Russell’s Theory of Definite Descriptions
The aim of this essay is to outline Russell’s Theory of Definite Descriptions. In short, Russell’s seeks to explain the significance of phrases of the form: ‘the’ followed by a noun phrase. Such phrases are: the current President of the United States; the author of Waverley and many others. To understand the significance of those phrases, which we will be dealing with one must first understand what they are not.
Descriptions can be both definite and indefinite. Definite descriptions take the form as stated above: ‘the F’, whereas indefinite descriptions deal with phrases in the form of ‘an F’. This statement may seem unproblematic; however, we soon encounter phrases like ‘the F’, which have a different meaning. Take for example ‘The students who took the exam’, note that it is a phrase of the form ‘the’ followed by a noun phrase, yet it is not taken into account in Russell’s theory because it is a plural description. There are others, which we must exclude, as well, e.g. ‘The blood in these students’, which is a mass term description, or ‘The human species is dominant’, which deals with a kind of things. As we can see definite descriptions have to contain not just a noun phrase, more specifically they deal with singular noun phrases.
Following this definition, definite descriptions introduce a particular object into the truth conditions of the sentence, within which they are contained. Can we then say that they are singular terms? Singular terms serve the purpose to introduce objects into the truth conditions of a sentence. It seems then that the concepts of definite descriptions and singular terms overlap. To see whether our conclusion is valid, we shall employ Frege’s three tests and above statement ‘the current President of the United States’.
1) The current President of the United States is liberal.
2) The current President of the United States is assertive.
3) Therefore, the current president of the United States is liberal and assertive.
1) The current President of the United States is liberal or assertive.
2) Therefore, the current President of the United States is liberal or the current President of the United States is assertive.
1) The current President of the United States is liberal.
2) Therefore, something is liberal.
As definite descriptions pass all three tests, we can still maintain that definite descriptions are singular terms. Yet, Russell asserts that they are not, how does he come to that conclusion?
Russell introduces three Puzzles in order to show how things go wrong, if we use a definitive description in the same fashion as we would use a singular term.
Russell’s three puzzles
The first puzzle concerns informative identities. ‘Scott is the author of Waverley’ according to Russell is something entirely different from the proposition ‘Scott is Scott’, yet if definite description were to be singular terms everything should be fine, since both ‘Scott’ and ‘The author of Waverley’ refer to the particular entity that is Scott.
The second puzzle Russell introduces is about negation pairs. Thanks to the Law of the excluded middle either ‘a is F’ or (note that this is an exclusive ‘or’) ‘a is not F’ must be true. Yet, as Russell points out neither ‘the present king of France is bald’ nor ‘the present king of France is not bald’ are true, if we assume that ‘the present king of France’ is a singular term. As a singular term it fails to introduce an object into the truth-conditions, as it does not correspond with any particular object, i.e. it does not refer since there is no present king of France.
The third and final puzzle: Russell makes use of singular negative existential statements. This puzzle assumes a rather ‘puzzling’ form in Russell’s original text. We shall try to spell out his main proposal in simpler terms. Let us start by using Russell’s formulation: “if A and B do not differ, to suppose either that there is, or that there is not, such an object as ‘the difference between A and B’ seems equally impossible.” (Russell, 1905, p.3) What Russell means here is that if the singular term ‘the difference between A and B’ fails to introduce an object into the truth-condition, which is the case ‘if A and B do not differ’ then it is impossible to assert either truth or falsity to this statement. Again equating a definite description with a singular term is problematic.
Russell’s Theory of Definite Descriptions
To counter those problems Russell devised his Theory of Definite Descriptions. Take as an example the phrase ‘the mother of Barack Obama is liberal’. According to Russell this proposition asserts that there is an x who is the mother of Barack Obama and that this x is liberal. By saying ‘the’ we mean that there is only one x. We therefore claim not only that x has this relationship with Barack Obama, but also that there is nothing else that has the same relationship with x. This view entails that definite descriptions are not singular terms – that indeed they are devices of quantification. This proposal can be put in more formal terms:
1) There is at least one mother of Barack Obama
2) There is at most one mother of Barack Obama
3) All mothers of Barack Obama are liberal.
Or to put it in abstract terms, with a proposition in the form of ‘the F is G’:
1) There is at least one F
2) There is at most one F
3) All Fs are Gs
We can abbreviate this by stating that ‘there is exactly one F and all Fs are G’. If this theory is to hold its ground it must render soluble the above mentioned puzzles.
Russell’s proposed solutions to his three puzzles
In the first puzzle Russell asserts that the statement ‘The author of Waverley is Scott’, is indeed much more complicated, i.e. it could not be true if Waverley had never been written, and it would certainly not be true if Waverley had been written by more than one person. The statement ‘Scott is the author of Waverley’ is not a statement of identity and as such dependent on whether Scott actually was the author of Waverley. It is therefore about Scott and about him being the author of Waverley. ‘Scott is Scott’ on the other hand is a statement of identity and therefore an analytic statement, i.e. true by definition. Furthermore the statement ‘the author of Waverley’ remains significant even without being aware of the particular thing it refers to. Hence, we can argue that in ‘there is exactly one author of Waverley and all authors of Waverley are Scott’ ‘author of Waverley’ does not introduce a particular object and hence corresponds to Russell’s account of a definite description.
The second puzzle concerning negation pairs is easily solved by applying Russell’s theory to it – Definite descriptions that fail to introduce an object produce either truth or falsity as they are devices of quantification. Let us first rephrase our example ‘the present king of France is bald’ so that it reads as ‘there is exactly one present king of France and all present kings of France are bald’. Note that our paraphrase retains the same meaning and that F and G are connected by a conjunction. The claim that ‘there is exactly one present king of France and all present kings of France are bald’ then comes out as false, as there is no such thing as a king of France, which renders the first part of the conjunction false and thus the whole proposition. We proceed now by introducing a second claim ‘the present king France is not bald’. Trying to paraphrase this proposition gives two different readings: either we assert that ‘it is not the case that there is exactly one present king of France and all present kings of France are bald’ or ‘there is exactly one present king of France and it is not the case that all present kings of France are bald’. Russell calls the former the secondary occurrence, the latter the primary occurrence. This distinction becomes clearer if we speak, instead of occurrences, of variations in scope, i.e. we call the former ‘external negation’, the latter ‘internal negation’. Partly symbolised the two readings would be as follows:
1) ~(There is exactly one present king of France and all present kings of France are bald)
2) There is exactly one present king of France and ~(all present kings of France are bald)
We now see that the first does come out as true, as the conjunction is again made false by the failure of ‘the present king of France’ to correspond and thus the negation renders this proposition true. The second reading, however, comes out as false. This suggests that the Law of the excluded middle may be preserved by reading the negating claim as a secondary occurrence (Russell, 1905, p.5). Furthermore it provides an explanation of our insecurity in asserting truth or falsity to the statement.
The third and final puzzle is solved similarly to the second puzzle: Let us make use of Russell’s example – ‘the difference between A and B does not exist’. If A and B do not differ, according to Russell’s account this will come out as true, as the above statement’s external negation reads ‘it is not the case that there is exactly one difference between A and B and all differences between A and B exist’ and is true when ‘there is exactly one difference between A and B’ is false, i.e. if A and B do not differ.
Strawson points out that our intuitions do not correspond with Russell’s view: he claims that ‘the present king of France is bald’ has no truth value – his proposal is that to say ‘the present king of France is bald’ is to imply, or presuppose, and not entail that there presently is a king of France. By responding ‘That is false.’ one would thus not contradict the proposition, but instead assert that since there is no corresponding object the question of truth and falsity never arises.
By asserting that there is a present king of France, if there is no corresponding object one simply utters a defective expression – it fails to refer in this particular case, yet it retains its significance since there are cases, in which such a statement could correspond. So, for Strawson an expression retains its significance even if there is a presupposition failure – it simply does not amount to saying something true or false, i.e. it is no genuine claim. (Strawson, 1950, p.8)
Russell or Strawson?
Yet, defenders of Russell’s theory claim that this can easily be accounted for: Suppose again that one would respond ‘That is false’. Using Grice’s theory of rules of conversation, just saying ‘That is false’ does not fulfil the maxim of quantity, i.e. one could negate different parts of the proposition. One could assume that there is no present king of France, that there is more than one, or that he is simply not bald. Thus Russell’s account is made to concur with what Strawson thinks would be an intuitive response by suggesting that saying ‘That is false’ is not a wrong thing to say, but instead a bad thing to say.
Furthermore we might say ‘The present king of France lies in that bed’ while pointing at an empty bed. It seems that this utterance produces truth and falsity, i.e. if the enunciation cannot be true even though we know that the subject does not exist, we intuitively judge it to be false. Hence we assign truth values independent of the presupposition failure that occurs.
Strawson’s challenge thus can be refuted and Russell’s account of definite descriptions still retains its explanatory potential, as a theory it can explain most uses of definite descriptions (note that we have not considered Russell’s account of proper names) and therefore maintains its significance.
Russell, B. (1905). On Denoting. In: Martinich, A.P., ed. (1996). The Philosophy of Language. 3rd edition. Oxford: Oxford University Press
Strawson, P.F. (1950). On Referring. In: Moore, A.W., ed. (1993). Meaning and Reference. Oxford: Oxford University Press