0. Background
It is, in a possible form, one of the central concerns of analysis philosophy to translate the ordinary utterances into predicate logic propositions. And I have increasingly felt that the goal, though important, might turn out to be inadequate and doom to fail. Indeed, I argue that the natural sentences may depend highly on context, and the context can be difficult or impossible to define by logic only.
Let us examine, for concreteness, Russell’s theory of definite description, namely the translation of the definite article “the” into predicate logic. The theory does not take account of linguistic context. Thus I am inclined to say that it is problematic.
According to Russell, a sentence that contains “the”, such as
(1) The F is G
Is identical to
(2) There is exactly one F, and F is G.
Thus,
(3) The capital of The UK is a beautiful city.
is identical, as of now, to
(4) There is exactly one entity so that: it is capital of The UK; and that entity is a beautiful city.
1. The example of incomplete description
The first objection, which is certainly not original, is of incomplete description. Say that: Alice has a dog, and the dog is ill. The sentence
(5) The dog of Alice’s is ill.
There are likely other people called Alice who keep dogs, and Alice may keep several dogs. And this is problematic even if we add other attributes that Alice’s dog possess:
(6) The dog of Alice’s, of black-dotted fur, of height 53.02cm, [etc….], is ill.
Possibly doesn’t point to a single dog either. In fact, the dog being referred is limited to the context (for example, what people in mind who is talking to Alice), and it is absurd to suggest the speaker of (5) intends (6).
2. The example of twin earth
Inspired by the Twin Earth Experiment, I think of a second objection. Consider that, in a possible world, there is another planet very far away, say in Andromeda, which is a Twin Earth, identical in every regard to our Earth, and every person on the Earth has an exact twin on the Twin Earth. Bob, from our Earth, arrives the Twin Earth in Andromeda, and says the sentence (3).
Now (3) does not translate to (4) in people in the Twin Earth. In the alien’s context, “The capital of The UK” is also called “London”, but it lies in the Twin Earth.
3. The example of physical reference
Moreover, I argue that the speaker who use the definite description usually does not really check the definition of the referred object, and may not even be capable in verifying the conditions that the description holds. Consider that Charlie is walking in the field and looks at a particular white duck. Later, Charlie saws and the duck again in a group of ducks. Charlie says to someone:
(7) I saw the white duck in the group this morning.
Russell would think that (7) can be translate to be
(8) There is only one thing so that: it is in the group, it is a duck, and was seen by Charlie this morning.
But it may be beyond Charlie’s capability to check (8), nor does he have good reasons to believe (8). The group of ducks may contain a white goose, which Charlie lacks the expertise to distinguish. Indeed, to justify (8), Charlie has to check, one by one, in the group, that “It is a duck” (which is difficult), and that he has saw it (which he did not really check). Most likely, Charlie does not know the precise definition of the duck, including that it is named under binomial nomenclature to be Anas platyrhynchos, that its bill width and wing length are within technical regulation, and so on. And in the group of duck there may be a white goose, which can be hard to tell from duck. In reality, the proposition “It is a duck” need not be evaluated as thus, for Charlie has physically followed the white duck, has pointed it out, and has good reasons to believe (7) is true.
4. Conclusion
In each case, I am inclined to think that it is unlikely that any countably-many conjunctions or disjunctions of predicate logic propositions can be faithfully translate the context of relevant dialogue. If the context is just “something more” than logical predication can deal with, will any theory of definite description ultimately fail?
5. References
- Peter Ludlow, “Descriptions“, The Stanford Encyclopedia of Philosophy.
- 王文方(2008)，形上學，台北:三民
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