zeus’. It is possible to interpret such names as disguised or abbreviated definite descriptions. Thus, we could interpret ‘Santa Claus’ as equivalent to ‘the man that lives at the North Pole and delivers presents on Christmas Eve’. Under this interpretation, the statement that Santa Claus does not exist is equivalent to the statement that there is no unique man living at the North Pole who delivers presents on Christmas Eve. No non-existent objects are needed.
12.1.2 Quantifiers and plural expressions
This Russellian analysis of definite descriptions is quite plausible, and Possibilists and Meinongians should not rest their case on uses of definite descriptions. There are, however, plenty of other plausibly true statements that do seem to require reference to non-existent things. Consider, for example, the use of plural expressions, like ‘round squares’ or ‘golden mountains’. We can say something like ‘Golden mountains do not exist’ or ‘Golden mountains could exist, but round squares could not.’ Russell's theory of descriptions does not apply to such statements. We do seem to be saying something like: some things (namely, golden mountains) have the property of possible, but not actual, existence.
Actualists can stick to their guns, however. They can insist that plurals (‘golden mountains’) and indefinite descriptions (‘a golden mountain’, ‘some golden mountain’) can also be interpreted as quantifiers, as expressions that simply indicate how many things there are of the described kind. To say that golden mountains do not exist is simply to say that nothing is a golden mountain, that there are absolutely no golden mountains. To say that round squares could not possibly exist is to say that it is impossible that anything could be a round square.
There are at least two kinds of quantifiers that could be used by Actualists in interpreting such plural expressions. They might take the phrase ‘golden mountains’ to be short for ‘all golden mountains’ or ‘every golden mountain’; these are universal quantifiers. Following Gottlob Frege, modern logicians generally interpret statements like ‘All F's are G's’, which involve a universal quantifier, as equivalent to the conditional, ‘for every x, if x is an F, then it is a G’. They interpret this conditional as a material conditional. It then is equivalent to, ‘for every x, either x is not an F or x is a G’. Given this interpretation, if there are no F's at all, then the universal statement ‘All F's are G's’ is true; indeed, modern logicians would say it is vacuously true. So, if there are no golden mountains, the statement ‘All golden mountains are G’ is vacuously true, no matter what adjective or predicative phrase we put in for G. ‘All golden mountains are flat’ is vacuously true, for example. Crucially, it is also true that all golden mountains are non-existent, not because the phrase ‘golden mountains’ refers to some things that have the property of non-existence, but simply because ‘golden mountains’ refers to nothing at all.
The other way of interpreting these bare plural expressions is as a form of generic quantification. For example, it seems to be true to say that mules are stubborn, even if there are a few exceptions to this rule. The sentence ‘Mules are stubborn’ could be taken as saying something about the property of being a mule and its causal or statistical connections to other properties, like the property of stubbornness. We could interpret ‘Mules are stubborn’ as saying something like the property of being a mule is normally or typically accompanied by the property of being stubborn.
Could Actualists make sense of ‘Golden mountains don't exist’ or ‘unicorns don't exist’ by means of generic quantification? Perhaps. They shouldn't interpret these sentences as saying that the properties of being a golden mountain or being a unicorn are normally or typically accompanied by the property of non-existence, since Actualists deny that anything has or could have the property of non-existence. However, they could take these sentences as saying something about the existing properties of being a golden mountain and of being a unicorn, namely, that absolutely nothing has those properties. Actualists can admit that the property of being a unicorn exists without admitting that anything has that property.
However, there are some sentences involving plural expressions that cannot be interpreted as quantifiers of any kind:
(11) Round squares are among my favorite things to think about.
(12) The explorers were seeking a golden mountain.
Proposition (11) is not vacuously true simply because there are no round squares, nor is (12) vacuously true simply because there are no golden mountains. I might like to think about round squares but not about cubical spheres, and the explorers could have been seeking a golden mountain without seeking a lake filled with lead.
In order to eliminate apparent reference to merely possible or impossible things in sentences like (11) and (12), Actualists can offer a different sort of paraphrase. They can propose that, at least in some cases, the use of plural expressions or indefinite descriptions refers to sets (the set of golden mountains or the set of round squares) or to properties (the property of being a golden mountain or a round square), or to concepts (the concept of a golden mountain) or to linguistic expressions (the description ‘a golden mountain’). These other entities, whether sets, properties, concepts, or expressions, exist even if golden mountains and round squares do not. If there are no golden mountains, then the set of golden mountains is identical to the empty set (the set with no members). Similarly, if there are no golden mountains, then the property of being a golden mountain exists, it just doesn't have any instances.
However, Meinongians and some Possibilists can respond that these paraphrases are much less plausible than the simpler interpretation in terms of quantifiers, including R
ussell's theory of descriptions. If we say that golden mountains do not exist, we do not seem to be saying anything about sets or properties. We are talking about mountains of a certain kind. These are ordinary, concrete things, nothing so exotic as a set or a property. Moreover, there are many philosophers who are skeptical about the existence of sets or properties, especially sets with no members and properties without instances. If such a philosopher says that sets do not exist or that properties do not exist, Actualists must interpret them as making the obviously self-contradictory claims that the set of sets is empty or the property of being a property has no instances.
Consequently, Actualists (and Possibilists in cases involving impossible objects) must argue that these expressions (definite and indefinite descriptions, and plurals) are ambiguous. In some cases they are to be interpreted as mere quantifiers, and in other cases as names of sets, properties, concepts or expressions. When we speak of golden mountains or round squares as the object of thought or desire, as in (11) and (12), we must interpret the phrases as referring to something like the property or concept of being a golden mountain or being a round square. In contrast, when we say that round squares do not or cannot exist, we are simply using quantifiers, saying that there are or could be no round squares. This is a demerit for Actualism. Other things being equal, we should minimize the attribution of ambiguity to our language.
The Atlas of Reality Page 42
