Quasi-Names and Definite Descriptions.

(P2.4) (a ≠ t) ≡ (b ≠ t).

is true. Finally, on the basis of both (P2.1) and (P2.4) as our premises, we can argue as follows:

        (6.1) a = b

        (6.2) (a ≠ t) ≡ (b ≠ t)

        (6.3) Ga = Gb

        (6.4) Ga ≠ Gt

        

        (6.5) Gb ≠ Gt

By both arguments, we now know that ‘the Philosopher’ ≠ ‘the philosopher’ and the grown capital letters confirm the characterisation of quasi-names provided by Strawson.

        Summing up, we can define a quasi-name as a certain designator such that it has the same primary reference possessed by the proper name to which it is associated. Therefore, if α is a proper name and if β is a quasi-name such that α= β, then if we replace β in every occurrence of α into a one place predicate F, then Fα=Fβ is true. In symbols

(C1) (α=β) ≡ (F)(Fα=Fβ).

Moreover, being ρ any definite description applicable to the same object being referred to by α, we claim that

        (C2)  (ρ) [(α≠ρ)→(F)(Fα≠Fρ)] → (ρ) [(β≠ρ)→ (F)(Fβ≠Fρ)]

is true when (C1) is true.

Therefore, (C1) and (C2) are the necessary and sufficient conditions for an expression to be a quasi-name.

        On the other hand, we must admit that we have arrived to the somehow strange conclusion that ‘Aristotle’ is the same thing as both ‘the Stagirite’ and ‘the Philosopher’, as the following argument shows intuitively:

        (7.1) a = b

        (7.2) a = c

        (7.3) b = c.

        The apparent misleading result is to be explained by the use of a criterion introduced by Samuel Kripke, who distinguishes designators according to the invariability of their references. Given a definite set of possible worlds, if a designator refers to the same object in each possible world, then the designator is rigid otherwise it is non-rigid.

        As Kripke has proved, proper names are rigid designators because they refer without connoting and thus ‘Aristotle’ refers to Aristotle in every possible world in which there is an individual human being who is Aristotle.

        This is not the case, however, for quasi-names. In fact, we can imagine a counterfactual in which Aristotle had not been born in Stagira – but, say, in Athens. In this case, ‘the Stagirite’ as a quasi-name would cease to refer to Aristotle. We can also imagine a counterfactual in which Aristotle had not gone into philosophy at all, in which case ‘the Philosopher’ would definitively cease to refer to Aristotle. In particular, we can stipulate a certain possible world in which Aristotle could have been born in Athens and could have been the philosopher he has been in the actual world. In such case, it would still be true that ‘Aristotle’ = ‘the Philosopher’, whereas ‘Aristotle’ = ‘the Stagirite’ would clearly be false contradicting (7.1)-(7.3).

        I argue that this is due to a particular feature possessed by quasi-names, which Strawson had in fact noticed, namely the fact that “the descriptive meaning of the words which follow the definite article is still relevant to their referring role”. This means that, although quasi-name have the same primary reference possessed by proper names, they still connote a property. In fact, ‘the Stagirite’ connotes the property of ‘being born in Stagira’ and ‘the Philosopher’ connotes the property of ‘being a person interested in philosophy’. If one of these properties ceases to belong to Aristotle in some possible worlds, then the corresponding  quasi-name fails to refer to Aristotle, as we have seen.

        On the other hand, we have proved both (1.1)-(1.3) and (3.1)-(3.3) to be valid, such that ‘the Stagirite’ and ‘the Philosopher’ cannot be the same thing as their respective definite descriptions ‘the Stagirite’ and ‘the philosopher’. It seems that some particular kind of connotation has occurred here such that the description connoted by quasi-names can fit uniquely the same individual to whom the quasi-name refers.

        I argue that this particular sort of connotation is what grammarians, since Ancient Greek, have always called predication by antonomasia. Looking up this word in The Oxford English Dictionary we find:

“the substitution of an epithet or appellative, or the name of an office or dignity, for a person’s name as ‘the Iron Duke’ for Wellington”.

Not only we have a definition which corresponds exactly to the sort of connotation we were looking for, but the mere fact that a new instance of a quasi-name (namely, ‘the Iron Duke’) is provided as an example predication by antonomasia strikingly confirms our ideas.

        In so far as connotation is concerned, any description individuates a set of individuals capable of fitting it as the extension of the property connoted by the description. Now, the extension individuated by the description connoted by a quasi-name is radically different from the one individuated by its correspondent definite description. In fact, ‘the philosopher’ individuates the extension of all the persons ‘being interested in philosophy’, whereas the extension individuated by ‘the Philosopher’ is narrowed down to one and only one individual. In fact, the description connoted by ‘the Philosopher’ has to be understood as ‘the philosopher par excellence’ or ‘the most important philosopher’. The description is applicable only to the individual who occupies the highest position in the hierarchy built up by ‘the Philosopher’. Within a definite set, we can be pick out an individual either among the others by adding further details in the description, or above the others in so far as the description used implies a hierarchy within the set. To do this, such description must connote its property in terms of descriptive degrees, which differs from adding further specifications since we are talking about different degrees of the same property. Thus, among all the philosophers, ‘the Philosopher’ is ‘the most important philosopher’ or ‘the philosopher par excellence’. Such phenomenon in connotation is what we call connotation by antonomasia.

 The same applies to ‘the Stagirite’. In fact, the definite description ‘the Stagirite’ individuates the extension of all the persons ‘being born in Stagira’, whereas the extension individuated by ‘the Stagirite’ is narrowed down to one and only one individual, namely ‘the most important person born in Stagira’.

Now if within a certain community of speakers there is knowledge about the fact that a certain description connoted by antonomasia can be fitted by one particular individual, then such knowledge fixes the reference and therefore the same description will refer uniquely to that individual by connoting him by antonomasia. This is what we have called predication by antonomasia, which is, as we have seen, the substitution of a description for a proper name. The predication by antonomasia fixes the reference in such a way that, since the unique connotation corresponds to a unique reference, the description possesses now a primary reference and ceases to perform its descriptive function. It becomes a quasi-name.

In other words, the description connoted by quasi-names can be applied only to one individual, namely the individual to whom a particular quasi-name uniquely and primarily refers.

         Having said so, we can now understand why quasi-names are non-rigid designators. Since they still connote a property, quasi-names cannot refer to the same individual once we conceive other possible worlds in which such property could have not belonged to such individual. On this regard, in fact, they are quasi-names. On the other hand, since their description is connoted by antonomasia, quasi-names have the same primary reference possessed by their correspondent proper names. On this other regard, they are quasi-names (and this has made possible to distinguish quasi-names from definite descriptions).

        We have come this far by taking up a characterisation drawn by Strawson as our starting point and following a chain of thoughts which has found confirmation in the evidence provided by the dictionary. If we have been reasoning correctly so far, then we have to recognise the logical existence of a peculiar type of designators, which combines surprisingly connotation and denotation in a unique manner. Instances of this special designator are far more common than what one might expect, as the cases of Mrs Margaret Thatcher being associated with ‘the Iron Lady’ and Louis XIV with ‘the King Sun’ clearly show.

        More importantly quasi-names have shown us that a description can denote an individual in virtue of a connotation by antonomasia in conjunction with the knowledge that such property can be predicated by antonomasia of only one individual. This, I think, can have important consequences on our understanding of definite descriptions and their connotation. This is what I wish to analyse in the second part of this essay.

II) Definite Descriptions

        In his well-known paper called Reference and Referents, Keith Donnellan’s a draws the distinction between the attributive use and the referential use of definite descriptions. According to Donnellan, we cannot decide whether a speaker uses a definite description attributively or referentially by simply looking at the structure of the sentence uttered, but rather by looking at “the speaker’s intentions in a particular case”.

        I shall argue that the difference between the referential use and the attributive use is instead grounded on a logical difference, which occurs when we talk about the world. If we refer to the actual world then a definite description is used referentially, if we refer to a set of possible worlds then the definite description is used attributively.

To show this I will analyse the example of “Smith’s murderer”, which is used by Donnellan in his paper to show that the same definite description employed in the very same sentence can be used in either way. The example is composed of two situations. In the first one a certain Smith has been killed but no one knows who the murderer is, thus in the sentence “Smith’s murderer is insane” the definite description cannot refer to any person in particular, although “there is, of course, the presupposition that someone or other did the murder”. In the second situation,  somebody has been charged of Smith’s murder, namely a certain Jones. According to Donnellan, in the sentence “Smith’s murderer is insane” the definite description is now used referentially since “if someone asks to whom we are referring, by using this description, the answer is ‘Jones’”. Let’s now take a closer look at both situations.

What does exactly “Smith’s murderer” connote in the first situation? Obviously, the property of ‘being Smith’s murderer”. However, as it not possible to talk about a property without assuming an hypothetical human being to whom such property would belong to, we should say more precisely that the definite description “Smith’s murderer” does not only connote a property, but also presupposes someone, an hypothetical individual, as its bearer. The speaker’s presupposition is such that there is or there must be a person, whoever this may be, to whom this property would belong to. Therefore, the sentence ‘Smith’s murderer is insane’ would turn out to be true regardless of the identity of the actual responsible for Smith’s death, since by ‘Smith’s murderer’ we can refer to someone who has committed such a horrible crime. If we knew who the responsible is, then ‘Smith’s murderer’ would cease to connote only a property and would also refer to a person in particular.

This is the crucial point. By using ‘Smith’s murderer’, as we said, we only connote a property. However, a property is not self-standing, nor is its connotation self-sufficient. In order to be meaningful, a property connoted by a definite description requires a bearer. As the reference has not been fixed yet, any individual could be the bearer of a property in so far as he is capable of fitting the description. We can imagine a set of different possible worlds where ‘Smith’s murderer’ could be a different person (within each possible world). The set composed of the possible Smith’s murderers is the extension of the connotation expressed by ‘Smith’s murderer’ used attributively. In other words, ‘Smith’s murderer’ designates the set of all the possible human beings who could fit or could have fitted this description.

Moreover, since ‘Smith’s murderer’ connotes this property uniquely, the set of possible persons capable of fitting such description must be unique. It is quite obvious, in fact, that the property connoted by ‘The President of the United States in 1960’ is not the same as that connoted by ‘Smith’s murderer’. Then, the set of possible persons capable of being ‘The President of United States in 1960’ in possible worlds cannot be the same as the set of all the possible people capable of being ‘Smith’s murderer’. These two definite descriptions connote different properties and therefore they individuate two different extensions.

If this is the case, then I argue that ‘Smith’s murderer’ by connoting a certain property denotes a certain object uniquely, namely the set of all possible Smith’s murderers in a definite set of possible worlds. In fact, the descriptive meaning of ‘Smith’s murderer’ connotes a unique property and leaves the question of the identity of its bearer undecided. We do not know if Jones or James or any other is Smith’s murderer. What we know is that whoever fits this description is also responsible for Smith’s death. In other words, this description would apply uniquely to the responsible for Smith’s death in all possible worlds. Therefore, each member of this set would fit such description in each possible world when individually taken. In brief, we should say that, by connoting uniquely such property, ‘Smith’s murderer’ refers uniquely not to an actual individual but to a set of possible individuals, namely the set of possible Smith’s murderers, given different possible worlds. This is why ‘Smith’s murderer is insane’ can be true of whoever has committed the crime.

Let us now consider what the function performed by ‘Smith’s murderer’ is in the second situation. Well, in this situation someone has been charged of the assassination, namely Jones. Thus, the definite description ‘Smith’s murderer’, used on the basis of such knowledge, refers uniquely to Jones as the actual Smith’s murderer. What has happened in this case? In my opinion, we may say that if ‘Smith’s murderer’ in the first situation was referring to the set of possible Smith’s murderers, then the circumstances of Jones being publicly charged of such crime must have had some serious consequence upon the task of fixing the reference. In fact, the ostension occurred here has selected a particular possible ‘Smith’s murderer’ as the actual one, namely Jones. The possible world in which Jones is ‘Smith’s murderer’ is now regarded as the actual one, and therefore the reference has been fixed uniquely. The audience is entitled from now on to use ‘Smith’s murderer’ referentially as in ‘Smith’s murderer is insane’. In so far as they are acknowledged as necessary facts, the circumstances of Jones being charged of Smith’s murder are responsible for fixing the reference uniquely, or, in other words, for selecting a possible situation among all other conceivable. This latter statement shows the metaphysical significance of the event of Jones being charged of Smith’s murder. The audience at the process has now some knowledge about the identity of ‘Smith’s murderer’: this knowledge allows the audience to refer to Jones as ‘Smith’s murderer’, and such referential use of the definite description would be correct even if, at the end of the process, Jones turned out to be innocent.

We can say that what really makes the difference here is that the identity of the bearer of the property connoted by ‘Smith’s murderer’ has been decided. Through the public ostension of Jones as the responsible for Smith’s death, all other possible cases have been excluded and the reference has been fixed once and for all. This point is crucially important since it takes account for both the attributive and the referential use of a definite description. The shift between the two uses does not depend on the speaker’s intension, as Donnellan had stated. It rather depends on the metaphysical significance involved in an individual being shown (and thus being known) as the reference of such description. There is no difference for a definite description when used in either way. What makes the difference is whether the identity of the referent has been decided. If it has, then the definite description can be used only referentially. If it has not, the definite description can be used only attributively. In neither case can the definite description fix the reference by itself since it only connotes a property.

From a logical point of view, the metaphysical significance of an ostension corresponds to the introduction of an existential quantifier, which binds the variable in “Smith’s murderer is insane’. We can write it out as:

(I) Ex(Mx→Ix).

In this case the definite description does not refer to an individual as its primary reference, but only by the means of its descriptive meaning in conjunction with a reference which has already been fixed.

On the other hand, the apparent lack of reference of ‘Smith’s murderer’ in the first situation has turned out to be a different kind of reference. According to our analysis, ‘Smith’s murderer’ refers to the unique set of all possible Smith’s murderers individuated in each single possible world. As a consequence of having left the question of Smith’s murderer identity undecided, this mild referential use of ‘Smith’s murderer’ can be now regarded as the introduction of a quantifier, namely the universal quantifier in possible worlds. We can introduce a notation for it, and I propose “U” to be placed before the variable for the analysis of ‘Smith’s murderer is insane’. Therefore we can write this latter as:

(II) Ux(Mx→Ix),

which is to be read as ‘Smith’s murderer, whoever he is, is insane’.

In (II) ‘Ux’ expresses, then, a universal-possible reference entailed by this quantifier when it is applied to definite description used attributively. ‘Ux’ is then to be read ‘for all possible x’.

Having occurred as the main factor differentiating the second situation from the first one, Jones’ ostension is responsible for the transformation of ‘Ux’ into ‘Ex’ because it has assigned an identity to the bearer of the property expressed by ‘being Smith’s murderer’. Fixing the reference is essentially the same as selecting a possible world among others as the actual one.

        However, we must admit that there is a difference between uttering the sentence ‘Smith’s murderer is insane’ in the first situation and analysing the same sentence within the same context from a logical point of view. The difference is that a speaker uses such sentence considering only the actual world as the only one possible. Such speaker presupposes that, even though the question of the identity of ‘Smith’s murderer’ is left undecided, one and only one person has committed the crime under consideration. In other words, the intensionality underlying such an utterance is presupposed by the speaker at the time of the utterance, and I hold that it is presupposed in all our utterances since we continuously presuppose that there be one and only one world, which we call ‘the world’. We cannot blame the speaker who uttered ‘Smith’s murderer is insane’ in the context of the situation described for not having considered that in each single possible world of a certain set ‘Smith’s murderer’ might be or might have been a different person. The speaker, in fact, assumes that (within this world) one and only person is responsible for Smith’s murder, whoever this person might be. The presupposition that there be one and only one world is in fact an essential part of our common knowledge, on which we ground all our utterances. This is why Kripke clarifies that ‘other possible worlds’ are indeed ‘counterfactuals’, which are stipulated to analyse what would have happened to certain objects present in the actual world if things had been otherwise.

        Having said that, we can still consider a sentence of the type ‘Smith’s murderer is insane’ from a logical point of view, and be able to use ‘Smith’s murderer’ as a designator whose extension ranges over the definite set of possible worlds under consideration in virtue of the quantifier ‘U’. This will become evident as soon as we paraphrase the sentence

φ = ‘Smith’s murderer is insane’

 into

ψ = ‘Smith’s murderer must be insane’.

In this case ψ can still be rewritten into (II). If (II) turns out to be true in some possible world, then ψ is contingently true, that is to say it is true for some values of x. If (II) turns out to be true if it is true in all possible worlds, then ψ is necessarily true, for all possible values of x. Other example can be ‘The president of the United States in 1960 must have been very busy’, which we can now rewrite into

(III) Ux(Px→Bx)

 by which we consider a possible president of the United States in 1960 in each possible world. If this proposition turns out to be true in each possible world considered, then we can regard this sentence as necessarily true. This can be possible if and only if we clearly assume that we consider not only the actual world, but also its counterfactuals.

        Now, if I am right, we can see what has caused Russell’s difficulty when treating definite descriptions. It was precisely Russell’s presupposition that a definite description attributively used had to imply an existential quantifier, which has lead him to the analysis he developed. In fact, in the sentence ‘the author of Waverly was a man’ – without any further specification – the definite description refers to the set of all possible persons who could fit the description. Therefore, we can rewrite it as

        (IV) ‘Ux(Mx) is a man’

 or

(V) Ux(Wx→Mx).

Russell had instead put so much effort to rewrite the same sentence as Ex(Wx→Mx). Once again, the initial assumption (presupposed by Russell) that the analysis had to be concerned only with the actual world was the cause of all problems. Once we assume our analysis should consider also other possible worlds beside the actual one, then our analysis should hold, and it should therefore be possible to elucidate other logical puzzles which have become ‘classic dilemmas’ in the history of logic.

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