Marc Horowitz 24.151 April 22, 1992

I

One of the fundamental difficulties which any theory on language must take into account is the Russell Problem. The basis of this problem is that there should be no exceptions to the Principle of Excluded middle. This Principle states that for any proposition A, A ∨ ¬A is true. The difficulty can be seen by looking at how Frege, Russell, and Strawson would interpret the sentence

(1) ‘The present King of France is bald or the present King of France is not bald.’

Apparently, there is a problem. Since ‘the present King of France’ (call this sign ‘(2)’) does not refer to anything, it is not obvious how to interpret this sentence.

Frege’s solution to this problem is to refute the ’Fido’-Fido claim that every singular term has a reference. According to Frege’s theory, the logical form of language consists of arguments and single-argument functions. Since the innermost argument in (1) has no reference, none of the functions can have references either, and the entire sentence lacks any truth value at all. The flaw in Frege’s argument is his insistence that signs with no reference cannot have any cognitive significance. As much as Frege apparently would like to have language be as logical and unambiguous as first-order logic, he can’t have it. Natural languages have inherent inconsitencies. Frege’s “solution” seems more like a way to ignore the Russell problem rather than actually addressing it.

Russell’s solution involves manipulating the logical form of the sentence. It is not clear if (1) should be interpreted with the definite description (2) in primary occurrence as ‘the present King of France is bald or the present King of France is not-bald.’ or in secondary occurrence as ‘The present King of France is bald or not the-present-King-of-France-is-bald.’ If the logical form used is that corresponding to the latter interpretation, then the sentence is true, regardless of the existence of the reference of ‘the present King of France’. Russell’s solution is attractive from a logical point of view. However, there is a feeling that something is lost in translation to logical form. Although Russell’s solution solves the problem at hand, it is not clear (to me at least) that there is any other reason to choose one logical form over another.

Strawson’s solution is similar to Frege’s. He also asserts that a statement does not necessarily have a truth value. But rather than doing what Frege says, and constructing a system of logic where functions with no arguments have no value, Strawson deals with the grammatical form of the speech act. Under this theory, a sentence which is neither true or false is simply meaningless. Strawson’s theory also deals with other than “eternal sentences”. Rather, Strawson would consider (1) to be an “occasion sentence”. It’s reference changes with each utterance. If I were to utter (1) 300 years ago, there would be little difficulty in interpreting it.

I think that Strawson’s solution is the best. Logical forms tend to have the quality that it is difficult to express concepts which have no reference. By not trying to come up with an explanation in logical form, the explanation has a much stronger intuitive feel to it; there is no feeling that something was contrived.

Another significant problem in theories of language is that of the Negative Existential. When interpreting a language, what is existence? Is it a predicate? Or is it something else?

Frege simply fails to adequately explain this case. In his theory, everything is an argument or a function. Functions whose arguments have no reference themselves have no reference. Since “existence” must be a function, it can never return false, since the argument would have no reference, and the function would have no value. This theory is just too simple to handle existentials.

Strawson’s theory explains negative existentials as a kind of assertion. We already know that a sentence can be meaningless. If it is widely known what the meaning of an utterance with no reference is, then a sentence such as ‘Santa Claus does not exist.’ is meaningful, and true. A sentence such as ‘Freddled gruntbugglies do not exist.’ is meaningless, so it has no truth value. Since people can conceive of fictional objects, they can name them, and refer to them, even though they do not exist.

The Russell theory is the only one of the three which recognizes that existence is special; saying that something does or does not exist is fundamentally different from saying that something is or is not green. This is expressed in the logical form, which is entirely different for statements of the two types.

I prefer Russell’s solution to the Negative Existential problem. Strawson solves the problem, but doesn’t make any distinction about existence, which seems like a special concept. There is no real fundamental difference between ‘Santa Claus does not exist’ and ‘Santa Claus does not like ARA food‘. Russell does make this distinction, and it is in this distinction which I find the strong appeal of Russell’s solution.

(A) A type is an abstract instance within a class. For instance, an example of a word type would be the word ‘class’. The word type ‘class’ has four letter types in it. A Token is an instance of a type. This paragraph is comprised of word tokens. Since types are abstract, there is only one word type ‘class’, but there can be many instances of it; there are five instances in this paragraph. Occurrences are abstract, but can occur multiple times. Earlier, I noted that in the word type of ‘class’, there are four letter types. However, one of them has two occurrences. Since occurrences are abstract, it makes no sense to talk about them when referring to tokens.

(C) An eternal sentence is a sentence whose truth value is time-independent. The most common form of these are mathematical proofs, such as 2 + 2 = 4. An occasion sentence is one which can have a new reference each time is is spoken. For instance, ‘I am hungry’ may be true as I write this, but it does not have to remain true. It needs to be reevaluated each time.

(D) A locutionary act is a the physical act of enunciating words. An illocutionary act is a statement made according to social convention, such as an observation (‘The sky is red.’) or an order (‘Stand up.’). A perlocutionary act is a side-effect of an illocutionary act, such as causing a person to look at the sky, or embarrassing the recipient of an order.

Although there is no Santa Claus, the sentence ‘Santa Claus is a legendary old man with a white beard.’ is true. This sentence is true because by calling Santa Claus a “legendary old man”, one can be said to be presupposing the existence of a legend describing Santa Claus. In this legend, there does exists a Santa Claus, and he is indeed an old man with a white beard. If the legend did not exist, or if the legend had Santa Claus as a young, clean-shaven man, then the sentence would be false. But the non-existence of Santa Claus does not prevent the sentence from having a truth value.

Consider another example, ‘The intersection of the parallel lines in the hypothetical space is labelled X.’ Although this is not the case in reality, there exist topological spaces where parallel lines do intersect. This statement presupposes the existence of such a space, in the same way that Santa Claus presupposes a particular legend.

So, the lack of references in this universe of ‘Santa Claus’ or of intersecting parallel lines does not preclude making statements about them, as long as an appropriate universe is presupposed, implicitly or explicitly.