Descriptions and Determiners

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Here is how the central problem for this course is usually characterised.

‘What is the mechanism of reference?

‘In other words, in virtue of what
does a word (of the referring sort)
attach to a particular object/individual?’

‘Reference’, Stanford Enyclopedia of Philosophy

‘What is the mechanism of reference? In other words, in virtue of what does a word (of the referring sort) attach to a particular object/individual?’ \citep{reimer:2018_reference}.

The question is radically underspecified. There are lots of attachments. Everything is related to everything; everything attached to everything. What this article doesn’t make clear, like so much philosophy, is why what we want reference to explain. But let this pass : the whole course is really about trying to understand what features of communication might be explained by relating words to things.

I think this is a mistake because I think that lexical innovation is fundamental in communicating with words, at least in the way humans do this. But this is a minority view (very small minority), so let’s work with the standard view ...

Which words (and phrases) are ‘of the referring sort’?

communicating about vs referring

‘Ayesha is eating lunch’

‘Someone is eating lunch’

‘Ayesha is fluffy’

‘The smelliest cat in my house is fluffy’

Which words (and phrases) are ‘of the referring sort’?

‘By a ‘description’ I mean any phrase of the form ‘a so-and-so’ or ‘the so-and-so’.

... a phrase of the form ‘the so-and-so’ (in the singular) I shall call a ‘definite’ description. Thus ‘the smelliest cat’ is a definite description’

Russell, 1910 [1963] p. 205

“By a ‘description’ I mean any phrase of the form ‘a so-and-so’ or ‘the so-and-so’. A phrase of the form ‘a so-and-so’ I shall call an ‘ambiguous’ [i.e. indefinite] description; a phrase of the form ‘the so-and-so’ (in the singular) I shall call a ‘definite’ description. Thus ‘a man’ is an ambiguous [i.e. indefinite] description, and ‘the man with the iron mask’ is a definite description” \citep[p.~205]{Russell:1910fa}

“The Theory of Descriptions has a natural place within a general theory of natural language quantification in which determiners like ‘some’, ‘all’, ‘a’,’ the’, etc. are treated as members of a unified syntactical and semantical category” \citep[p.~48]{Neale:1990hg}

Are definite descriptions phrases ‘of the referring sort’?

Let’s take a look at Russell’s theory, according to which they are not.

‘If I say “Ayesha is fluffy” that is a statement of the form “x is fluffy,” and it has Ayesha for its subject.

But if I say “the smelliest cat in my house is fluffy,” that is not a statement of the form “x is fluffy,” and does not have “the smelliest cat in my house” for its subject.

we may put, in place of “the smelliest cat in my house,” the following: “One and only one entity is the smelliest cat in my house, and that cat is fluffy”’

Russell, 1905 p. 488

‘If I say “Ayesha is fluffy” that is a statement of the form “x is fluffy,” and it has Ayesha for its subject. But if I say “the smelliest cat in my house is fluffy,” that is not a statement of the form “x is fluffy,” and does not have “the smelliest cat in my house” for its subject. Abbreviating the statement made at the beginning of this article, we may put, in place of “the smelliest cat in my house,” the following: “One and only one entity is the smelliest cat in my house, and that cat is fluffy”’ \citep[p.~488]{Russell:1905sc}

Formally ...

Russell’s theory of descriptions

[the x; Fx](Gx)
is true iff
|F – G| = 0 and |F| = 1

Three applications

Analysis of definite descriptions

Analysis of names (they are usually really disguised descriptions)

Distinguishing knowledge by description from knowledge by acquaintance

‘Ayesha is fluffy’

‘The smelliest cat in my house is fluffy’

Negating

Name

‘Ayesha is fluffy’

There is one and only one smelliest cat in my house, and it is fluffy.

Definite description

‘The smelliest cat in my house is fluffy’

‘It is untrue that Ayesha is fluffy’

It is untrue that there is one and only one smelliest cat in my house, and it is fluffy

‘It is untrue that the smelliest cat in my house is fluffy’

‘Ayesha is not fluffy’

There is one and only one smelliest cat in my house, and it is not fluffy.

‘The smelliest cat in my house is not fluffy’

Are these the same?

Recall our question: if Russell is right, definite descriptions are not phrases of the referring sort.

Which words (and phrases) are ‘of the referring sort’?

Question: is Russell right about descriptions?

Three applications

Analysis of definite descriptions

Analysis of names (they are usually really disguised descriptions)

Distinguishing knowledge by description from knowledge by acquaintance

Objection 1

You can use definite descriptions without implying uniqueness

“if I say ‘the table is covered with books’, I do not mean to be suggesting that there is only one table in the world. Unfortunately, that seems to be precisely what the Russellian theory of descriptions is committed to”

\citep{Ludlow:2004wb}

Ludlow, 2004

Put the book on the book.

Shall we go to the pub?

Ok, which one?

I don’t mind. You choose.

Shall we make the following statement true? There is exactly one pub and we go to it.

Ok, which one? …

‘Jolly’s the name

Truckin’s the game’

Note the correct use of apostrophes

There is one and only one name and that name is Jolly.

There is one and only one game and that game is truckin’.

Objection 1

You can use definite descriptions without implying uniqueness

Objection 2

Determiners do not behave like quantifier phrases.

A mistake about language.

‘Determiners are rare in the world’s languages [...]

even in languages that deploy determiners, it is not clear that the determiners are behaving as quantificational operators.

... For example, it is plausible to think that one central function of the definite determiner is to provide genitive case when needed’

Ludlow, 2004

‘Determiners are rare in the world’s languages [...] even in languages that deploy determiners, it is not clear that the determiners are behaving as quantificational operators. ... For example, it is plausible to think that one central function of the definite determiner is to provide genitive case when needed’ \citep{Ludlow:2004wb}.

‘constructions of the form ‘the F’ and ‘an F’ are not only rare in natural languages, but potentially misleading in languages like English.

These expressions really don’t carry out the logical roles that Russell and subsequent authors have thought.

However, Russell’s core insight remains intact:

The critical question is whether the sentences in which they appear are quantificational or referential, and Russell may well be right about the critical cases here.

That is, many apparently referential constructions may in fact be quantificational.’

Ludlow, 2004

The core insight (‘many apparently referential constructions may in fact be quantificational’) is exactly what we are about to challenge in Donnellan ...

‘constructions of the form ‘the F’ and ‘an F’ are not only rare in natural languages, but potentially misleading in languages like English. These expressions really don’t carry out the logical roles that Russell and subsequent authors have thought. However, Russell’s core insight remains intact: The critical question is whether the sentences in which they appear are quantificational or referential, and Russell may well be right about the critical cases here. That is, many apparently referential constructions may in fact be quantificational.’ \citep{Ludlow:2004wb}.

summary

Which words (and phrases) are ‘of the referring sort’?

A definite description is a phrase of the form ‘the so-and-so’.

Russell’s theory: we may put, in place of “the smelliest cat in my house,” the following: “One and only one entity is the smelliest cat in my house, and that cat is fluffy”’

In favour: the argument from negation

Objection 1: You can use definite descriptions without implying uniqueness.

Objection 2: Determiners do not behave like quantifier phrases.

\section{Definite Descriptions: Summary} \begin{enumerate} \item A definite description is a phrase of the form ‘the so-and-so’. \item Russell’s theory: we may put, in place of “the smelliest cat in my house,” the following: “One and only one entity is the smelliest cat in my house, and that cat is fluffy”’ \item In favour: the argument from negation \item Objection 1: You can use definite descriptions without implying uniqueness. \item Objection 2: Determiners do not behave like quantifier phrases. \end{enumerate}

conclusion

In conclusion, ...

In conclusion, we can take three positive messages

Any theory of definite descriptions must explain their behaviour when negated ...

... and why they (sometimes) behave like quantifier phrases.

The distinction between knowledge by acquaintance and knowledge by description has a firm foundation.

‘we have acquaintance with anything of which we are directly aware, without the intermediary of any process of inference or any knowledge of truths’

\citep[chapter 5]{Russell:1912ln}

Russell, 1912 chapter 5

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