[10.4.] Definite Descriptions.

 

definite description (df.): a descriptive phrase that uniquely picks out a single individual or at least appears to do so, e.g., “the tallest student in this class,” “the first dog in space,” “the president of the United States,” “the winner of the 2008 Oscar for Best Motion Picture,” “the artist formerly known as Prince,” etc.

 

We have to use the identity symbol to symbolize statements containing definite descriptions.[1] For example: “The CEO of Apple Computer, Inc. is wealthy.”

 

Part of what this asserts is that there is one and only CEO of Apple. So we should symbolize it as follows:

 

Cxy: x is CEO of y

Wx: x is wealthy

a: Apple Computer, Inc.

 

($x){{Cxa · (y)[Cya É (y = x)]} · Wx}

 

 

Another example: “The author of Gone with the Wind is deceased.” In part, this asserts that there is one and only one author of Gone with the Wind:

 

Axy: x is the author of y

g: Gone with the Wind

Dx: x is deceased

 

($x){{Axg · (y)[Ayg É (y = x )]} · Dx}

 

 

And another: “The tallest student in this class is blond.” This asserts, in part, that there is one and only one tallest student in this class--

 

Txy: x is taller than y

Bx: x is blond

Sx: x is a student in this class

 

($x){{Sx · (y){[Sy · (y ¹ x)] É Txy}} · Bx}

 

And yet another: “Everyone hates the tallest student in this class.”

 

Hxy: x hates y

 

($x){{Sx · (y){[Sy · (y ¹ x)] É Txy}} · (z)Hzx}

 

See further, more complicated examples in the Examples box, pp.289-90.

 

 

[10.4.1.] Ambiguous Statements Containing Definite Descriptions.

 

Some statements containing definite descriptions are ambiguous. The following is an example made famous by Bertrand Russell:

 

“The present king of France is not bald.”

 

DISCUSSION: is this statement true or false?

 

It is not clear which of the following this statement means:

a.       There is one and only one individual who is presently king of France, and that individual is not bald.

b.       It is not the case that there is one and only one individual who is presently king of France and bald.

 

If the sentence means (a), then it should be symbolized as follows (letting “Kxy” mean “x is presently king of y” and “Bx” mean “x is bald”):

 

($x){Kxf · {(y)[Kyf É (y = x)] · ~Bx}}   [a false statement]

 

But if it means (b), then it should be symbolized:

 

~($x){Kxf · {(y)[Kyf É (y = x)] · Bx}}  [a true statement]

 

 

[10.4.2.] Merely Apparent Definite Descriptions, and Non-Obvious Definite Descriptions.

 

Some seeming definite descriptions are not genuine definite descriptions, e.g. “The next person who moves will get shot” as spoken by a bank robber (p.290). What the robber means is that anyone who moves will get shot:

 

(x)[(Px · Mx) É Sx]

 

And some expressions that don’t seem to be definite descriptions actually are, e.g. “The senator from Georgia.” This is how either one of Georgia’s two senators (Saxby Chambliss and Johnny Isakson) is referred to when recognized by the presiding officer, so you might not think it is a definite description. Even though there are two senators from each state, the construction “The senator from …”, when used in context, means the senator from … who has just  requested  the floor. So the presiding officer is using the phrase to unambiguously pick out one senator from the state in question.

 

Exercise 13-3 (p.291)

·         complete this exercise for next time

 

 

Stopping point for Wednesday April 23. For next time, finish ex.13-3 and read ch.10:3 (pp.291-94)